From 3f723f4ec210e8e836bc29f0a63c7fca37b50d73 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Thu, 19 Jan 2017 12:08:15 -0500
Subject: [PATCH 01/37] lecture 2 notes

---
 lecture_01/lecture_01_notes.pdf | Bin 0 -> 26146 bytes
 lecture_02/README.md            | 174 ++++++++++
 lecture_02/lecture_02.ipynb     | 597 ++++++++++++++++++++++++++++++++
 lecture_02/notes.pdf            | Bin 0 -> 273422 bytes
 4 files changed, 771 insertions(+)
 create mode 100644 lecture_01/lecture_01_notes.pdf
 create mode 100644 lecture_02/README.md
 create mode 100644 lecture_02/lecture_02.ipynb
 create mode 100755 lecture_02/notes.pdf

diff --git a/lecture_01/lecture_01_notes.pdf b/lecture_01/lecture_01_notes.pdf
new file mode 100644
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diff --git a/lecture_02/README.md b/lecture_02/README.md
new file mode 100644
index 0000000..12365ce
--- /dev/null
+++ b/lecture_02/README.md
@@ -0,0 +1,174 @@
+
+# Solution to Form #1
+
+
+```octave
+[1,2,3]*[1;2;3]
+```
+
+    ans =
+    
+       14
+    
+
+
+
+```octave
+[1,2,3]*[1;2;3]=?
+```
+
+
+```octave
+
+```
+
+# The first source of error is roundoff error
+## Just storing a number in a computer requires rounding
+
+
+```octave
+fprintf('realmax = %1.20e\n',realmax)
+fprintf('realmin = %1.20e\n',realmin)
+fprintf('maximum relative error = %1.20e\n',eps)
+
+```
+
+    realmax = 1.79769313486231570815e+308
+    realmin = 2.22507385850720138309e-308
+    maximum relative error = 2.22044604925031308085e-16
+
+
+
+```octave
+s=1;
+for i=1:1000
+    s=s+eps/10;
+end
+s==1
+```
+
+    ans =  1
+
+
+# Freefall Model (revisited)
+## Octave solution (will run same on Matlab)
+
+Set default values in Octave for linewidth and text size
+
+
+```octave
+%plot --format svg
+```
+
+
+```octave
+set (0, "defaultaxesfontname", "Helvetica")
+set (0, "defaultaxesfontsize", 18)
+set (0, "defaulttextfontname", "Helvetica")
+set (0, "defaulttextfontsize", 18) 
+set (0, "defaultlinelinewidth", 4)
+```
+
+Define time from 0 to 12 seconds with `N` timesteps 
+function defined as `freefall`
+
+
+```octave
+function [v_analytical,v_terminal,t]=freefall(N)
+    t=linspace(0,12,N)';
+    c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c);
+
+    v_analytical = v_terminal*tanh(g*t/v_terminal);
+    v_numerical=zeros(length(t),1);
+    delta_time =diff(t);
+    for i=1:length(t)-1
+        v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*delta_time(i);
+    end
+    % Print values near 0,2,4,6,8,10,12 seconds
+    indices = round(linspace(1,length(t),7));
+    fprintf('time (s)|vel analytical (m/s)|vel numerical (m/s)\n')
+    fprintf('-----------------------------------------------\n')
+    M=[t(indices),v_analytical(indices),v_numerical(indices)];
+    fprintf('%7.1f | %18.2f | %15.2f\n',M(:,1:3)');
+    plot(t,v_analytical,'-',t,v_numerical,'o-')
+end
+    
+```
+
+
+```octave
+[v_analytical,v_terminal,t]=freefall(120);
+```
+
+    time (s)|vel analytical (m/s)|vel numerical (m/s)
+    -----------------------------------------------
+        0.0 |               0.00 |            0.00
+        2.0 |              18.76 |           18.82
+        4.0 |              32.64 |           32.80
+        6.1 |              40.79 |           40.97
+        8.0 |              44.80 |           44.94
+       10.0 |              46.84 |           46.93
+       12.0 |              47.77 |           47.82
+
+
+
+![svg](output_13_1.svg)
+
+
+# Types of error
+## Freefall is example of "truncation error"
+### Truncation error results from approximating exact mathematical procedure
+
+We approximated the derivative as $\delta v/\delta t\approx\Delta v/\Delta t$
+
+Can reduce error by decreasing step size -> $\Delta t$=`delta_time`
+
+## Another example of truncation error is a Taylor series (or Maclaurin if centered at a=0)
+
+Taylor series:
+$f(x)=f(a)+f'(a)(x-a)+\frac{f''(a)}{2!}(x-a)^{2}+\frac{f'''(a)}{3!}(x-a)^{3}+...$
+
+We can approximate the next value in a function by adding Taylor series terms:
+
+|Approximation | formula |
+|---|-------------------------|
+|$0^{th}$-order | $f(x_{i+1})=f(x_{i})+R_{1}$ |
+|$1^{st}$-order | $f(x_{i+1})=f(x_{i})+f'(x_{i})h+R_{2}$ |
+|$2^{nd}$-order | $f(x_{i+1})=f(x_{i})+f'(x_{i})h+\frac{f''(x_{i})}{2!}h^{2}+R_{3}$|
+|$n^{th}$-order | $f(x_{i+1})=f(x_{i})+f'(x_{i})h+\frac{f''(x_{i})}{2!}h^{2}+...\frac{f^{(n)}}{n!}h^{n}+R_{n}$|
+
+Where $R_{n}=\frac{f^{(n+1)}(\xi)}{(n+1)!}h^{n+1}$ is the error associated with truncating the approximation at order $n$.
+
+The $n^{th}$-order approximation estimates that the unknown function, $f(x)$, is equal to an $n^{th}$-order polynomial. 
+
+In the Freefall example, we estimated the function with a $1^{st}$-order approximation, so 
+
+$v(t_{i+1})=v(t_{i})+v'(t_{i})(t_{i+1}-t_{i})+R_{1}$
+
+$v'(t_{i})=\frac{v(t_{i+1})-v(t_{i})}{t_{i+1}-t_{i}}-\frac{R_{1}}{t_{i+1}-t_{i}}$
+
+$\frac{R_{1}}{t_{i+1}-t_{i}}=\frac{v''(\xi)}{2!}(t_{i+1}-t_{i})$
+
+or the truncation error for a first-order Taylor series approximation is
+
+$\frac{R_{1}}{t_{i+1}-t_{i}}=O(\Delta t)$
+
+
+1. digital representation of a number is rarely exact
+
+2. arithmetic (+,-,/,\*) causes roundoff error
+
+
+```octave
+fprintf('%1.20f\n',double(pi))
+fprintf('%1.20f\n',single(pi))
+```
+
+    3.14159265358979311600
+    3.14159274101257324219
+
+
+
+```octave
+
+```
diff --git a/lecture_02/lecture_02.ipynb b/lecture_02/lecture_02.ipynb
new file mode 100644
index 0000000..3e0a9e6
--- /dev/null
+++ b/lecture_02/lecture_02.ipynb
@@ -0,0 +1,597 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Solution to Form #1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "   1   2   3\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "[1,2,3]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "[1,2,3]*[1;2;3]=?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# The first source of error is roundoff error\n",
+    "## Just storing a number in a computer requires rounding"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "realmax = 1.79769313486231570815e+308\n",
+      "realmin = 2.22507385850720138309e-308\n",
+      "maximum relative error = 2.22044604925031308085e-16\n"
+     ]
+    }
+   ],
+   "source": [
+    "fprintf('realmax = %1.20e\\n',realmax)\n",
+    "fprintf('realmin = %1.20e\\n',realmin)\n",
+    "fprintf('maximum relative error = %1.20e\\n',eps)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  1\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "s=1;\n",
+    "for i=1:1000\n",
+    "    s=s+eps/10;\n",
+    "end\n",
+    "s==1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Freefall Model (revisited)\n",
+    "## Octave solution (will run same on Matlab)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Set default values in Octave for linewidth and text size"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%plot --format svg"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "set (0, \"defaultaxesfontname\", \"Helvetica\")\n",
+    "set (0, \"defaultaxesfontsize\", 18)\n",
+    "set (0, \"defaulttextfontname\", \"Helvetica\")\n",
+    "set (0, \"defaulttextfontsize\", 18) \n",
+    "set (0, \"defaultlinelinewidth\", 4)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Define time from 0 to 12 seconds with `N` timesteps \n",
+    "function defined as `freefall`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "function [v_analytical,v_terminal,t]=freefall(N)\n",
+    "    t=linspace(0,12,N)';\n",
+    "    c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c);\n",
+    "\n",
+    "    v_analytical = v_terminal*tanh(g*t/v_terminal);\n",
+    "    v_numerical=zeros(length(t),1);\n",
+    "    delta_time =diff(t);\n",
+    "    for i=1:length(t)-1\n",
+    "        v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*delta_time(i);\n",
+    "    end\n",
+    "    % Print values near 0,2,4,6,8,10,12 seconds\n",
+    "    indices = round(linspace(1,length(t),7));\n",
+    "    fprintf('time (s)|vel analytical (m/s)|vel numerical (m/s)\\n')\n",
+    "    fprintf('-----------------------------------------------\\n')\n",
+    "    M=[t(indices),v_analytical(indices),v_numerical(indices)];\n",
+    "    fprintf('%7.1f | %18.2f | %15.2f\\n',M(:,1:3)');\n",
+    "    plot(t,v_analytical,'-',t,v_numerical,'o-')\n",
+    "end\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "time (s)|vel analytical (m/s)|vel numerical (m/s)\n",
+      "-----------------------------------------------\n",
+      "    0.0 |               0.00 |            0.00\n",
+      "    2.0 |              18.76 |           18.82\n",
+      "    4.0 |              32.64 |           32.80\n",
+      "    6.1 |              40.79 |           40.97\n",
+      "    8.0 |              44.80 |           44.94\n",
+      "   10.0 |              46.84 |           46.93\n",
+      "   12.0 |              47.77 |           47.82\n"
+     ]
+    },
+    {
+     "data": {
+      "image/svg+xml": [
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+       "</g>\n",
+       "\t<g id=\"gnuplot_plot_1a\"><title>gnuplot_plot_1a</title>\n",
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+       "\t</g>\n",
+       "\t<g id=\"gnuplot_plot_2a\"><title>gnuplot_plot_2a</title>\n",
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+       "</g>\n",
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+       "</g>\n",
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+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "[v_analytical,v_terminal,t]=freefall(120);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Types of error\n",
+    "## Freefall is example of \"truncation error\"\n",
+    "### Truncation error results from approximating exact mathematical procedure"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We approximated the derivative as $\\delta v/\\delta t\\approx\\Delta v/\\Delta t$\n",
+    "\n",
+    "Can reduce error by decreasing step size -> $\\Delta t$=`delta_time`"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Another example of truncation error is a Taylor series (or Maclaurin if centered at a=0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Taylor series:\n",
+    "$f(x)=f(a)+f'(a)(x-a)+\\frac{f''(a)}{2!}(x-a)^{2}+\\frac{f'''(a)}{3!}(x-a)^{3}+...$\n",
+    "\n",
+    "We can approximate the next value in a function by adding Taylor series terms:\n",
+    "\n",
+    "|Approximation | formula |\n",
+    "|---|-------------------------|\n",
+    "|$0^{th}$-order | $f(x_{i+1})=f(x_{i})+R_{1}$ |\n",
+    "|$1^{st}$-order | $f(x_{i+1})=f(x_{i})+f'(x_{i})h+R_{2}$ |\n",
+    "|$2^{nd}$-order | $f(x_{i+1})=f(x_{i})+f'(x_{i})h+\\frac{f''(x_{i})}{2!}h^{2}+R_{3}$|\n",
+    "|$n^{th}$-order | $f(x_{i+1})=f(x_{i})+f'(x_{i})h+\\frac{f''(x_{i})}{2!}h^{2}+...\\frac{f^{(n)}}{n!}h^{n}+R_{n}$|\n",
+    "\n",
+    "Where $R_{n}=\\frac{f^{(n+1)}(\\xi)}{(n+1)!}h^{n+1}$ is the error associated with truncating the approximation at order $n$.\n",
+    "\n",
+    "The $n^{th}$-order approximation estimates that the unknown function, $f(x)$, is equal to an $n^{th}$-order polynomial. \n",
+    "\n",
+    "In the Freefall example, we estimated the function with a $1^{st}$-order approximation, so \n",
+    "\n",
+    "$v(t_{i+1})=v(t_{i})+v'(t_{i})(t_{i+1}-t_{i})+R_{1}$\n",
+    "\n",
+    "$v'(t_{i})=\\frac{v(t_{i+1})-v(t_{i})}{t_{i+1}-t_{i}}-\\frac{R_{1}}{t_{i+1}-t_{i}}$\n",
+    "\n",
+    "$\\frac{R_{1}}{t_{i+1}-t_{i}}=\\frac{v''(\\xi)}{2!}(t_{i+1}-t_{i})$\n",
+    "\n",
+    "or the truncation error for a first-order Taylor series approximation is\n",
+    "\n",
+    "$\\frac{R_{1}}{t_{i+1}-t_{i}}=O(\\Delta t)$\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "1. digital representation of a number is rarely exact\n",
+    "\n",
+    "2. arithmetic (+,-,/,\\*) causes roundoff error"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "3.14159265358979311600\n",
+      "3.14159274101257324219\n"
+     ]
+    }
+   ],
+   "source": [
+    "fprintf('%1.20f\\n',double(pi))\n",
+    "fprintf('%1.20f\\n',single(pi))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Octave",
+   "language": "octave",
+   "name": "octave"
+  },
+  "language_info": {
+   "file_extension": ".m",
+   "help_links": [
+    {
+     "text": "MetaKernel Magics",
+     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+    }
+   ],
+   "mimetype": "text/x-octave",
+   "name": "octave",
+   "version": "0.19.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/lecture_02/notes.pdf b/lecture_02/notes.pdf
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From e6166c345e8af7341bf1a65a60f873386b1a23dd Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Thu, 19 Jan 2017 12:19:28 -0500
Subject: [PATCH 02/37] HW 1 add collaborator

---
 HW1/README.md |   4 ++++
 HW1/g9.png    | Bin 0 -> 78564 bytes
 2 files changed, 4 insertions(+)
 create mode 100644 HW1/g9.png

diff --git a/HW1/README.md b/HW1/README.md
index 426c9c5..bb1c7b4 100644
--- a/HW1/README.md
+++ b/HW1/README.md
@@ -55,3 +55,7 @@
         vii. Paste this into the Homework #1 Google form reponse.
         (https://goo.gl/forms/jINjsioRLwQOiYtl2)[https://goo.gl/forms/jINjsioRLwQOiYtl2]
 
+![Step 9](g9.png)
+
+        viii. Click on the gear for "Settings" then "Collaborators" on the left menu. Add
+        `rcc02007` (Ryan C. Cooper) as a collaborator. 
diff --git a/HW1/g9.png b/HW1/g9.png
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From 88f2c758bdfad34a22abe59fb52de2fbb7d0d12e Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Thu, 19 Jan 2017 15:15:00 -0500
Subject: [PATCH 03/37] office hours updated

---
 README.md                 |   2 +-
 lecture_02/lecture_02.pdf | Bin 0 -> 126338 bytes
 2 files changed, 1 insertion(+), 1 deletion(-)
 create mode 100644 lecture_02/lecture_02.pdf

diff --git a/README.md b/README.md
index a7c930e..ca1565e 100644
--- a/README.md
+++ b/README.md
@@ -19,7 +19,7 @@ matlab/octave functions and programming best practices.
 
 **Instructor**: Prof. Ryan C. Cooper (ryan.c.cooper@uconn.edu)
 
-**Office hours**: Fridays 10am-12pm in Engineering II room 315
+**Office hours**: Mon 2:30-4:30pm and Thur 11am-1pm in Engineering II room 315
 
 ## Teaching Assistants:
 - Graduate: **TBD**
diff --git a/lecture_02/lecture_02.pdf b/lecture_02/lecture_02.pdf
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HcmV?d00001


From afbd43c297271784433a22621a71361354da0d29 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Tue, 24 Jan 2017 11:01:13 -0500
Subject: [PATCH 04/37] welcome to Peiyu

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index ca1565e..eebd665 100644
--- a/README.md
+++ b/README.md
@@ -22,8 +22,8 @@ matlab/octave functions and programming best practices.
 **Office hours**: Mon 2:30-4:30pm and Thur 11am-1pm in Engineering II room 315
 
 ## Teaching Assistants:
-- Graduate: **TBD**
-- Office hours: 2 hours / week in office **TBD**
+- Graduate: Peiyu Zhang <peiyu.zhang@uconn.edu>
+- Office hours: 2 hours / week 
 
 **Prerequisite:** CE 3110, MATH 2410Q 
 

From 3f676141d42c2570d286828a51a0a990d9464b88 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Wed, 25 Jan 2017 21:01:03 -0500
Subject: [PATCH 05/37] added lectures 3 and 4

---
 lecture_03/file.txt         |    5 +
 lecture_03/lecture_03.ipynb | 6077 +++++++++++++++++++++++++++++++++++
 lecture_03/lecture_03.md    | 1447 +++++++++
 lecture_03/octave-workspace |  Bin 0 -> 28302 bytes
 lecture_03/output_58_0.png  |  Bin 0 -> 17421 bytes
 lecture_03/output_63_0.svg  |  270 ++
 lecture_03/output_64_0.svg  | 1632 ++++++++++
 lecture_03/output_65_0.svg  | 2146 +++++++++++++
 lecture_04/lecture_4.md     |  309 ++
 lecture_04/myscript.m       |   11 +
 lecture_04/output_10_0.png  |  Bin 0 -> 29697 bytes
 lecture_04/output_11_0.png  |  Bin 0 -> 64822 bytes
 lecture_04/output_12_0.png  |  Bin 0 -> 17167 bytes
 lecture_04/output_20_0.png  |  Bin 0 -> 20897 bytes
 lecture_04/output_24_0.png  |  Bin 0 -> 19815 bytes
 lecture_04/output_5_0.png   |  Bin 0 -> 17993 bytes
 16 files changed, 11897 insertions(+)
 create mode 100644 lecture_03/file.txt
 create mode 100644 lecture_03/lecture_03.ipynb
 create mode 100644 lecture_03/lecture_03.md
 create mode 100644 lecture_03/octave-workspace
 create mode 100644 lecture_03/output_58_0.png
 create mode 100644 lecture_03/output_63_0.svg
 create mode 100644 lecture_03/output_64_0.svg
 create mode 100644 lecture_03/output_65_0.svg
 create mode 100644 lecture_04/lecture_4.md
 create mode 100644 lecture_04/myscript.m
 create mode 100644 lecture_04/output_10_0.png
 create mode 100644 lecture_04/output_11_0.png
 create mode 100644 lecture_04/output_12_0.png
 create mode 100644 lecture_04/output_20_0.png
 create mode 100644 lecture_04/output_24_0.png
 create mode 100644 lecture_04/output_5_0.png

diff --git a/lecture_03/file.txt b/lecture_03/file.txt
new file mode 100644
index 0000000..0fb2c92
--- /dev/null
+++ b/lecture_03/file.txt
@@ -0,0 +1,5 @@
+computational mechanics
+the dog had 4 legs and weighed 10.0 lbs
+are you awake?computational mechanics
+the dog had 4 legs and weighed 10.0 lbs
+are you awake?
\ No newline at end of file
diff --git a/lecture_03/lecture_03.ipynb b/lecture_03/lecture_03.ipynb
new file mode 100644
index 0000000..e205d15
--- /dev/null
+++ b/lecture_03/lecture_03.ipynb
@@ -0,0 +1,6077 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Matlab basic use\n",
+    "## 1- the environment, path and working directory"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Matlab environment can be called by:\n",
+    "1. Starting the matlab executable (the gui)\n",
+    "2. Starting a jupyter notebook with Matlab kernel\n",
+    "3. Starting matlab with command-line interface (no gui)\n",
+    "\n",
+    "The main requirement is that matlab kernel (main matlab program) is running and accepting commands\n",
+    "\n",
+    "When you start, you can call matlab built-in functions or anything you write that is in your `MATLABPATH` or working directory (`pwd`)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "MATLABPATH\n",
+      "\n",
+      "\t/usr/local/lib/python2.7/dist-packages/matlab_kernel/toolbox\n",
+      "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab\n",
+      "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/usrprog\n",
+      "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util\n",
+      "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2\n",
+      "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/json\n",
+      "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/json/java\n",
+      "\t/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/test\n",
+      "\t/home/ryan/Documents/MATLAB\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/strfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/datatypes\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/elfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/ops\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/timefun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/elmat\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/datafun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/iofun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/mvm\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/randfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/funfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/general\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/polyfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/matfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/lang\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/specfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/sparfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/images\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/performance\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/parallel\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/optimfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/ext\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/guide\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/measurement\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/icons\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/demos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/helptools\n",
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+      "\t/usr/local/MATLAB/R2016a/toolbox/database/vqb\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/map/mapdemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/cxxfe_mi/cxxfe_mi\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/stats/mlearnapp\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/eda/fpgaautomation\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/eda/fpgaautomation/obsolete\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/comm/commdemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/pe/pedemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/slrequirements\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/slcontrollib\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/geoweb/geoweb\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/configset\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/comm/cdma2000\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/signal/signalanalyzer\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotics\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/can\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/can/canblks\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/can/canmasks\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/can/canmex\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/fixedandfloat\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/fixedandfloat/obsolete\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/common/data/mli/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/sm/foundation/mech\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/imaq/imaq\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/pm_visimpl/pm_visimpl\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/bioinfo/biodemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/sigbldr\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/dsp/dsp\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/dsp/dsputilities\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/dsp/dsputilities/dspinit\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/dsp/dsputilities/dspmex\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/dsp/dsp/compiled\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/symbolic/symbolic\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/optim/optimdemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/curvefit/curvefitdemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/instrument\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/common/external/library/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/slproject\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/slproject/menu\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/mech/mech\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/mech/importer\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/simulation_data_repository\n",
+      "\t/usr/local/MATLAB/R2016a/help/toolbox/control/examples\n",
+      "\t/usr/local/MATLAB/R2016a/help/toolbox/vision/examples\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo/meascontrol\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo/power_utility\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/sm/ssci/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/sl_async_streaming\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/simulink/slcheck_services\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/measure\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo/simple\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/trace\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/compiler_sdk\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/diagnostic\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/templates\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/sldv/sldvdemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/sta/repository\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/sta/repository/util\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/stats/stats\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/stats/classreg\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/stats/clustering\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/hdlcoder/hdllib/ml_lib\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/iodata/ioformat\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/audiovideo\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/webcam\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/mldatx\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robust/robust\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robust/rctlmi\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robust/rctutil\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robust/rctobsolete/robust\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robust/rctobsolete/lmi\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robust/rctobsolete/mutools/commands\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robust/rctobsolete/mutools/subs\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/codeinstrum/codeinstrum\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/control/control\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/control/ctrlmodels\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/control/ctrlanalysis\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/control/ctrldesign\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/control/ctrlplots\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/control/ctrlguis\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/control/ctrlobsolete\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/control/ctrlutil\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/simscape/compiler/sli/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/dastudio\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/stats/statsdemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/curvefitlib\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/slpir\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/eda/fpgabase\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/common/dataservices/mli/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/hdlshared/hdlshared_gui\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/eda/hdlparser\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/network_engine/network_engine\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/intelhost/tfl\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/coverage\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/dsp/hdl\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/spf/matlabhost\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/mpc/mpc\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/mpc/mpcguis\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/mpc/mpcobsolete\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/mpc/mpcutils\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/slexportprevious\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/sl3d/sl3d\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/comm/comm\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/comm/commutilities/comminit\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/comm/commutilities/commmex\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/comm/commutilities\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/comm/commdeprecated\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/comm/comm/compiled\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/connectivity\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/rtw/targets/connectivity\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/slhistory\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/simscape/templates\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/spreadsheet\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/fixpoint\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/fixpoint/fpca\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/ros\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/ne_sli/ne_sli\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/dsp/simulink/dsp\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/system\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/eda/fil\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/eda/fil/filmapi\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/rtiostream\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/pde\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powersys\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/hotpluglib\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/multimedia\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/testmeaslib/graphics\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/addons_toolbox\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/imageslib\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/pm_sli/pm_sli\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/dastudio/seqdiagram\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/sm/templates\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/sm/gui/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/ident/ident\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/ident/nlident\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/ident/idobsolete\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/ident/idguis\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/ident/idutils\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/ident/idrecursive\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/ident/idhelp\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo/machines\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/target/extensions/operatingsystem/windows/blks\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/target/extensions/operatingsystem/windows/blks/masks\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/target/extensions/operatingsystem/windows/blks/mex\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/networklib\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/sm/sli/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/sm/sm/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/advisor\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/filterdesignlib\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/connector/connector\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/idelink/foundation\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/idelink/foundation/util\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/idelink/foundation/errorhandler\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/idelink/foundation/xmakefile\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/idelink/foundation/hookpoints\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/comparisons\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/signal/sigdemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/configtools\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simbio/simbio\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/external/interfaces/python\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/m3i\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/toolstrip\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/dsp/dspdeployabledemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/slvnv/styleguide\n",
+      "\t/usr/local/MATLAB/R2016a/help/toolbox/robust/examples\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/deviceplugindetection\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/simscape/compiler/mli/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/gui/gfx/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/sm/import/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/compiler/java\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/pe/utils/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/rtw/rtw\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/foundation\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/foundation/build\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/foundation/build/tools/registry\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/foundation/tfl\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/foundation/tfl/AUTOSAR/AUTOSAR4p0/IFX\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/foundation/tfl/AUTOSAR/AUTOSAR4p0/IFL\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/foundation/tfl/gui\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/foundation/templates\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/simtargets\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/mech/mechdemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/maputils\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/foundation/passmanager\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/iodata/iomap\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/fininst/fininstdemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nncontrol\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnadapt\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nndatafun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnderivative\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nndistance\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nndivision\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nninitlayer\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nninitnetwork\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nninitweight\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnlearn\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnnetfun\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnnetinput\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnnetwork\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnperformance\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnplot\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnprocess\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnsearch\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nntopology\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nntrain\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nntransfer\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnweight\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnguis\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnobsolete\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/nnet/nnutils\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/matlab/addons_product\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/tracking/trackinglib\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/simulink/sysarch/sysarch\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/slreportgen/reportexplorer\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/embeddedcoder_templates\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/coder/wizard\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/sm/core/m\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/ros\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/ros/helpers\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotalgs\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotalgs/helpers\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotcore\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotcore/helpers\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotsimulink\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotsimulink/helpers\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/numerics\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/options\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/optim\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/blocks\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/dsp/filterdesign\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/finance/findemos\n",
+      "\t/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/facts/facts\n"
+     ]
+    }
+   ],
+   "source": [
+    "path"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "/home/ryan/Documents/UConn/ME3255/me3255_S2017/lecture_03\n"
+     ]
+    }
+   ],
+   "source": [
+    "pwd"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "path"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Assignments (`=`-operator)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Matlab is interpreted language so each line of code (either saved text file or command-line) is executed as a standalone command\n",
+    "\n",
+    "These are reffered to \"scripts\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "    40\n"
+     ]
+    }
+   ],
+   "source": [
+    "a=10; % line one assigns a to 10\n",
+    "b=a*3; % line two assigns b to 10 times 3 by calling 'a' from line one\n",
+    "a+b % line three does not assign anything directly, but leaving off the \";\" prints the result\n",
+    "    % ans"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Matlab has a number of \"objects\" that you can assign to variables\n",
+    "1. arrays (vectors and matrices `[`...`]`) \n",
+    "2. strings (text `\"`...`\"` )\n",
+    "3. cells (combination of strings, text, even function calls `{`...`}`)\n",
+    "3. functions (both built-in, defined or developed)\n",
+    "4. and more... (classes defined by `classdef` - you can create your own object to help organize data)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 1- Arrays"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Default in matlab is that when you assign a value to a variable, it is stored as an array\n",
+    "\n",
+    "arrays are N x M x ... values of integers or floating point numbers or complex integers/floating point numbers\n",
+    "\n",
+    "Use the parantheses to access values in an array `...(n,m)`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "     1\n"
+     ]
+    }
+   ],
+   "source": [
+    "a=10; % a is 1x1 array where a(1,1)==10\n",
+    "a(1,1)==10\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\u001b[0;31mIndex exceeds matrix dimensions.\n",
+      "\u001b[0m"
+     ]
+    }
+   ],
+   "source": [
+    "a(2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "A =\n",
+      "\n",
+      "     1     2     3\n",
+      "     4     5     6\n",
+      "     7     8     9\n",
+      "    10    11    12\n",
+      "\n",
+      "size of A is 4 x 3\n",
+      "\n",
+      "ans =\n",
+      "\n",
+      "     7\n",
+      "\n",
+      "\n",
+      "ans =\n",
+      "\n",
+      "     5\n"
+     ]
+    }
+   ],
+   "source": [
+    "A = [1 2 3;4,5,6;7,8,9;10,11,12]\n",
+    "fprintf('size of A is %i x %i\\n',size(A))\n",
+    "A(3,1)\n",
+    "A(6)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "vectors are either 1xN or Nx1 arrays for row and column"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "v_row =\n",
+      "\n",
+      "     1     2     3\n",
+      "\n",
+      "\n",
+      "v_column =\n",
+      "\n",
+      "     1\n",
+      "     2\n",
+      "     3\n"
+     ]
+    }
+   ],
+   "source": [
+    "v_row = [1,2,3] %row vector\n",
+    "v_column = [1;2;3] %column vector\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Matrices are MxN arrays\n",
+    "the `:`-symbol can substitute for a counting"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "     1     2     3\n"
+     ]
+    }
+   ],
+   "source": [
+    "A(1,:) % the colon assumes you want the first value, 1, counting up by 1 to the last value, 4"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "You can also use every 2nd value or any other integer up to `end` which is the largest value of that row or column of the array"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "     1\n",
+      "     7\n"
+     ]
+    }
+   ],
+   "source": [
+    "A(1:2:end,1) % you can also use `end` "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "     1\n",
+      "     4\n",
+      "     7\n",
+      "    10\n",
+      "     2\n",
+      "     5\n",
+      "     8\n",
+      "    11\n",
+      "     3\n",
+      "     6\n",
+      "     9\n",
+      "    12\n"
+     ]
+    }
+   ],
+   "source": [
+    "A(:)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In general, arrays can be any size \n",
+    "\n",
+    "take rolling 4 die and determining the sum of the components"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "A_6666 = zeros(6,6,6,6); %make a 6 x 6 x 6 x 6 array (1296 different values)\n",
+    "for i=1:6\n",
+    "    for j=1:6\n",
+    "        for k=1:6\n",
+    "            for l=1:6\n",
+    "                A_6666(i,j,k,l)=i+j+k+l; % each value is the sum of the indices\n",
+    "            end\n",
+    "        end\n",
+    "    end\n",
+    "end\n",
+    "            "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "    14\n",
+      "\n",
+      "\n",
+      "ans =\n",
+      "\n",
+      "    3.4170\n"
+     ]
+    }
+   ],
+   "source": [
+    "mean(A_6666(:))\n",
+    "std(A_6666(:))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "    12\n"
+     ]
+    }
+   ],
+   "source": [
+    "A_6666(1,4,2,5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Cells combine different size arrays and text\n",
+    "### but, you cannot use math operators 'binary operators'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "C={};\n",
+    "C{1}=linspace(0,1,10);\n",
+    "C{2}=linspace(0,1,3);\n",
+    "C{'z'}='holy cow';"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "    3.5185\n"
+     ]
+    }
+   ],
+   "source": [
+    "C{1}*C{1}'"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Strings can be combined and printed"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "computational mechanics\n"
+     ]
+    }
+   ],
+   "source": [
+    "string1 = 'computational'; string2 = 'mechanics';\n",
+    "[string1, ' ', string2]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "use `fprintf` to format strings and numbers for output and `sprintf` to save variables\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "computational mechanics\n",
+      "\n",
+      "\n",
+      "string =\n",
+      "\n",
+      "the dog had 4 legs and weighed 10.0 lbs\n"
+     ]
+    }
+   ],
+   "source": [
+    "fprintf([string1,' ',string2,'\\n\\n'])\n",
+    "string = sprintf('the dog had %i legs and weighed %1.1f lbs',4,10.0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "the `\\` signifies a special character e.g. `\\n` = newline, `\\t` = tab\n",
+    "\n",
+    "to actually print the \"\\\", use `\\\\`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\\\n"
+     ]
+    }
+   ],
+   "source": [
+    "fprintf('\\\\')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## This is helpful to create reports of computed data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "    23\n",
+      "\n",
+      "\n",
+      "ans =\n",
+      "\n",
+      "     1\n",
+      "\n",
+      "\n",
+      "ans =\n",
+      "\n",
+      "    39\n",
+      "\n",
+      "\n",
+      "ans =\n",
+      "\n",
+      "     1\n",
+      "\n",
+      "\n",
+      "ans =\n",
+      "\n",
+      "    14\n"
+     ]
+    }
+   ],
+   "source": [
+    "%fid = fopen('file.txt','w');\n",
+    "fprintf(fid,[string1, ' ', string2])\n",
+    "fprintf(fid,'\\n')\n",
+    "fprintf(fid,string)\n",
+    "fprintf(fid,'\\n')\n",
+    "fprintf(fid,'are you awake?')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Math operators (=, +, -, /, *, ^)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Because matlab assumes all variables are matrices, then all operators are matrix operations"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  20\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "a+a % add two 1x1 arrays"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "    2    4    6\n",
+      "    8   10   12\n",
+      "   14   16   18\n",
+      "   20   22   24\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "A+A % add two 4 x 3 arrays"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "    14    32    50    68\n",
+      "    32    77   122   167\n",
+      "    50   122   194   266\n",
+      "    68   167   266   365\n"
+     ]
+    }
+   ],
+   "source": [
+    "A*A'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "     1     4     9\n",
+      "    16    25    36\n",
+      "    49    64    81\n",
+      "   100   121   144\n"
+     ]
+    }
+   ],
+   "source": [
+    "A.^2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "     1     4     9\n",
+      "    16    25    36\n",
+      "    49    64    81\n",
+      "   100   121   144\n"
+     ]
+    }
+   ],
+   "source": [
+    "A.*A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[\b> In pymat_eval (line 31)\n",
+      "  In matlabserver (line 24)]\b \n",
+      "[\bWarning: Rank deficient, rank = 2, tol =  1.696862e-14.]\b \n",
+      "\n",
+      "ans =\n",
+      "\n",
+      "    1.0000         0         0   -0.0000\n",
+      "    0.6667         0         0    0.3333\n",
+      "    0.3333         0         0    0.6667\n",
+      "    0.0000         0         0    1.0000\n"
+     ]
+    }
+   ],
+   "source": [
+    "A/A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "/   Slash or right matrix divide.\n",
+      "    A/B is the matrix division of B into A, which is roughly the\n",
+      "    same as A*INV(B) , except it is computed in a different way.\n",
+      "    More precisely, A/B = (B'\\A')'. See MLDIVIDE for details.\n",
+      " \n",
+      "    C = MRDIVIDE(A,B) is called for the syntax 'A / B' when A or B is an\n",
+      "    object.\n",
+      " \n",
+      "    See also MLDIVIDE, RDIVIDE, LDIVIDE.\n",
+      "\n",
+      "    Reference page in Doc Center\n",
+      "       doc mrdivide\n",
+      "\n",
+      "    Other functions named mrdivide\n",
+      "\n",
+      "       codistributed/mrdivide    gf/mrdivide          laurpoly/mrdivide\n",
+      "       duration/mrdivide         gpuArray/mrdivide    StaticModel/mrdivide\n",
+      "       DynamicSystem/mrdivide    LagOp/mrdivide       timeseries/mrdivide\n",
+      "       fints/mrdivide\n"
+     ]
+    }
+   ],
+   "source": [
+    "help /"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To accomplish one-by-one operations, need to include a `.`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "   1   1   1\n",
+      "   1   1   1\n",
+      "   1   1   1\n",
+      "   1   1   1\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "A./A"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "But, for 1x1 arrays, these are considered scalars and you get a free-pass"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "    10    20    30\n",
+      "    40    50    60\n",
+      "    70    80    90\n",
+      "   100   110   120\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "a*A % where a=10 and A is 1:12 in a 3 x 4 matrix"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Some built in Matlab functions (e.g. the reasons to run Matlab)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "t_linear =\n",
+      "\n",
+      "  Columns 1 through 7\n",
+      "\n",
+      "         0    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000\n",
+      "\n",
+      "  Columns 8 through 11\n",
+      "\n",
+      "    0.7000    0.8000    0.9000    1.0000\n"
+     ]
+    }
+   ],
+   "source": [
+    "t_linear=linspace(0,1,11)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "t_log =\n",
+      "\n",
+      "     1    10   100\n"
+     ]
+    }
+   ],
+   "source": [
+    "t_log = logspace(0,2,3) % log interval from 10^0 to 10^2 split into 3 values"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "'logspace' is a function from the file /usr/share/octave/4.0.0/m/general/logspace.m\n",
+      "\n",
+      " -- Function File: logspace (A, B)\n",
+      " -- Function File: logspace (A, B, N)\n",
+      " -- Function File: logspace (A, pi, N)\n",
+      "     Return a row vector with N elements logarithmically spaced from\n",
+      "     10^A to 10^B.\n",
+      "\n",
+      "     If N is unspecified it defaults to 50.\n",
+      "\n",
+      "     If B is equal to pi, the points are between 10^A and pi, _not_ 10^A\n",
+      "     and 10^pi, in order to be compatible with the corresponding MATLAB\n",
+      "     function.\n",
+      "\n",
+      "     Also for compatibility with MATLAB, return the second argument B if\n",
+      "     fewer than two values are requested.\n",
+      "\n",
+      "     See also: linspace.\n",
+      "\n",
+      "Additional help for built-in functions and operators is\n",
+      "available in the online version of the manual.  Use the command\n",
+      "'doc <topic>' to search the manual index.\n",
+      "\n",
+      "Help and information about Octave is also available on the WWW\n",
+      "at http://www.octave.org and via the help@octave.org\n",
+      "mailing list.\n"
+     ]
+    }
+   ],
+   "source": [
+    "help logspace"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%myscript"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%plot --format svg"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "When using the GUI, your command history is saved, but it is better to save your work either as a script or a function or combination of both\n",
+    "\n",
+    "Creating a default graph script:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "set(0, 'defaultAxesFontSize', 16)\n",
+    "set(0,'defaultTextFontSize',14)\n",
+    "set(0,'defaultLineLineWidth',3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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IsrIy41QFAGB+mMzbxFi8GCsSiWJjYwkhfn5+hYWFpaWlUVFR9vb27u7uGsfd8Xi88+fP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\ncAICCQAAOAGBBAAAnPD/AHltgbQ+BHrdAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot(t_linear,t_linear.^2)\n",
+    "xlabel('time (s)')\n",
+    "ylabel('displacement (m)')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#EOL"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Graphics can be produced with a number of functions"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "2-D plots, 3-D plots, contour plots, 3D contour plots ... "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Z =\n",
+      "\n",
+      " Columns 1 through 8:\n",
+      "\n",
+      "   0.00000   0.17100   0.28800   0.35700   0.38400   0.37500   0.33600   0.27300\n",
+      "  -0.17100   0.00000   0.12240   0.20160   0.24300   0.25200   0.23400   0.19440\n",
+      "  -0.28800  -0.12240   0.00000   0.08400   0.13440   0.15600   0.15360   0.13200\n",
+      "  -0.35700  -0.20160  -0.08400   0.00000   0.05460   0.08400   0.09240   0.08400\n",
+      "  -0.38400  -0.24300  -0.13440  -0.05460   0.00000   0.03300   0.04800   0.04860\n",
+      "  -0.37500  -0.25200  -0.15600  -0.08400  -0.03300   0.00000   0.01800   0.02400\n",
+      "  -0.33600  -0.23400  -0.15360  -0.09240  -0.04800  -0.01800   0.00000   0.00840\n",
+      "  -0.27300  -0.19440  -0.13200  -0.08400  -0.04860  -0.02400  -0.00840   0.00000\n",
+      "  -0.19200  -0.13860  -0.09600  -0.06300  -0.03840  -0.02100  -0.00960  -0.00300\n",
+      "  -0.09900  -0.07200  -0.05040  -0.03360  -0.02100  -0.01200  -0.00600  -0.00240\n",
+      "   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000\n",
+      "   0.09900   0.07200   0.05040   0.03360   0.02100   0.01200   0.00600   0.00240\n",
+      "   0.19200   0.13860   0.09600   0.06300   0.03840   0.02100   0.00960   0.00300\n",
+      "   0.27300   0.19440   0.13200   0.08400   0.04860   0.02400   0.00840  -0.00000\n",
+      "   0.33600   0.23400   0.15360   0.09240   0.04800   0.01800  -0.00000  -0.00840\n",
+      "   0.37500   0.25200   0.15600   0.08400   0.03300   0.00000  -0.01800  -0.02400\n",
+      "   0.38400   0.24300   0.13440   0.05460  -0.00000  -0.03300  -0.04800  -0.04860\n",
+      "   0.35700   0.20160   0.08400  -0.00000  -0.05460  -0.08400  -0.09240  -0.08400\n",
+      "   0.28800   0.12240   0.00000  -0.08400  -0.13440  -0.15600  -0.15360  -0.13200\n",
+      "   0.17100  -0.00000  -0.12240  -0.20160  -0.24300  -0.25200  -0.23400  -0.19440\n",
+      "   0.00000  -0.17100  -0.28800  -0.35700  -0.38400  -0.37500  -0.33600  -0.27300\n",
+      "\n",
+      " Columns 9 through 16:\n",
+      "\n",
+      "   0.19200   0.09900   0.00000  -0.09900  -0.19200  -0.27300  -0.33600  -0.37500\n",
+      "   0.13860   0.07200   0.00000  -0.07200  -0.13860  -0.19440  -0.23400  -0.25200\n",
+      "   0.09600   0.05040   0.00000  -0.05040  -0.09600  -0.13200  -0.15360  -0.15600\n",
+      "   0.06300   0.03360   0.00000  -0.03360  -0.06300  -0.08400  -0.09240  -0.08400\n",
+      "   0.03840   0.02100   0.00000  -0.02100  -0.03840  -0.04860  -0.04800  -0.03300\n",
+      "   0.02100   0.01200   0.00000  -0.01200  -0.02100  -0.02400  -0.01800   0.00000\n",
+      "   0.00960   0.00600   0.00000  -0.00600  -0.00960  -0.00840   0.00000   0.01800\n",
+      "   0.00300   0.00240   0.00000  -0.00240  -0.00300   0.00000   0.00840   0.02400\n",
+      "   0.00000   0.00060   0.00000  -0.00060   0.00000   0.00300   0.00960   0.02100\n",
+      "  -0.00060   0.00000   0.00000   0.00000   0.00060   0.00240   0.00600   0.01200\n",
+      "   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000\n",
+      "   0.00060  -0.00000   0.00000   0.00000  -0.00060  -0.00240  -0.00600  -0.01200\n",
+      "  -0.00000  -0.00060   0.00000   0.00060   0.00000  -0.00300  -0.00960  -0.02100\n",
+      "  -0.00300  -0.00240   0.00000   0.00240   0.00300   0.00000  -0.00840  -0.02400\n",
+      "  -0.00960  -0.00600   0.00000   0.00600   0.00960   0.00840   0.00000  -0.01800\n",
+      "  -0.02100  -0.01200   0.00000   0.01200   0.02100   0.02400   0.01800   0.00000\n",
+      "  -0.03840  -0.02100   0.00000   0.02100   0.03840   0.04860   0.04800   0.03300\n",
+      "  -0.06300  -0.03360   0.00000   0.03360   0.06300   0.08400   0.09240   0.08400\n",
+      "  -0.09600  -0.05040   0.00000   0.05040   0.09600   0.13200   0.15360   0.15600\n",
+      "  -0.13860  -0.07200   0.00000   0.07200   0.13860   0.19440   0.23400   0.25200\n",
+      "  -0.19200  -0.09900   0.00000   0.09900   0.19200   0.27300   0.33600   0.37500\n",
+      "\n",
+      " Columns 17 through 21:\n",
+      "\n",
+      "  -0.38400  -0.35700  -0.28800  -0.17100   0.00000\n",
+      "  -0.24300  -0.20160  -0.12240   0.00000   0.17100\n",
+      "  -0.13440  -0.08400   0.00000   0.12240   0.28800\n",
+      "  -0.05460   0.00000   0.08400   0.20160   0.35700\n",
+      "   0.00000   0.05460   0.13440   0.24300   0.38400\n",
+      "   0.03300   0.08400   0.15600   0.25200   0.37500\n",
+      "   0.04800   0.09240   0.15360   0.23400   0.33600\n",
+      "   0.04860   0.08400   0.13200   0.19440   0.27300\n",
+      "   0.03840   0.06300   0.09600   0.13860   0.19200\n",
+      "   0.02100   0.03360   0.05040   0.07200   0.09900\n",
+      "   0.00000   0.00000   0.00000   0.00000   0.00000\n",
+      "  -0.02100  -0.03360  -0.05040  -0.07200  -0.09900\n",
+      "  -0.03840  -0.06300  -0.09600  -0.13860  -0.19200\n",
+      "  -0.04860  -0.08400  -0.13200  -0.19440  -0.27300\n",
+      "  -0.04800  -0.09240  -0.15360  -0.23400  -0.33600\n",
+      "  -0.03300  -0.08400  -0.15600  -0.25200  -0.37500\n",
+      "   0.00000  -0.05460  -0.13440  -0.24300  -0.38400\n",
+      "   0.05460   0.00000  -0.08400  -0.20160  -0.35700\n",
+      "   0.13440   0.08400   0.00000  -0.12240  -0.28800\n",
+      "   0.24300   0.20160   0.12240   0.00000  -0.17100\n",
+      "   0.38400   0.35700   0.28800   0.17100   0.00000\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "x=linspace(-1,1,21); y=linspace(-1,1,21);\n",
+    "[X,Y]=meshgrid(x,y);\n",
+    "Z=(X.*Y.^3-X.^3.*Y)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
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+   "metadata": {
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+   "source": [
+    "mesh(X,Y,Z)"
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+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
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+       "\t\t<text><tspan font-family=\"{}\">1</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pcolor(X,Y,Z)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "## "
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Matlab",
+   "language": "matlab",
+   "name": "matlab"
+  },
+  "language_info": {
+   "codemirror_mode": "octave",
+   "file_extension": ".m",
+   "help_links": [
+    {
+     "text": "MetaKernel Magics",
+     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+    }
+   ],
+   "mimetype": "text/x-octave",
+   "name": "matlab",
+   "version": "0.11.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/lecture_03/lecture_03.md b/lecture_03/lecture_03.md
new file mode 100644
index 0000000..ce76e7f
--- /dev/null
+++ b/lecture_03/lecture_03.md
@@ -0,0 +1,1447 @@
+
+# Matlab basic use
+## 1- the environment, path and working directory
+
+Matlab environment can be called by:
+1. Starting the matlab executable (the gui)
+2. Starting a jupyter notebook with Matlab kernel
+3. Starting matlab with command-line interface (no gui)
+
+The main requirement is that matlab kernel (main matlab program) is running and accepting commands
+
+When you start, you can call matlab built-in functions or anything you write that is in your `MATLABPATH` or working directory (`pwd`)
+
+
+```matlab
+path
+```
+
+    MATLABPATH
+    
+    	/usr/local/lib/python2.7/dist-packages/matlab_kernel/toolbox
+    	/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab
+    	/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/usrprog
+    	/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util
+    	/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2
+    	/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/json
+    	/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/json/java
+    	/usr/local/lib/python2.7/dist-packages/pymatbridge/matlab/util/json_v0.2.2/test
+    	/home/ryan/Documents/MATLAB
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/strfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/datatypes
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/elfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/ops
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/timefun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/elmat
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/datafun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/iofun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/mvm
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/randfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/funfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/general
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/polyfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/matfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/lang
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/specfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/sparfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/images
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/performance
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/parallel
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/optimfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/ext
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/guide
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/measurement
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/icons
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/demos
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/helptools
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/winfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/winfun/NET
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/datamanager
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/verctrl
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/graph2d
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/graph3d
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/graphics
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/graphics/obsolete
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/plottools
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/scribe
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/scribe/obsolete
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/specgraph
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/uitools
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/uitools/obsolete
+    	/usr/local/MATLAB/R2016a/toolbox/hdlcoder/matlabhdlcoder/matlabhdlcoder
+    	/usr/local/MATLAB/R2016a/toolbox/hdlcoder/matlabhdlcoder
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/core
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/testframework/obsolete
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/hardware/stubs
+    	/usr/local/MATLAB/R2016a/toolbox/local
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/datastoreio
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/codetools
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/codetools/embeddedoutputs
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/graphfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/depfun
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/mapreduceio
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/findfiles
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/asap2/asap2/dataclasses
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/asap2/asap2
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/asap2/asap2/user
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/common/can/blocks/dataclasses
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/common/can/blocks
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/common/can/blocks/tlc_c
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/common/tgtcommon
+    	/usr/local/MATLAB/R2016a/toolbox/coder/simulinkcoder/cgv/API
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/rtw/misra
+    	/usr/local/MATLAB/R2016a/toolbox/coder/simulinkcoder
+    	/usr/local/MATLAB/R2016a/toolbox/coder/simulinkcoder/templates
+    	/usr/local/MATLAB/R2016a/toolbox/coder/simulinkcoder/targets
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/pil
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/AUTOSAR/AUTOSAR/dataclasses
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/AUTOSAR/AUTOSAR
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/accel
+    	/usr/local/MATLAB/R2016a/toolbox/coder/simulinkcoder_core
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/rtwdemos
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/rtwdemos/rsimdemos
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/simfeatures
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/simfeatures/modelreference
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/simfeatures/datadictionary
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/sysarch/sysarch
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/simgeneral
+    	/usr/local/MATLAB/R2016a/toolbox/slde/examples
+    	/usr/local/MATLAB/R2016a/toolbox/coder/advisor
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/modeladvisor
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/modeladvisor/fixpt
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/automotive/fuelsys
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/components
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/dee
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/aerospace
+    	/usr/local/MATLAB/R2016a/toolbox/simulinktest/core/simharness/simharness
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/frameedit
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/industrial
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/automotive
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/blocks/library
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/blocks/library/simulinkcoder
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/blocks/obsolete
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/dataclasses
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/blocks
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/dataclasses
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/MPlayIO
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/dataobjectwizard
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/slresolve
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/units
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/resources
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/sdi
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/core_templates
+    	/usr/local/MATLAB/R2016a/toolbox/simulinktest/core/testsequence/testsequence
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simdemos/automotive/powerwindow
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/sldependency
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/hmi
+    	/usr/local/MATLAB/R2016a/toolbox/coder/objectives
+    	/usr/local/MATLAB/R2016a/toolbox/slde/slde
+    	/usr/local/MATLAB/R2016a/toolbox/slde/slde/resources
+    	/usr/local/MATLAB/R2016a/toolbox/stateflow/stateflow
+    	/usr/local/MATLAB/R2016a/toolbox/stateflow/coder
+    	/usr/local/MATLAB/R2016a/toolbox/stateflow/sfdemos
+    	/usr/local/MATLAB/R2016a/toolbox/stateflow/sftemplates
+    	/usr/local/MATLAB/R2016a/toolbox/shared/testmeaslib/general
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/blocks/sb2sl
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/DR/DR
+    	/usr/local/MATLAB/R2016a/toolbox/shared/reqmgt
+    	/usr/local/MATLAB/R2016a/toolbox/shared/reqmgt/mmutils
+    	/usr/local/MATLAB/R2016a/toolbox/shared/controllib/graphics
+    	/usr/local/MATLAB/R2016a/toolbox/shared/controllib/graphics/utils
+    	/usr/local/MATLAB/R2016a/toolbox/shared/controllib/graphics/plotoptions
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/sledittimecheck
+    	/usr/local/MATLAB/R2016a/toolbox/hdlcoder/slhdltemplates
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/distcomp
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/user
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/mpi
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/parallel
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/parallel/util
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/lang
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/cluster
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/gpu
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/array
+    	/usr/local/MATLAB/R2016a/toolbox/target/codertarget
+    	/usr/local/MATLAB/R2016a/toolbox/target/codertarget/rtw
+    	/usr/local/MATLAB/R2016a/toolbox/target/codertarget/matlabcoder
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/simscape/simscapedemos
+    	/usr/local/MATLAB/R2016a/toolbox/comm/templates
+    	/usr/local/MATLAB/R2016a/toolbox/shared/simulink
+    	/usr/local/MATLAB/R2016a/toolbox/hdlcoder/hdlcoderdemos
+    	/usr/local/MATLAB/R2016a/toolbox/hdlcoder/hdlcoderdemos/matlabhdlcoderdemos
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/tic5000/tic5000demos
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/common/gl/sli/m
+    	/usr/local/MATLAB/R2016a/toolbox/shared/system/simulink
+    	/usr/local/MATLAB/R2016a/toolbox/images/colorspaces
+    	/usr/local/MATLAB/R2016a/toolbox/images/images
+    	/usr/local/MATLAB/R2016a/toolbox/images/imdata
+    	/usr/local/MATLAB/R2016a/toolbox/images/imuitools
+    	/usr/local/MATLAB/R2016a/toolbox/images/iptformats
+    	/usr/local/MATLAB/R2016a/toolbox/images/iptutils
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/tic6000
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/tic6000/rtw
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/tic6000/tfl
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/tic6000/utils
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/tic6000/blks/sysobj_mex
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/tic6000/blks/mex
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/pctdemos
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/appdesigner/appdesigner
+    	/usr/local/MATLAB/R2016a/toolbox/shared/mlreportgen/ppt
+    	/usr/local/MATLAB/R2016a/toolbox/shared/mlreportgen/ppt/ppt
+    	/usr/local/MATLAB/R2016a/toolbox/shared/mlreportgen/ppt/ppt/help
+    	/usr/local/MATLAB/R2016a/toolbox/coder/matlabcoder
+    	/usr/local/MATLAB/R2016a/toolbox/coder/matlabcoder/templates
+    	/usr/local/MATLAB/R2016a/toolbox/dsp/templates
+    	/usr/local/MATLAB/R2016a/toolbox/globaloptim
+    	/usr/local/MATLAB/R2016a/toolbox/globaloptim/globaloptim
+    	/usr/local/MATLAB/R2016a/toolbox/shared/appdes/services
+    	/usr/local/MATLAB/R2016a/toolbox/coder/emlcodermex
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo/power_electronics
+    	/usr/local/MATLAB/R2016a/toolbox/pde/pdedemos
+    	/usr/local/MATLAB/R2016a/toolbox/slvnv/slvnvdemos
+    	/usr/local/MATLAB/R2016a/toolbox/sl_pir_cap
+    	/usr/local/MATLAB/R2016a/toolbox/target
+    	/usr/local/MATLAB/R2016a/toolbox/target/foundation
+    	/usr/local/MATLAB/R2016a/toolbox/target/foundation/utils
+    	/usr/local/MATLAB/R2016a/toolbox/target/foundation/utils/resource_config
+    	/usr/local/MATLAB/R2016a/toolbox/target/foundation/blks
+    	/usr/local/MATLAB/R2016a/toolbox/target/foundation/blks/mex
+    	/usr/local/MATLAB/R2016a/toolbox/target/foundation/blks/masks
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/shared
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/shared/ti
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/shared/ti/mdlinfo
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/shared/ti/utils
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/shared/ti/blks
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/shared/ti/blks/mex
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/shared/ti/blks/masks
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/ARM/tfl
+    	/usr/local/MATLAB/R2016a/toolbox/shared/etargets/etargets
+    	/usr/local/MATLAB/R2016a/toolbox/shared/etargets/etargets/demoutils
+    	/usr/local/MATLAB/R2016a/toolbox/optim/optim
+    	/usr/local/MATLAB/R2016a/toolbox/optim
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/simscape/advisor/m
+    	/usr/local/MATLAB/R2016a/toolbox/target/targetdemos
+    	/usr/local/MATLAB/R2016a/toolbox/shared/hadoopserializer
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/external/engines/engine_api
+    	/usr/local/MATLAB/R2016a/toolbox/shared/siglib
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/performance
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/performance/performancea
+    	/usr/local/MATLAB/R2016a/toolbox/simevents/examples
+    	/usr/local/MATLAB/R2016a/toolbox/shared/hdlshared
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/sm/local/m
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/uicomponents/uicomponents
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/uicomponents/uicomponents/pending
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/uicomponents/uicomponents/graphics
+    	/usr/local/MATLAB/R2016a/toolbox/fixedpoint/fixedpointconverter
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/drives/drivesdemo
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/simscape/library/m
+    	/usr/local/MATLAB/R2016a/toolbox/shared/sdi
+    	/usr/local/MATLAB/R2016a/toolbox/shared/asynciolib
+    	/usr/local/MATLAB/R2016a/toolbox/shared/cmlink/api
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/toolboxmanagement/matlab_api
+    	/usr/local/MATLAB/R2016a/toolbox/mpc/mpcdemos
+    	/usr/local/MATLAB/R2016a/toolbox/distcomp/mapreduce
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/networklib
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+    	/usr/local/MATLAB/R2016a/toolbox/map/map
+    	/usr/local/MATLAB/R2016a/toolbox/map/mapgeodesy
+    	/usr/local/MATLAB/R2016a/toolbox/map/mapdisp
+    	/usr/local/MATLAB/R2016a/toolbox/map/mapformats
+    	/usr/local/MATLAB/R2016a/toolbox/map/mapproj
+    	/usr/local/MATLAB/R2016a/toolbox/map/mapdata
+    	/usr/local/MATLAB/R2016a/toolbox/map/mapdata/sdts
+    	/usr/local/MATLAB/R2016a/toolbox/shared/statslib
+    	/usr/local/MATLAB/R2016a/toolbox/shared/statslib/sensitivity
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/drives/drives
+    	/usr/local/MATLAB/R2016a/toolbox/slcontrol/slcontrol
+    	/usr/local/MATLAB/R2016a/toolbox/slcontrol/slctrlguis
+    	/usr/local/MATLAB/R2016a/toolbox/slcontrol/slctrlutil
+    	/usr/local/MATLAB/R2016a/toolbox/slcontrol/slctrlobsolete
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/spf/matlabservices
+    	/usr/local/MATLAB/R2016a/toolbox/shared/dsp/dialog
+    	/usr/local/MATLAB/R2016a/toolbox/imaq/imaqdemos
+    	/usr/local/MATLAB/R2016a/toolbox/symbolic/symbolicdemos
+    	/usr/local/MATLAB/R2016a/toolbox/instrument/instrument
+    	/usr/local/MATLAB/R2016a/toolbox/instrument/instrumentblks/instrumentblks
+    	/usr/local/MATLAB/R2016a/toolbox/instrument/instrumentblks/instrumentmex
+    	/usr/local/MATLAB/R2016a/toolbox/instrument/instrumentblks/instrumentmasks
+    	/usr/local/MATLAB/R2016a/toolbox/eml/eml
+    	/usr/local/MATLAB/R2016a/toolbox/coder/profile
+    	/usr/local/MATLAB/R2016a/toolbox/database/database
+    	/usr/local/MATLAB/R2016a/toolbox/database/vqb
+    	/usr/local/MATLAB/R2016a/toolbox/map/mapdemos
+    	/usr/local/MATLAB/R2016a/toolbox/shared/cxxfe_mi/cxxfe_mi
+    	/usr/local/MATLAB/R2016a/toolbox/stats/mlearnapp
+    	/usr/local/MATLAB/R2016a/toolbox/shared/eda/fpgaautomation
+    	/usr/local/MATLAB/R2016a/toolbox/shared/eda/fpgaautomation/obsolete
+    	/usr/local/MATLAB/R2016a/toolbox/comm/commdemos
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/pe/pedemos
+    	/usr/local/MATLAB/R2016a/toolbox/slrequirements
+    	/usr/local/MATLAB/R2016a/toolbox/shared/slcontrollib
+    	/usr/local/MATLAB/R2016a/toolbox/geoweb/geoweb
+    	/usr/local/MATLAB/R2016a/toolbox/shared/configset
+    	/usr/local/MATLAB/R2016a/toolbox/comm/cdma2000
+    	/usr/local/MATLAB/R2016a/toolbox/signal/signalanalyzer
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotics
+    	/usr/local/MATLAB/R2016a/toolbox/shared/can
+    	/usr/local/MATLAB/R2016a/toolbox/shared/can/canblks
+    	/usr/local/MATLAB/R2016a/toolbox/shared/can/canmasks
+    	/usr/local/MATLAB/R2016a/toolbox/shared/can/canmex
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/fixedandfloat
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/fixedandfloat/obsolete
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/common/data/mli/m
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/sm/foundation/mech
+    	/usr/local/MATLAB/R2016a/toolbox/imaq/imaq
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/pm_visimpl/pm_visimpl
+    	/usr/local/MATLAB/R2016a/toolbox/bioinfo/biodemos
+    	/usr/local/MATLAB/R2016a/toolbox/shared/sigbldr
+    	/usr/local/MATLAB/R2016a/toolbox/dsp/dsp
+    	/usr/local/MATLAB/R2016a/toolbox/dsp/dsputilities
+    	/usr/local/MATLAB/R2016a/toolbox/dsp/dsputilities/dspinit
+    	/usr/local/MATLAB/R2016a/toolbox/dsp/dsputilities/dspmex
+    	/usr/local/MATLAB/R2016a/toolbox/dsp/dsp/compiled
+    	/usr/local/MATLAB/R2016a/toolbox/symbolic/symbolic
+    	/usr/local/MATLAB/R2016a/toolbox/optim/optimdemos
+    	/usr/local/MATLAB/R2016a/toolbox/curvefit/curvefitdemos
+    	/usr/local/MATLAB/R2016a/toolbox/shared/instrument
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/common/external/library/m
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/slproject
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/slproject/menu
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/mech/mech
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/mech/importer
+    	/usr/local/MATLAB/R2016a/toolbox/shared/simulation_data_repository
+    	/usr/local/MATLAB/R2016a/help/toolbox/control/examples
+    	/usr/local/MATLAB/R2016a/help/toolbox/vision/examples
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo/meascontrol
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo/power_utility
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/sm/ssci/m
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/sl_async_streaming
+    	/usr/local/MATLAB/R2016a/toolbox/shared/simulink/slcheck_services
+    	/usr/local/MATLAB/R2016a/toolbox/shared/measure
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo/simple
+    	/usr/local/MATLAB/R2016a/toolbox/coder/trace
+    	/usr/local/MATLAB/R2016a/toolbox/compiler_sdk
+    	/usr/local/MATLAB/R2016a/toolbox/shared/diagnostic
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/templates
+    	/usr/local/MATLAB/R2016a/toolbox/sldv/sldvdemos
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/sta/repository
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/sta/repository/util
+    	/usr/local/MATLAB/R2016a/toolbox/stats/stats
+    	/usr/local/MATLAB/R2016a/toolbox/stats/classreg
+    	/usr/local/MATLAB/R2016a/toolbox/stats/clustering
+    	/usr/local/MATLAB/R2016a/toolbox/hdlcoder/hdllib/ml_lib
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/iodata/ioformat
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/audiovideo
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/webcam
+    	/usr/local/MATLAB/R2016a/toolbox/shared/mldatx
+    	/usr/local/MATLAB/R2016a/toolbox/robust/robust
+    	/usr/local/MATLAB/R2016a/toolbox/robust/rctlmi
+    	/usr/local/MATLAB/R2016a/toolbox/robust/rctutil
+    	/usr/local/MATLAB/R2016a/toolbox/robust/rctobsolete/robust
+    	/usr/local/MATLAB/R2016a/toolbox/robust/rctobsolete/lmi
+    	/usr/local/MATLAB/R2016a/toolbox/robust/rctobsolete/mutools/commands
+    	/usr/local/MATLAB/R2016a/toolbox/robust/rctobsolete/mutools/subs
+    	/usr/local/MATLAB/R2016a/toolbox/shared/codeinstrum/codeinstrum
+    	/usr/local/MATLAB/R2016a/toolbox/control/control
+    	/usr/local/MATLAB/R2016a/toolbox/control/ctrlmodels
+    	/usr/local/MATLAB/R2016a/toolbox/control/ctrlanalysis
+    	/usr/local/MATLAB/R2016a/toolbox/control/ctrldesign
+    	/usr/local/MATLAB/R2016a/toolbox/control/ctrlplots
+    	/usr/local/MATLAB/R2016a/toolbox/control/ctrlguis
+    	/usr/local/MATLAB/R2016a/toolbox/control/ctrlobsolete
+    	/usr/local/MATLAB/R2016a/toolbox/control/ctrlutil
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/simscape/compiler/sli/m
+    	/usr/local/MATLAB/R2016a/toolbox/shared/dastudio
+    	/usr/local/MATLAB/R2016a/toolbox/stats/statsdemos
+    	/usr/local/MATLAB/R2016a/toolbox/shared/curvefitlib
+    	/usr/local/MATLAB/R2016a/toolbox/shared/slpir
+    	/usr/local/MATLAB/R2016a/toolbox/shared/eda/fpgabase
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/common/dataservices/mli/m
+    	/usr/local/MATLAB/R2016a/toolbox/shared/hdlshared/hdlshared_gui
+    	/usr/local/MATLAB/R2016a/toolbox/shared/eda/hdlparser
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/network_engine/network_engine
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/processor/intelhost/tfl
+    	/usr/local/MATLAB/R2016a/toolbox/coder/coverage
+    	/usr/local/MATLAB/R2016a/toolbox/shared/dsp/hdl
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/spf/matlabhost
+    	/usr/local/MATLAB/R2016a/toolbox/mpc/mpc
+    	/usr/local/MATLAB/R2016a/toolbox/mpc/mpcguis
+    	/usr/local/MATLAB/R2016a/toolbox/mpc/mpcobsolete
+    	/usr/local/MATLAB/R2016a/toolbox/mpc/mpcutils
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/slexportprevious
+    	/usr/local/MATLAB/R2016a/toolbox/sl3d/sl3d
+    	/usr/local/MATLAB/R2016a/toolbox/comm/comm
+    	/usr/local/MATLAB/R2016a/toolbox/comm/commutilities/comminit
+    	/usr/local/MATLAB/R2016a/toolbox/comm/commutilities/commmex
+    	/usr/local/MATLAB/R2016a/toolbox/comm/commutilities
+    	/usr/local/MATLAB/R2016a/toolbox/comm/commdeprecated
+    	/usr/local/MATLAB/R2016a/toolbox/comm/comm/compiled
+    	/usr/local/MATLAB/R2016a/toolbox/coder/connectivity
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/targets/connectivity
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/slhistory
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/simscape/templates
+    	/usr/local/MATLAB/R2016a/toolbox/shared/spreadsheet
+    	/usr/local/MATLAB/R2016a/toolbox/fixpoint
+    	/usr/local/MATLAB/R2016a/toolbox/fixpoint/fpca
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/ros
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/ne_sli/ne_sli
+    	/usr/local/MATLAB/R2016a/toolbox/shared/dsp/simulink/dsp
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/system
+    	/usr/local/MATLAB/R2016a/toolbox/shared/eda/fil
+    	/usr/local/MATLAB/R2016a/toolbox/shared/eda/fil/filmapi
+    	/usr/local/MATLAB/R2016a/toolbox/coder/rtiostream
+    	/usr/local/MATLAB/R2016a/toolbox/pde
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powersys
+    	/usr/local/MATLAB/R2016a/toolbox/shared/hotpluglib
+    	/usr/local/MATLAB/R2016a/toolbox/shared/multimedia
+    	/usr/local/MATLAB/R2016a/toolbox/shared/testmeaslib/graphics
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/addons_toolbox
+    	/usr/local/MATLAB/R2016a/toolbox/shared/imageslib
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/pm_sli/pm_sli
+    	/usr/local/MATLAB/R2016a/toolbox/shared/dastudio/seqdiagram
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/sm/templates
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/sm/gui/m
+    	/usr/local/MATLAB/R2016a/toolbox/ident/ident
+    	/usr/local/MATLAB/R2016a/toolbox/ident/nlident
+    	/usr/local/MATLAB/R2016a/toolbox/ident/idobsolete
+    	/usr/local/MATLAB/R2016a/toolbox/ident/idguis
+    	/usr/local/MATLAB/R2016a/toolbox/ident/idutils
+    	/usr/local/MATLAB/R2016a/toolbox/ident/idrecursive
+    	/usr/local/MATLAB/R2016a/toolbox/ident/idhelp
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/powerdemo/machines
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/operatingsystem/windows/blks
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/operatingsystem/windows/blks/masks
+    	/usr/local/MATLAB/R2016a/toolbox/target/extensions/operatingsystem/windows/blks/mex
+    	/usr/local/MATLAB/R2016a/toolbox/shared/networklib
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/sm/sli/m
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/sm/sm/m
+    	/usr/local/MATLAB/R2016a/toolbox/shared/advisor
+    	/usr/local/MATLAB/R2016a/toolbox/shared/filterdesignlib
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/connector/connector
+    	/usr/local/MATLAB/R2016a/toolbox/idelink/foundation
+    	/usr/local/MATLAB/R2016a/toolbox/idelink/foundation/util
+    	/usr/local/MATLAB/R2016a/toolbox/idelink/foundation/errorhandler
+    	/usr/local/MATLAB/R2016a/toolbox/idelink/foundation/xmakefile
+    	/usr/local/MATLAB/R2016a/toolbox/idelink/foundation/hookpoints
+    	/usr/local/MATLAB/R2016a/toolbox/shared/comparisons
+    	/usr/local/MATLAB/R2016a/toolbox/signal/sigdemos
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/configtools
+    	/usr/local/MATLAB/R2016a/toolbox/simbio/simbio
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/external/interfaces/python
+    	/usr/local/MATLAB/R2016a/toolbox/shared/m3i
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/toolstrip
+    	/usr/local/MATLAB/R2016a/toolbox/dsp/dspdeployabledemos
+    	/usr/local/MATLAB/R2016a/toolbox/slvnv/styleguide
+    	/usr/local/MATLAB/R2016a/help/toolbox/robust/examples
+    	/usr/local/MATLAB/R2016a/toolbox/shared/deviceplugindetection
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/simscape/compiler/mli/m
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/gui/gfx/m
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/sm/import/m
+    	/usr/local/MATLAB/R2016a/toolbox/compiler/java
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/pe/utils/m
+    	/usr/local/MATLAB/R2016a/toolbox/rtw/rtw
+    	/usr/local/MATLAB/R2016a/toolbox/coder/foundation
+    	/usr/local/MATLAB/R2016a/toolbox/coder/foundation/build
+    	/usr/local/MATLAB/R2016a/toolbox/coder/foundation/build/tools/registry
+    	/usr/local/MATLAB/R2016a/toolbox/coder/foundation/tfl
+    	/usr/local/MATLAB/R2016a/toolbox/coder/foundation/tfl/AUTOSAR/AUTOSAR4p0/IFX
+    	/usr/local/MATLAB/R2016a/toolbox/coder/foundation/tfl/AUTOSAR/AUTOSAR4p0/IFL
+    	/usr/local/MATLAB/R2016a/toolbox/coder/foundation/tfl/gui
+    	/usr/local/MATLAB/R2016a/toolbox/coder/foundation/templates
+    	/usr/local/MATLAB/R2016a/toolbox/shared/simtargets
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/mech/mechdemos
+    	/usr/local/MATLAB/R2016a/toolbox/shared/maputils
+    	/usr/local/MATLAB/R2016a/toolbox/coder/foundation/passmanager
+    	/usr/local/MATLAB/R2016a/toolbox/simulink/simulink/iodata/iomap
+    	/usr/local/MATLAB/R2016a/toolbox/fininst/fininstdemos
+    	/usr/local/MATLAB/R2016a/toolbox/nnet
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nncontrol
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnadapt
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nndatafun
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnderivative
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nndistance
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nndivision
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nninitlayer
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nninitnetwork
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nninitweight
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnlearn
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnnetfun
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnnetinput
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnnetwork
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnperformance
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnplot
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnprocess
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnsearch
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nntopology
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nntrain
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nntransfer
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnet/nnweight
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnguis
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnobsolete
+    	/usr/local/MATLAB/R2016a/toolbox/nnet/nnutils
+    	/usr/local/MATLAB/R2016a/toolbox/matlab/addons_product
+    	/usr/local/MATLAB/R2016a/toolbox/shared/tracking/trackinglib
+    	/usr/local/MATLAB/R2016a/toolbox/shared/simulink/sysarch/sysarch
+    	/usr/local/MATLAB/R2016a/toolbox/shared/slreportgen/reportexplorer
+    	/usr/local/MATLAB/R2016a/toolbox/coder/embeddedcoder_templates
+    	/usr/local/MATLAB/R2016a/toolbox/coder/wizard
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/sm/core/m
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/ros
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/ros/helpers
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotalgs
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotalgs/helpers
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotcore
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotcore/helpers
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotsimulink
+    	/usr/local/MATLAB/R2016a/toolbox/robotics/robotexamples/robotsimulink/helpers
+    	/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine
+    	/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/numerics
+    	/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/options
+    	/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/optim
+    	/usr/local/MATLAB/R2016a/toolbox/shared/controllib/engine/blocks
+    	/usr/local/MATLAB/R2016a/toolbox/dsp/filterdesign
+    	/usr/local/MATLAB/R2016a/toolbox/finance/findemos
+    	/usr/local/MATLAB/R2016a/toolbox/physmod/powersys/facts/facts
+
+
+
+```matlab
+pwd
+```
+
+    ans =
+    
+    /home/ryan/Documents/UConn/ME3255/me3255_S2017/lecture_03
+
+
+
+path
+
+## Assignments (`=`-operator)
+
+Matlab is interpreted language so each line of code (either saved text file or command-line) is executed as a standalone command
+
+These are reffered to "scripts"
+
+
+```matlab
+a=10; % line one assigns a to 10
+b=a*3; % line two assigns b to 10 times 3 by calling 'a' from line one
+a+b % line three does not assign anything directly, but leaving off the ";" prints the result
+    % ans
+```
+
+    ans =
+    
+        40
+
+
+Matlab has a number of "objects" that you can assign to variables
+1. arrays (vectors and matrices `[`...`]`) 
+2. strings (text `"`...`"` )
+3. cells (combination of strings, text, even function calls `{`...`}`)
+3. functions (both built-in, defined or developed)
+4. and more... (classes defined by `classdef` - you can create your own object to help organize data)
+
+### 1- Arrays
+
+Default in matlab is that when you assign a value to a variable, it is stored as an array
+
+arrays are N x M x ... values of integers or floating point numbers or complex integers/floating point numbers
+
+Use the parantheses to access values in an array `...(n,m)`
+
+
+```matlab
+a=10; % a is 1x1 array where a(1,1)==10
+a(1,1)==10
+
+```
+
+    ans =
+    
+         1
+
+
+
+```matlab
+a(2)
+```
+
+    Index exceeds matrix dimensions.
+    
+
+
+```matlab
+A = [1 2 3;4,5,6;7,8,9;10,11,12]
+fprintf('size of A is %i x %i\n',size(A))
+A(3,1)
+A(6)
+```
+
+    A =
+    
+         1     2     3
+         4     5     6
+         7     8     9
+        10    11    12
+    
+    size of A is 4 x 3
+    
+    ans =
+    
+         7
+    
+    
+    ans =
+    
+         5
+
+
+vectors are either 1xN or Nx1 arrays for row and column
+
+
+```matlab
+v_row = [1,2,3] %row vector
+v_column = [1;2;3] %column vector
+
+```
+
+    v_row =
+    
+         1     2     3
+    
+    
+    v_column =
+    
+         1
+         2
+         3
+
+
+Matrices are MxN arrays
+the `:`-symbol can substitute for a counting
+
+
+```matlab
+A(1,:) % the colon assumes you want the first value, 1, counting up by 1 to the last value, 4
+```
+
+    ans =
+    
+         1     2     3
+
+
+You can also use every 2nd value or any other integer up to `end` which is the largest value of that row or column of the array
+
+
+```matlab
+A(1:2:end,1) % you can also use `end` 
+```
+
+    ans =
+    
+         1
+         7
+
+
+
+```matlab
+A(:)
+```
+
+    ans =
+    
+         1
+         4
+         7
+        10
+         2
+         5
+         8
+        11
+         3
+         6
+         9
+        12
+
+
+In general, arrays can be any size 
+
+take rolling 4 die and determining the sum of the components
+
+
+```matlab
+A_6666 = zeros(6,6,6,6); %make a 6 x 6 x 6 x 6 array (1296 different values)
+for i=1:6
+    for j=1:6
+        for k=1:6
+            for l=1:6
+                A_6666(i,j,k,l)=i+j+k+l; % each value is the sum of the indices
+            end
+        end
+    end
+end
+            
+```
+
+
+```matlab
+mean(A_6666(:))
+std(A_6666(:))
+```
+
+    ans =
+    
+        14
+    
+    
+    ans =
+    
+        3.4170
+
+
+
+```matlab
+A_6666(1,4,2,5)
+```
+
+    ans =
+    
+        12
+
+
+## Cells combine different size arrays and text
+### but, you cannot use math operators 'binary operators'
+
+
+```matlab
+C={};
+C{1}=linspace(0,1,10);
+C{2}=linspace(0,1,3);
+C{'z'}='holy cow';
+```
+
+
+```matlab
+C{1}*C{1}'
+```
+
+    ans =
+    
+        3.5185
+
+
+## Strings can be combined and printed
+
+
+```matlab
+string1 = 'computational'; string2 = 'mechanics';
+[string1, ' ', string2]
+```
+
+    ans =
+    
+    computational mechanics
+
+
+use `fprintf` to format strings and numbers for output and `sprintf` to save variables
+
+
+
+```matlab
+fprintf([string1,' ',string2,'\n\n'])
+string = sprintf('the dog had %i legs and weighed %1.1f lbs',4,10.0)
+```
+
+    computational mechanics
+    
+    
+    string =
+    
+    the dog had 4 legs and weighed 10.0 lbs
+
+
+the `\` signifies a special character e.g. `\n` = newline, `\t` = tab
+
+to actually print the "\", use `\\`
+
+
+```matlab
+fprintf('\\')
+```
+
+    \
+
+
+## This is helpful to create reports of computed data
+
+
+```matlab
+%fid = fopen('file.txt','w');
+fprintf(fid,[string1, ' ', string2])
+fprintf(fid,'\n')
+fprintf(fid,string)
+fprintf(fid,'\n')
+fprintf(fid,'are you awake?')
+```
+
+    ans =
+    
+        23
+    
+    
+    ans =
+    
+         1
+    
+    
+    ans =
+    
+        39
+    
+    
+    ans =
+    
+         1
+    
+    
+    ans =
+    
+        14
+
+
+## Math operators (=, +, -, /, *, ^)
+
+Because matlab assumes all variables are matrices, then all operators are matrix operations
+
+
+```matlab
+a+a % add two 1x1 arrays
+```
+
+    ans =  20
+
+
+
+```matlab
+A+A % add two 4 x 3 arrays
+```
+
+    ans =
+    
+        2    4    6
+        8   10   12
+       14   16   18
+       20   22   24
+    
+
+
+
+```matlab
+A*A'
+```
+
+    ans =
+    
+        14    32    50    68
+        32    77   122   167
+        50   122   194   266
+        68   167   266   365
+
+
+
+```matlab
+A.^2
+```
+
+    ans =
+    
+         1     4     9
+        16    25    36
+        49    64    81
+       100   121   144
+
+
+
+```matlab
+A.*A
+```
+
+    ans =
+    
+         1     4     9
+        16    25    36
+        49    64    81
+       100   121   144
+
+
+
+```matlab
+A/A
+```
+
+    [> In pymat_eval (line 31)
+      In matlabserver (line 24)] 
+    [Warning: Rank deficient, rank = 2, tol =  1.696862e-14.] 
+    
+    ans =
+    
+        1.0000         0         0   -0.0000
+        0.6667         0         0    0.3333
+        0.3333         0         0    0.6667
+        0.0000         0         0    1.0000
+
+
+
+```matlab
+help /
+```
+
+    /   Slash or right matrix divide.
+        A/B is the matrix division of B into A, which is roughly the
+        same as A*INV(B) , except it is computed in a different way.
+        More precisely, A/B = (B'\A')'. See MLDIVIDE for details.
+     
+        C = MRDIVIDE(A,B) is called for the syntax 'A / B' when A or B is an
+        object.
+     
+        See also MLDIVIDE, RDIVIDE, LDIVIDE.
+    
+        Reference page in Doc Center
+           doc mrdivide
+    
+        Other functions named mrdivide
+    
+           codistributed/mrdivide    gf/mrdivide          laurpoly/mrdivide
+           duration/mrdivide         gpuArray/mrdivide    StaticModel/mrdivide
+           DynamicSystem/mrdivide    LagOp/mrdivide       timeseries/mrdivide
+           fints/mrdivide
+
+
+To accomplish one-by-one operations, need to include a `.`
+
+
+```matlab
+A./A
+```
+
+    ans =
+    
+       1   1   1
+       1   1   1
+       1   1   1
+       1   1   1
+    
+
+
+But, for 1x1 arrays, these are considered scalars and you get a free-pass
+
+
+```matlab
+a*A % where a=10 and A is 1:12 in a 3 x 4 matrix
+```
+
+    ans =
+    
+        10    20    30
+        40    50    60
+        70    80    90
+       100   110   120
+    
+
+
+Some built in Matlab functions (e.g. the reasons to run Matlab)
+
+
+```matlab
+t_linear=linspace(0,1,11)
+```
+
+    t_linear =
+    
+      Columns 1 through 7
+    
+             0    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000
+    
+      Columns 8 through 11
+    
+        0.7000    0.8000    0.9000    1.0000
+
+
+
+```matlab
+t_log = logspace(0,2,3) % log interval from 10^0 to 10^2 split into 3 values
+```
+
+    t_log =
+    
+         1    10   100
+
+
+
+```matlab
+help logspace
+```
+
+    'logspace' is a function from the file /usr/share/octave/4.0.0/m/general/logspace.m
+    
+     -- Function File: logspace (A, B)
+     -- Function File: logspace (A, B, N)
+     -- Function File: logspace (A, pi, N)
+         Return a row vector with N elements logarithmically spaced from
+         10^A to 10^B.
+    
+         If N is unspecified it defaults to 50.
+    
+         If B is equal to pi, the points are between 10^A and pi, _not_ 10^A
+         and 10^pi, in order to be compatible with the corresponding MATLAB
+         function.
+    
+         Also for compatibility with MATLAB, return the second argument B if
+         fewer than two values are requested.
+    
+         See also: linspace.
+    
+    Additional help for built-in functions and operators is
+    available in the online version of the manual.  Use the command
+    'doc <topic>' to search the manual index.
+    
+    Help and information about Octave is also available on the WWW
+    at http://www.octave.org and via the help@octave.org
+    mailing list.
+
+
+## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects)
+
+
+```matlab
+%myscript
+```
+
+
+```matlab
+%plot --format svg
+```
+
+When using the GUI, your command history is saved, but it is better to save your work either as a script or a function or combination of both
+
+Creating a default graph script:
+
+
+```matlab
+set(0, 'defaultAxesFontSize', 16)
+set(0,'defaultTextFontSize',14)
+set(0,'defaultLineLineWidth',3)
+```
+
+
+```matlab
+plot(t_linear,t_linear.^2)
+xlabel('time (s)')
+ylabel('displacement (m)')
+```
+
+
+![png](output_58_0.png)
+
+
+#EOL
+
+## Graphics can be produced with a number of functions
+
+2-D plots, 3-D plots, contour plots, 3D contour plots ... 
+
+
+```matlab
+x=linspace(-1,1,21); y=linspace(-1,1,21);
+[X,Y]=meshgrid(x,y);
+Z=(X.*Y.^3-X.^3.*Y)
+```
+
+    Z =
+    
+     Columns 1 through 8:
+    
+       0.00000   0.17100   0.28800   0.35700   0.38400   0.37500   0.33600   0.27300
+      -0.17100   0.00000   0.12240   0.20160   0.24300   0.25200   0.23400   0.19440
+      -0.28800  -0.12240   0.00000   0.08400   0.13440   0.15600   0.15360   0.13200
+      -0.35700  -0.20160  -0.08400   0.00000   0.05460   0.08400   0.09240   0.08400
+      -0.38400  -0.24300  -0.13440  -0.05460   0.00000   0.03300   0.04800   0.04860
+      -0.37500  -0.25200  -0.15600  -0.08400  -0.03300   0.00000   0.01800   0.02400
+      -0.33600  -0.23400  -0.15360  -0.09240  -0.04800  -0.01800   0.00000   0.00840
+      -0.27300  -0.19440  -0.13200  -0.08400  -0.04860  -0.02400  -0.00840   0.00000
+      -0.19200  -0.13860  -0.09600  -0.06300  -0.03840  -0.02100  -0.00960  -0.00300
+      -0.09900  -0.07200  -0.05040  -0.03360  -0.02100  -0.01200  -0.00600  -0.00240
+       0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
+       0.09900   0.07200   0.05040   0.03360   0.02100   0.01200   0.00600   0.00240
+       0.19200   0.13860   0.09600   0.06300   0.03840   0.02100   0.00960   0.00300
+       0.27300   0.19440   0.13200   0.08400   0.04860   0.02400   0.00840  -0.00000
+       0.33600   0.23400   0.15360   0.09240   0.04800   0.01800  -0.00000  -0.00840
+       0.37500   0.25200   0.15600   0.08400   0.03300   0.00000  -0.01800  -0.02400
+       0.38400   0.24300   0.13440   0.05460  -0.00000  -0.03300  -0.04800  -0.04860
+       0.35700   0.20160   0.08400  -0.00000  -0.05460  -0.08400  -0.09240  -0.08400
+       0.28800   0.12240   0.00000  -0.08400  -0.13440  -0.15600  -0.15360  -0.13200
+       0.17100  -0.00000  -0.12240  -0.20160  -0.24300  -0.25200  -0.23400  -0.19440
+       0.00000  -0.17100  -0.28800  -0.35700  -0.38400  -0.37500  -0.33600  -0.27300
+    
+     Columns 9 through 16:
+    
+       0.19200   0.09900   0.00000  -0.09900  -0.19200  -0.27300  -0.33600  -0.37500
+       0.13860   0.07200   0.00000  -0.07200  -0.13860  -0.19440  -0.23400  -0.25200
+       0.09600   0.05040   0.00000  -0.05040  -0.09600  -0.13200  -0.15360  -0.15600
+       0.06300   0.03360   0.00000  -0.03360  -0.06300  -0.08400  -0.09240  -0.08400
+       0.03840   0.02100   0.00000  -0.02100  -0.03840  -0.04860  -0.04800  -0.03300
+       0.02100   0.01200   0.00000  -0.01200  -0.02100  -0.02400  -0.01800   0.00000
+       0.00960   0.00600   0.00000  -0.00600  -0.00960  -0.00840   0.00000   0.01800
+       0.00300   0.00240   0.00000  -0.00240  -0.00300   0.00000   0.00840   0.02400
+       0.00000   0.00060   0.00000  -0.00060   0.00000   0.00300   0.00960   0.02100
+      -0.00060   0.00000   0.00000   0.00000   0.00060   0.00240   0.00600   0.01200
+       0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
+       0.00060  -0.00000   0.00000   0.00000  -0.00060  -0.00240  -0.00600  -0.01200
+      -0.00000  -0.00060   0.00000   0.00060   0.00000  -0.00300  -0.00960  -0.02100
+      -0.00300  -0.00240   0.00000   0.00240   0.00300   0.00000  -0.00840  -0.02400
+      -0.00960  -0.00600   0.00000   0.00600   0.00960   0.00840   0.00000  -0.01800
+      -0.02100  -0.01200   0.00000   0.01200   0.02100   0.02400   0.01800   0.00000
+      -0.03840  -0.02100   0.00000   0.02100   0.03840   0.04860   0.04800   0.03300
+      -0.06300  -0.03360   0.00000   0.03360   0.06300   0.08400   0.09240   0.08400
+      -0.09600  -0.05040   0.00000   0.05040   0.09600   0.13200   0.15360   0.15600
+      -0.13860  -0.07200   0.00000   0.07200   0.13860   0.19440   0.23400   0.25200
+      -0.19200  -0.09900   0.00000   0.09900   0.19200   0.27300   0.33600   0.37500
+    
+     Columns 17 through 21:
+    
+      -0.38400  -0.35700  -0.28800  -0.17100   0.00000
+      -0.24300  -0.20160  -0.12240   0.00000   0.17100
+      -0.13440  -0.08400   0.00000   0.12240   0.28800
+      -0.05460   0.00000   0.08400   0.20160   0.35700
+       0.00000   0.05460   0.13440   0.24300   0.38400
+       0.03300   0.08400   0.15600   0.25200   0.37500
+       0.04800   0.09240   0.15360   0.23400   0.33600
+       0.04860   0.08400   0.13200   0.19440   0.27300
+       0.03840   0.06300   0.09600   0.13860   0.19200
+       0.02100   0.03360   0.05040   0.07200   0.09900
+       0.00000   0.00000   0.00000   0.00000   0.00000
+      -0.02100  -0.03360  -0.05040  -0.07200  -0.09900
+      -0.03840  -0.06300  -0.09600  -0.13860  -0.19200
+      -0.04860  -0.08400  -0.13200  -0.19440  -0.27300
+      -0.04800  -0.09240  -0.15360  -0.23400  -0.33600
+      -0.03300  -0.08400  -0.15600  -0.25200  -0.37500
+       0.00000  -0.05460  -0.13440  -0.24300  -0.38400
+       0.05460   0.00000  -0.08400  -0.20160  -0.35700
+       0.13440   0.08400   0.00000  -0.12240  -0.28800
+       0.24300   0.20160   0.12240   0.00000  -0.17100
+       0.38400   0.35700   0.28800   0.17100   0.00000
+    
+
+
+
+```matlab
+contour(X,Y,Z)
+```
+
+
+![svg](output_63_0.svg)
+
+
+
+```matlab
+mesh(X,Y,Z)
+```
+
+
+![svg](output_64_0.svg)
+
+
+
+```matlab
+pcolor(X,Y,Z)
+```
+
+
+![svg](output_65_0.svg)
+
+
+## 
diff --git a/lecture_03/octave-workspace b/lecture_03/octave-workspace
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+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+		<polygon fill="rgb(  0,  34, 255)" points="194.5,67.8 173.1,67.8 173.1,52.7 194.5,52.7 "/>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M194.5,67.8 L194.5,52.7 L173.1,52.7 L173.1,67.8 L194.5,67.8  " stroke="rgb(  0,   0,   0)"/>	<g shape-rendering="crispEdges" stroke="none">
+		<polygon fill="rgb(  0,  51, 255)" points="173.1,67.8 151.7,67.8 151.7,52.7 173.1,52.7 "/>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M173.1,67.8 L173.1,52.7 L151.7,52.7 L151.7,67.8 L173.1,67.8  " stroke="rgb(  0,   0,   0)"/>	<g shape-rendering="crispEdges" stroke="none">
+		<polygon fill="rgb(  0, 115, 255)" points="151.7,67.8 130.3,67.8 130.3,52.7 151.7,52.7 "/>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M151.7,67.8 L151.7,52.7 L130.3,52.7 L130.3,67.8 L151.7,67.8  " stroke="rgb(  0,   0,   0)"/>	<g shape-rendering="crispEdges" stroke="none">
+		<polygon fill="rgb(  0, 212, 255)" points="130.3,67.8 108.9,67.8 108.9,52.7 130.3,52.7 "/>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M130.3,67.8 L130.3,52.7 L108.9,52.7 L108.9,67.8 L130.3,67.8  " stroke="rgb(  0,   0,   0)"/>	<g shape-rendering="crispEdges" stroke="none">
+		<polygon fill="rgb(119, 255, 136)" points="108.9,67.8 87.5,67.8 87.5,52.7 108.9,52.7 "/>
+	</g>
+</g>
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+		<text><tspan font-family="{}">-1</tspan></text>
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+		<text><tspan font-family="{}">-0.5</tspan></text>
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+		<text><tspan font-family="{}">0</tspan></text>
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+</g>
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+		<text><tspan font-family="{}">0.5</tspan></text>
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+		<text><tspan font-family="{}">1</tspan></text>
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+		<text><tspan font-family="{}">-1</tspan></text>
+	</g>
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+</g>
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+		<text><tspan font-family="{}">-0.5</tspan></text>
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diff --git a/lecture_04/lecture_4.md b/lecture_04/lecture_4.md
new file mode 100644
index 0000000..50921c3
--- /dev/null
+++ b/lecture_04/lecture_4.md
@@ -0,0 +1,309 @@
+
+
+```matlab
+## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects)
+```
+
+    Error: The input character is not valid in MATLAB statements or expressions.
+    
+
+
+```matlab
+%myscript
+```
+
+
+```matlab
+%plot --format svg
+```
+
+When using the GUI, your command history is saved, but it is better to save your work either as a script or a function or combination of both
+
+Creating a default graph script: `setdefaults.m`
+
+```matlab
+set(0, 'defaultAxesFontSize', 16)
+set(0,'defaultTextFontSize',14)
+set(0,'defaultLineLineWidth',3)
+```
+
+
+```matlab
+set(0, 'defaultAxesFontSize', 16)
+set(0,'defaultTextFontSize',14)
+set(0,'defaultLineLineWidth',3)
+```
+
+
+```matlab
+t_linear=linspace(0,10,100);
+plot(t_linear,t_linear.^2)
+xlabel('time (s)')
+ylabel('displacement (m)')
+```
+
+
+![png](output_5_0.png)
+
+
+#EOL
+
+## Graphics can be produced with a number of functions
+
+2-D plots, 3-D plots, contour plots, 3D contour plots ... 
+
+
+```matlab
+x=linspace(-1,1,21); y=linspace(-1,1,21);
+[X,Y]=meshgrid(x,y);
+Z=(X.*Y.^3-X.^3.*Y)
+```
+
+    Z =
+    
+      Columns 1 through 7
+    
+             0    0.1710    0.2880    0.3570    0.3840    0.3750    0.3360
+       -0.1710         0    0.1224    0.2016    0.2430    0.2520    0.2340
+       -0.2880   -0.1224         0    0.0840    0.1344    0.1560    0.1536
+       -0.3570   -0.2016   -0.0840         0    0.0546    0.0840    0.0924
+       -0.3840   -0.2430   -0.1344   -0.0546         0    0.0330    0.0480
+       -0.3750   -0.2520   -0.1560   -0.0840   -0.0330         0    0.0180
+       -0.3360   -0.2340   -0.1536   -0.0924   -0.0480   -0.0180         0
+       -0.2730   -0.1944   -0.1320   -0.0840   -0.0486   -0.0240   -0.0084
+       -0.1920   -0.1386   -0.0960   -0.0630   -0.0384   -0.0210   -0.0096
+       -0.0990   -0.0720   -0.0504   -0.0336   -0.0210   -0.0120   -0.0060
+             0         0         0         0         0         0         0
+        0.0990    0.0720    0.0504    0.0336    0.0210    0.0120    0.0060
+        0.1920    0.1386    0.0960    0.0630    0.0384    0.0210    0.0096
+        0.2730    0.1944    0.1320    0.0840    0.0486    0.0240    0.0084
+        0.3360    0.2340    0.1536    0.0924    0.0480    0.0180    0.0000
+        0.3750    0.2520    0.1560    0.0840    0.0330         0   -0.0180
+        0.3840    0.2430    0.1344    0.0546   -0.0000   -0.0330   -0.0480
+        0.3570    0.2016    0.0840         0   -0.0546   -0.0840   -0.0924
+        0.2880    0.1224         0   -0.0840   -0.1344   -0.1560   -0.1536
+        0.1710    0.0000   -0.1224   -0.2016   -0.2430   -0.2520   -0.2340
+             0   -0.1710   -0.2880   -0.3570   -0.3840   -0.3750   -0.3360
+    
+      Columns 8 through 14
+    
+        0.2730    0.1920    0.0990         0   -0.0990   -0.1920   -0.2730
+        0.1944    0.1386    0.0720         0   -0.0720   -0.1386   -0.1944
+        0.1320    0.0960    0.0504         0   -0.0504   -0.0960   -0.1320
+        0.0840    0.0630    0.0336         0   -0.0336   -0.0630   -0.0840
+        0.0486    0.0384    0.0210         0   -0.0210   -0.0384   -0.0486
+        0.0240    0.0210    0.0120         0   -0.0120   -0.0210   -0.0240
+        0.0084    0.0096    0.0060         0   -0.0060   -0.0096   -0.0084
+             0    0.0030    0.0024         0   -0.0024   -0.0030         0
+       -0.0030         0    0.0006         0   -0.0006         0    0.0030
+       -0.0024   -0.0006         0         0    0.0000    0.0006    0.0024
+             0         0         0         0         0         0         0
+        0.0024    0.0006   -0.0000         0         0   -0.0006   -0.0024
+        0.0030         0   -0.0006         0    0.0006         0   -0.0030
+             0   -0.0030   -0.0024         0    0.0024    0.0030         0
+       -0.0084   -0.0096   -0.0060         0    0.0060    0.0096    0.0084
+       -0.0240   -0.0210   -0.0120         0    0.0120    0.0210    0.0240
+       -0.0486   -0.0384   -0.0210         0    0.0210    0.0384    0.0486
+       -0.0840   -0.0630   -0.0336         0    0.0336    0.0630    0.0840
+       -0.1320   -0.0960   -0.0504         0    0.0504    0.0960    0.1320
+       -0.1944   -0.1386   -0.0720         0    0.0720    0.1386    0.1944
+       -0.2730   -0.1920   -0.0990         0    0.0990    0.1920    0.2730
+    
+      Columns 15 through 21
+    
+       -0.3360   -0.3750   -0.3840   -0.3570   -0.2880   -0.1710         0
+       -0.2340   -0.2520   -0.2430   -0.2016   -0.1224   -0.0000    0.1710
+       -0.1536   -0.1560   -0.1344   -0.0840         0    0.1224    0.2880
+       -0.0924   -0.0840   -0.0546         0    0.0840    0.2016    0.3570
+       -0.0480   -0.0330    0.0000    0.0546    0.1344    0.2430    0.3840
+       -0.0180         0    0.0330    0.0840    0.1560    0.2520    0.3750
+       -0.0000    0.0180    0.0480    0.0924    0.1536    0.2340    0.3360
+        0.0084    0.0240    0.0486    0.0840    0.1320    0.1944    0.2730
+        0.0096    0.0210    0.0384    0.0630    0.0960    0.1386    0.1920
+        0.0060    0.0120    0.0210    0.0336    0.0504    0.0720    0.0990
+             0         0         0         0         0         0         0
+       -0.0060   -0.0120   -0.0210   -0.0336   -0.0504   -0.0720   -0.0990
+       -0.0096   -0.0210   -0.0384   -0.0630   -0.0960   -0.1386   -0.1920
+       -0.0084   -0.0240   -0.0486   -0.0840   -0.1320   -0.1944   -0.2730
+             0   -0.0180   -0.0480   -0.0924   -0.1536   -0.2340   -0.3360
+        0.0180         0   -0.0330   -0.0840   -0.1560   -0.2520   -0.3750
+        0.0480    0.0330         0   -0.0546   -0.1344   -0.2430   -0.3840
+        0.0924    0.0840    0.0546         0   -0.0840   -0.2016   -0.3570
+        0.1536    0.1560    0.1344    0.0840         0   -0.1224   -0.2880
+        0.2340    0.2520    0.2430    0.2016    0.1224         0   -0.1710
+        0.3360    0.3750    0.3840    0.3570    0.2880    0.1710         0
+
+
+
+```matlab
+contour(X,Y,Z)
+```
+
+
+![png](output_10_0.png)
+
+
+
+```matlab
+mesh(X,Y,Z)
+```
+
+
+![png](output_11_0.png)
+
+
+
+```matlab
+pcolor(X,Y,Z)
+```
+
+
+![png](output_12_0.png)
+
+
+## Functions
+
+So far, everything has been executed as a script, or calling a built-in function. Now we begin building our own functions.
+
+Functions are saved in memory (or better yet) in a folder in your path or current directory
+
+Example of storing function in memory
+
+$f(x,y) = (xy^{3}-x^{3}y)$
+
+
+```matlab
+f= @(x,y) (x.*y.^3-x.^3.*y)
+```
+
+    f = 
+    
+        @(x,y)(x.*y.^3-x.^3.*y)
+
+
+
+```matlab
+f(0.1,-0.5)
+```
+
+    ans =
+    
+       -0.0120
+
+
+Here we will save a function called `my_function` as `my_function.m`
+
+```matlab 
+function [vx,vy] = my_function(x,y,t)
+    % Help documentation of "my_function"
+    % This function computes the velocity in the x- and y-directions given
+    % three vectors of position in x- and y-directions as a function of time
+    % x = x-position
+    % y = y-position
+    % t = time
+    % output
+    % vx = velocity in x-direction
+    % vy = velocity in y-direction
+    
+    vx=zeros(length(t),1);
+    vy=zeros(length(t),1);
+    
+    vx(1:end-1) = diff(x)./diff(t); % calculate vx as delta x/delta t
+    vy(1:end-1) = diff(y)./diff(t); % calculate vy as delta y/delta t
+    
+    vx(end) = vx(end-1);
+    vy(end) = vy(end-1);
+
+end
+```
+
+
+```matlab
+help my_function
+```
+
+    Help documentation of "my_function"
+      This function computes the velocity in the x- and y-directions given
+      three vectors of position in x- and y-directions as a function of time
+      x = x-position
+      y = y-position
+      t = time
+      output
+      vx = velocity in x-direction
+      vy = velocity in y-direction
+
+
+
+```matlab
+t=linspace(0,10,100)'; 
+x=t.^3; % vx = 3*t^2
+y=t.^2/2;  % vy = t
+[vx,vy]=my_function(x,y,t);
+```
+
+
+```matlab
+yyaxis left
+plot(t(1:10:end),vx(1:10:end),'o',t,3*t.^2)
+ylabel('v_{x}')
+yyaxis right
+plot(t(1:10:end),vy(1:10:end),'s',t, t)
+ylabel('v_{y}')
+xlabel('time')
+```
+
+
+![png](output_20_0.png)
+
+
+Now, create a new function that calls 'my_function' called, `my_caller.m`
+
+
+```matlab
+help my_caller
+```
+
+    Help documentation of "my_caller"
+      This function computes the acceleration in the x- and y-directions given
+      three vectors of position in x- and y-directions as a function of time
+      x = x-position
+      y = y-position
+      t = time
+      output
+      ax = velocity in x-direction
+      ay = velocity in y-direction
+
+
+
+```matlab
+[ax,ay]=my_caller(x,y,t);
+```
+
+
+```matlab
+yyaxis left
+plot(t(1:10:end),ax(1:10:end),'o',t,6*t)
+ylabel('a_{x}')
+yyaxis right
+plot(t(1:10:end),ay(1:10:end),'s',t, 1*t./t)
+ylabel('a_{x}')
+xlabel('time')
+axis([0,10,0,3])
+```
+
+
+![png](output_24_0.png)
+
+
+
+```matlab
+diff_match_dims(x,t)
+```
+
+    Undefined function 'diff_match_dims' for input arguments of type 'double'.
+    
+
+
+```matlab
+
+```
diff --git a/lecture_04/myscript.m b/lecture_04/myscript.m
new file mode 100644
index 0000000..4488e0f
--- /dev/null
+++ b/lecture_04/myscript.m
@@ -0,0 +1,11 @@
+f=100;
+
+for i=1:10
+  g=i^2;
+  if f==g
+    fprintf('we made it\n')
+  else
+    fprintf('not yet\n')
+  end
+end
+    
diff --git a/lecture_04/output_10_0.png b/lecture_04/output_10_0.png
new file mode 100644
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HcmV?d00001


From 8785ec42feab7df586825cf0a5451493869cc348 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Wed, 25 Jan 2017 21:22:50 -0500
Subject: [PATCH 06/37] added temporary_file to test github desktop

---
 temporary_file.txt | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 temporary_file.txt

diff --git a/temporary_file.txt b/temporary_file.txt
new file mode 100644
index 0000000..5422329
--- /dev/null
+++ b/temporary_file.txt
@@ -0,0 +1 @@
+just checking github desktop

From 225c5020dd0b034735238205c059a23d58444250 Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Wed, 25 Jan 2017 21:24:50 -0500
Subject: [PATCH 07/37] Delete temporary_file.txt

---
 temporary_file.txt | 1 -
 1 file changed, 1 deletion(-)
 delete mode 100644 temporary_file.txt

diff --git a/temporary_file.txt b/temporary_file.txt
deleted file mode 100644
index 5422329..0000000
--- a/temporary_file.txt
+++ /dev/null
@@ -1 +0,0 @@
-just checking github desktop

From bd5e59dcaea7d079644ed1162f3081b5b90b3383 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Thu, 26 Jan 2017 09:04:23 -0500
Subject: [PATCH 08/37] updated lecture_04

---
 lecture_04/lecture_4.md                       |  48 ++++++++++++++----
 lecture_04/lecture_4_files/lecture_4_12_0.png | Bin 0 -> 29697 bytes
 lecture_04/lecture_4_files/lecture_4_13_0.png | Bin 0 -> 64822 bytes
 lecture_04/lecture_4_files/lecture_4_14_0.png | Bin 0 -> 17167 bytes
 lecture_04/lecture_4_files/lecture_4_22_0.png | Bin 0 -> 20897 bytes
 lecture_04/lecture_4_files/lecture_4_26_0.png | Bin 0 -> 19815 bytes
 lecture_04/lecture_4_files/lecture_4_7_0.png  | Bin 0 -> 17993 bytes
 7 files changed, 39 insertions(+), 9 deletions(-)
 create mode 100644 lecture_04/lecture_4_files/lecture_4_12_0.png
 create mode 100644 lecture_04/lecture_4_files/lecture_4_13_0.png
 create mode 100644 lecture_04/lecture_4_files/lecture_4_14_0.png
 create mode 100644 lecture_04/lecture_4_files/lecture_4_22_0.png
 create mode 100644 lecture_04/lecture_4_files/lecture_4_26_0.png
 create mode 100644 lecture_04/lecture_4_files/lecture_4_7_0.png

diff --git a/lecture_04/lecture_4.md b/lecture_04/lecture_4.md
index 50921c3..dd549aa 100644
--- a/lecture_04/lecture_4.md
+++ b/lecture_04/lecture_4.md
@@ -1,11 +1,41 @@
 
+## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects)
+
+Questions from last class:
+- I downloaded GitHub to my desktop but I cannot sign into my UConn account like I can online. 
+- I checked my grades on HuskyCt recently and I received a 0 / 100 for Homework 1.
+- It is very hard to tell if what I'm doing on github is right or wrong.
+- How often will be using our laptops during the lecture?
+- How many frogs would it take to move a car that is stuck in the snow? And what would be the approximate cost to do so
+
+$m_{frog}$=22.7 g (https://en.wikipedia.org/wiki/Common_frog)
+
+$v_{frog}$=17 kph = 4.72 m/s (http://purelyfacts.com/question/14/is-a-toad-faster-than-a-frog?DDA=113&DDB=40)
+
+$m_{car}$=1000 kg (reasonable guess)
+
+conservation of momentum:
+
+$mv_{1} +mv_{2} = mv_{1}'+mv_{2}' = m_{total}v_{2}'$
+
 
 ```matlab
-## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects)
+number_of_frogs = 1;
+v2=0;
+while v2 < 1 % 1 m/s
+    m_frogs=number_of_frogs*22.7e-3;
+    number_of_frogs=number_of_frogs+1;
+    p1=(m_frogs)*4.72; % momentum 1
+    v2=p1/(m_frogs+1000); % p2=p1, so v2=p1/m_total
+end
+number_of_frogs
+    
 ```
 
-    Error: The input character is not valid in MATLAB statements or expressions.
-    
+    number_of_frogs =
+    
+           11844
+
 
 
 ```matlab
@@ -43,7 +73,7 @@ ylabel('displacement (m)')
 ```
 
 
-![png](output_5_0.png)
+![png](lecture_4_files/lecture_4_7_0.png)
 
 
 #EOL
@@ -140,7 +170,7 @@ contour(X,Y,Z)
 ```
 
 
-![png](output_10_0.png)
+![png](lecture_4_files/lecture_4_12_0.png)
 
 
 
@@ -149,7 +179,7 @@ mesh(X,Y,Z)
 ```
 
 
-![png](output_11_0.png)
+![png](lecture_4_files/lecture_4_13_0.png)
 
 
 
@@ -158,7 +188,7 @@ pcolor(X,Y,Z)
 ```
 
 
-![png](output_12_0.png)
+![png](lecture_4_files/lecture_4_14_0.png)
 
 
 ## Functions
@@ -253,7 +283,7 @@ xlabel('time')
 ```
 
 
-![png](output_20_0.png)
+![png](lecture_4_files/lecture_4_22_0.png)
 
 
 Now, create a new function that calls 'my_function' called, `my_caller.m`
@@ -292,7 +322,7 @@ axis([0,10,0,3])
 ```
 
 
-![png](output_24_0.png)
+![png](lecture_4_files/lecture_4_26_0.png)
 
 
 
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From 10234c822fa052dfebf4ed84b39af373680fc5b0 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Thu, 26 Jan 2017 09:06:08 -0500
Subject: [PATCH 09/37] remove old plot pngs

---
 lecture_04/output_10_0.png | Bin 29697 -> 0 bytes
 lecture_04/output_11_0.png | Bin 64822 -> 0 bytes
 lecture_04/output_12_0.png | Bin 17167 -> 0 bytes
 lecture_04/output_20_0.png | Bin 20897 -> 0 bytes
 lecture_04/output_24_0.png | Bin 19815 -> 0 bytes
 lecture_04/output_5_0.png  | Bin 17993 -> 0 bytes
 6 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 lecture_04/output_10_0.png
 delete mode 100644 lecture_04/output_11_0.png
 delete mode 100644 lecture_04/output_12_0.png
 delete mode 100644 lecture_04/output_20_0.png
 delete mode 100644 lecture_04/output_24_0.png
 delete mode 100644 lecture_04/output_5_0.png

diff --git a/lecture_04/output_10_0.png b/lecture_04/output_10_0.png
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From a623138b46a5dad4a14375bf7e8d9c6a89b0aab9 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Thu, 26 Jan 2017 09:08:23 -0500
Subject: [PATCH 10/37] add pdf of lecture_4

---
 lecture_04/lecture_4.pdf | Bin 0 -> 152101 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 lecture_04/lecture_4.pdf

diff --git a/lecture_04/lecture_4.pdf b/lecture_04/lecture_4.pdf
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HcmV?d00001


From e5b6204f74057db169d098c86d55df9a8a823b65 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Thu, 26 Jan 2017 13:00:43 -0500
Subject: [PATCH 11/37] added lecture_05

---
 .../lecture_05-checkpoint.ipynb               |   6 +
 lecture_05/lecture_05.ipynb                   | 208 ++++++++++++++++++
 lecture_05/lecture_05.md                      | 109 +++++++++
 lecture_05/lecture_05.pdf                     | Bin 0 -> 28490 bytes
 lecture_05/octave-workspace                   | Bin 0 -> 158 bytes
 5 files changed, 323 insertions(+)
 create mode 100644 lecture_05/.ipynb_checkpoints/lecture_05-checkpoint.ipynb
 create mode 100644 lecture_05/lecture_05.ipynb
 create mode 100644 lecture_05/lecture_05.md
 create mode 100644 lecture_05/lecture_05.pdf
 create mode 100644 lecture_05/octave-workspace

diff --git a/lecture_05/.ipynb_checkpoints/lecture_05-checkpoint.ipynb b/lecture_05/.ipynb_checkpoints/lecture_05-checkpoint.ipynb
new file mode 100644
index 0000000..2fd6442
--- /dev/null
+++ b/lecture_05/.ipynb_checkpoints/lecture_05-checkpoint.ipynb
@@ -0,0 +1,6 @@
+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/lecture_05/lecture_05.ipynb b/lecture_05/lecture_05.ipynb
new file mode 100644
index 0000000..c04b9f5
--- /dev/null
+++ b/lecture_05/lecture_05.ipynb
@@ -0,0 +1,208 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Good coding habits\n",
+    "## naming folders and files"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "[Stanford file naming best practices](https://library.stanford.edu/research/data-management-services/data-best-practices/best-practices-file-naming)\n",
+    "\n",
+    "1. Include information to distinguish file name e.g. project name, objective of function, name/initials, type of data, conditions, version of file, \n",
+    "2. if using dates, use YYYYMMDD, so the computer organizes by year, then month, then day\n",
+    "3. avoid special characters e.g. !, #, \\$, ...\n",
+    "4. avoid using spaces if not necessary, some programs consider a space as a break in code use dashes `-` or underscores `_` or CamelCase"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Commenting your code"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Its important to comment your code to mention what a variable's units are, what the function is supposed to do, etc. \n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "function i=code(j)\n",
+    "    % Example of bad variable names and bad function name\n",
+    "    for w=1:j\n",
+    "        i(w)=w;\n",
+    "    end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "'code' is a command-line function\n",
+      "\n",
+      " Example of bad variable names and bad function name\n",
+      "\n",
+      "\n",
+      "Additional help for built-in functions and operators is\n",
+      "available in the online version of the manual.  Use the command\n",
+      "'doc <topic>' to search the manual index.\n",
+      "\n",
+      "Help and information about Octave is also available on the WWW\n",
+      "at http://www.octave.org and via the help@octave.org\n",
+      "mailing list.\n"
+     ]
+    }
+   ],
+   "source": [
+    "help code"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Choose variable names that describe the variable"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "function count_vector=counting_function(max_value)\n",
+    "    % Good variable names and better help documentation\n",
+    "    % \n",
+    "    % counting function creates a vector from 1 to max_value where each index, i, is \n",
+    "    % stored in each vector spot\n",
+    "    for i=1:max_value\n",
+    "        count_vector(i)=i; % set each element in count_vector to i\n",
+    "    end\n",
+    "end      "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "'counting_function' is a command-line function\n",
+      "\n",
+      " Good variable names and better help documentation\n",
+      " \n",
+      " counting function creates a vector from 1 to max_value where each index, i, is \n",
+      " stored in each vector spot\n",
+      "\n",
+      "\n",
+      "Additional help for built-in functions and operators is\n",
+      "available in the online version of the manual.  Use the command\n",
+      "'doc <topic>' to search the manual index.\n",
+      "\n",
+      "Help and information about Octave is also available on the WWW\n",
+      "at http://www.octave.org and via the help@octave.org\n",
+      "mailing list.\n"
+     ]
+    }
+   ],
+   "source": [
+    "help counting_function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "## Putting it all together"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "1. Clone your homework_1 to your computer\n",
+    "2. open Matlab (cli, jupyter or gui)\n",
+    "3. Change working directory to homework_1 *e.g.* Windows:`cd('C:\\Users\\rcc02007\\Documents\\Github\\homework_1')`, Mac: `cd('/Users/rcc02007/Documents/Github/homework_1')`\n",
+    "4. You have already created your first script `myscript.m` (if not see lecture_4)\n",
+    "5. Run `>> my_script.m`\n",
+    "6. Create a new m-file called nitrogen_pressure.m\n",
+    "7. Create a function based upon the ideal gas law for nitrogen, Pv=RT\n",
+    "    1. R=0.2968 kJ/(kg-K)\n",
+    "    2. inputs to function are v (specific volume m^3/kg), and T, temperature (K)\n",
+    "    3. output is P, pressure (kPa)\n",
+    "8. Once the function works, commit the change to the repository (add a message, like 'added file nitrogen_pressure.m'\n",
+    "9. After file is 'committed', 'push' the changes to your github account\n",
+    "\n",
+    "for the command-line git user, this is steps 8 and 9:\n",
+    "1. `$ git add *`\n",
+    "2. `$ git commit -m 'added file nitrogen_pressure.m'`\n",
+    "3. `$ git push -u origin master\n",
+    "    Username for 'https://github.uconn.edu':rcc02007 <enter>\n",
+    "    Password for 'https://rcc02007@github.uconn.edu': `\n",
+    "   "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Octave",
+   "language": "octave",
+   "name": "octave"
+  },
+  "language_info": {
+   "file_extension": ".m",
+   "help_links": [
+    {
+     "text": "MetaKernel Magics",
+     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+    }
+   ],
+   "mimetype": "text/x-octave",
+   "name": "octave",
+   "version": "0.19.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/lecture_05/lecture_05.md b/lecture_05/lecture_05.md
new file mode 100644
index 0000000..3c53f57
--- /dev/null
+++ b/lecture_05/lecture_05.md
@@ -0,0 +1,109 @@
+
+# Good coding habits
+## naming folders and files
+
+[Stanford file naming best practices](https://library.stanford.edu/research/data-management-services/data-best-practices/best-practices-file-naming)
+
+1. Include information to distinguish file name e.g. project name, objective of function, name/initials, type of data, conditions, version of file, 
+2. if using dates, use YYYYMMDD, so the computer organizes by year, then month, then day
+3. avoid special characters e.g. !, #, \$, ...
+4. avoid using spaces if not necessary, some programs consider a space as a break in code use dashes `-` or underscores `_` or CamelCase
+
+## Commenting your code
+
+Its important to comment your code to mention what a variable's units are, what the function is supposed to do, etc. 
+
+
+
+```octave
+function i=code(j)
+    % Example of bad variable names and bad function name
+    for w=1:j
+        i(w)=w;
+    end
+end
+```
+
+
+```octave
+help code
+```
+
+    'code' is a command-line function
+    
+     Example of bad variable names and bad function name
+    
+    
+    Additional help for built-in functions and operators is
+    available in the online version of the manual.  Use the command
+    'doc <topic>' to search the manual index.
+    
+    Help and information about Octave is also available on the WWW
+    at http://www.octave.org and via the help@octave.org
+    mailing list.
+
+
+## Choose variable names that describe the variable
+
+
+```octave
+function count_vector=counting_function(max_value)
+    % Good variable names and better help documentation
+    % 
+    % counting function creates a vector from 1 to max_value where each index, i, is 
+    % stored in each vector spot
+    for i=1:max_value
+        count_vector(i)=i; % set each element in count_vector to i
+    end
+end      
+```
+
+
+```octave
+help counting_function
+```
+
+    'counting_function' is a command-line function
+    
+     Good variable names and better help documentation
+     
+     counting function creates a vector from 1 to max_value where each index, i, is 
+     stored in each vector spot
+    
+    
+    Additional help for built-in functions and operators is
+    available in the online version of the manual.  Use the command
+    'doc <topic>' to search the manual index.
+    
+    Help and information about Octave is also available on the WWW
+    at http://www.octave.org and via the help@octave.org
+    mailing list.
+
+
+## Putting it all together
+
+1. Clone your homework_1 to your computer
+2. open Matlab (cli, jupyter or gui)
+3. Change working directory to homework_1 *e.g.* Windows:`cd('C:\Users\rcc02007\Documents\Github\homework_1')`, Mac: `cd('/Users/rcc02007/Documents/Github/homework_1')`
+4. You have already created your first script `myscript.m` (if not see lecture_4)
+5. Run `>> my_script.m`
+6. Create a new m-file called nitrogen_pressure.m
+7. Create a function based upon the ideal gas law for nitrogen, Pv=RT
+    1. R=0.2968 kJ/(kg-K)
+    2. inputs to function are v (specific volume m^3/kg), and T, temperature (K)
+    3. output is P, pressure (kPa)
+8. Once the function works, commit the change to the repository (add a message, like 'added file nitrogen_pressure.m'
+9. After file is 'committed', 'push' the changes to your github account
+
+for the command-line git user, this is steps 8 and 9:
+1. `$ git add *`
+2. `$ git commit -m 'added file nitrogen_pressure.m'`
+3. `$ git push -u origin master
+    Username for 'https://github.uconn.edu':rcc02007 <enter>
+    `
+   
+
+
+```octave
+
+```
diff --git a/lecture_05/lecture_05.pdf b/lecture_05/lecture_05.pdf
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From e44a490ca4eab7abe92cdd7ae84f5c4111276e1b Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Thu, 26 Jan 2017 13:02:41 -0500
Subject: [PATCH 12/37] added lecture_05

---
 lecture_05/lecture_05.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lecture_05/lecture_05.md b/lecture_05/lecture_05.md
index 3c53f57..e0bea24 100644
--- a/lecture_05/lecture_05.md
+++ b/lecture_05/lecture_05.md
@@ -96,6 +96,7 @@ help counting_function
 9. After file is 'committed', 'push' the changes to your github account
 
 for the command-line git user, this is steps 8 and 9:
+
 1. `$ git add *`
 2. `$ git commit -m 'added file nitrogen_pressure.m'`
 3. `$ git push -u origin master

From af7ae19feb7508e526665d28312674df16674d9b Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Fri, 27 Jan 2017 17:24:51 -0500
Subject: [PATCH 13/37] added HW 2

---
 HW2/README.md | 30 ++++++++++++++++++++++++++++++
 1 file changed, 30 insertions(+)
 create mode 100644 HW2/README.md

diff --git a/HW2/README.md b/HW2/README.md
new file mode 100644
index 0000000..f3d0952
--- /dev/null
+++ b/HW2/README.md
@@ -0,0 +1,30 @@
+# Homework #2
+## due 2/3/17
+
+1. Now that you have created your own repository, 'homework_1', that has a README.md file.
+Create a new file in this repository called `setdefaults.m`. This file is a matlab/octave
+script that will set default plotting parameters. In this file, add the following lines:
+
+```matlab
+set(0, 'defaultAxesFontSize', 16)
+set(0,'defaultTextFontSize',14)
+set(0,'defaultLineLineWidth',3)
+```
+
+Commit the changes to your repository. 
+
+2. Clone your 'homework_1' repository to your own computer. Create a function,
+`projectile.m` that will calculate the location of an object with an initial velocity. The
+function inputs are v_mag (initial speed), theta (initial angle). The output is the height
+of the object 2.37 m from its starting position. Assume g=9.81 m/s^2 and its initial
+height is 1.72 m. 
+
+```matlab
+>> h=projectile(v_mag,theta)
+
+  h= 1
+```
+
+In addition to the output of `h`-height at 2.37 m-plot the path of the object from its
+initial position its position at 2.37 m away from the start. *Note: use your
+`setdefaults.m` to set the plot defaults before outputting the result.*

From 76969854639064c294b27884a5a3911b5380447d Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Fri, 27 Jan 2017 17:26:55 -0500
Subject: [PATCH 14/37] format HW2

---
 HW2/README.md | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/HW2/README.md b/HW2/README.md
index f3d0952..6255141 100644
--- a/HW2/README.md
+++ b/HW2/README.md
@@ -5,13 +5,13 @@
 Create a new file in this repository called `setdefaults.m`. This file is a matlab/octave
 script that will set default plotting parameters. In this file, add the following lines:
 
-```matlab
-set(0, 'defaultAxesFontSize', 16)
-set(0,'defaultTextFontSize',14)
-set(0,'defaultLineLineWidth',3)
-```
+    ```matlab
+    set(0, 'defaultAxesFontSize', 16)
+    set(0,'defaultTextFontSize',14)
+    set(0,'defaultLineLineWidth',3)
+    ```
 
-Commit the changes to your repository. 
+    Commit the changes to your repository. 
 
 2. Clone your 'homework_1' repository to your own computer. Create a function,
 `projectile.m` that will calculate the location of an object with an initial velocity. The
@@ -19,12 +19,12 @@ function inputs are v_mag (initial speed), theta (initial angle). The output is
 of the object 2.37 m from its starting position. Assume g=9.81 m/s^2 and its initial
 height is 1.72 m. 
 
-```matlab
->> h=projectile(v_mag,theta)
+    ```matlab
+    >> h=projectile(v_mag,theta)
 
-  h= 1
-```
+      h= 1
+    ```
 
-In addition to the output of `h`-height at 2.37 m-plot the path of the object from its
-initial position its position at 2.37 m away from the start. *Note: use your
-`setdefaults.m` to set the plot defaults before outputting the result.*
+    In addition to the output of `h`-height at 2.37 m-plot the path of the object from its
+    initial position its position at 2.37 m away from the start. *Note: use your
+    `setdefaults.m` to set the plot defaults before outputting the result.*

From 7f933800b2280fe5f495baa509403b651e94a94b Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Fri, 27 Jan 2017 17:28:16 -0500
Subject: [PATCH 15/37] fix typo in HW2

---
 HW2/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/HW2/README.md b/HW2/README.md
index 6255141..b182619 100644
--- a/HW2/README.md
+++ b/HW2/README.md
@@ -26,5 +26,5 @@ height is 1.72 m.
     ```
 
     In addition to the output of `h`-height at 2.37 m-plot the path of the object from its
-    initial position its position at 2.37 m away from the start. *Note: use your
+    initial position to its position at 2.37 m away from the start. *Note: use your
     `setdefaults.m` to set the plot defaults before outputting the result.*

From a498831d1ff6fda80c3ec8723ae0d626efa1c36e Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Fri, 27 Jan 2017 20:21:29 -0500
Subject: [PATCH 16/37] add HW2 figure

---
 HW2/README.md      |   8 +-
 HW2/projectile.svg | 331 +++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 338 insertions(+), 1 deletion(-)
 create mode 100644 HW2/projectile.svg

diff --git a/HW2/README.md b/HW2/README.md
index 6255141..cb85553 100644
--- a/HW2/README.md
+++ b/HW2/README.md
@@ -13,7 +13,13 @@ script that will set default plotting parameters. In this file, add the followin
 
     Commit the changes to your repository. 
 
-2. Clone your 'homework_1' repository to your own computer. Create a function,
+![projectile(v_mag,theta) predicts the height of the projectile based upon initial
+velocity and position, as see in the Figure](projectile.png)
+
+2. Clone your 'homework_1' repository to your own computer. Now, we want to create a
+function that uses kinematic formulas to predict the path of a projectile. The dimensions
+are taken from official dart board dimensions
+[darts](http://dartbrokers.com/dartboard-height.html). Create a function,
 `projectile.m` that will calculate the location of an object with an initial velocity. The
 function inputs are v_mag (initial speed), theta (initial angle). The output is the height
 of the object 2.37 m from its starting position. Assume g=9.81 m/s^2 and its initial
diff --git a/HW2/projectile.svg b/HW2/projectile.svg
new file mode 100644
index 0000000..bb33043
--- /dev/null
+++ b/HW2/projectile.svg
@@ -0,0 +1,331 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   xmlns:dc="http://purl.org/dc/elements/1.1/"
+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:xlink="http://www.w3.org/1999/xlink"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   width="4in"
+   height="3in"
+   viewBox="0 0 360 270"
+   id="svg2"
+   version="1.1"
+   inkscape:version="0.91 r13725"
+   sodipodi:docname="projectile.svg">
+  <defs
+     id="defs4">
+    <marker
+       inkscape:stockid="Arrow1Mend"
+       orient="auto"
+       refY="0.0"
+       refX="0.0"
+       id="marker5950"
+       style="overflow:visible;"
+       inkscape:isstock="true">
+      <path
+         id="path5952"
+         d="M 0.0,0.0 L 5.0,-5.0 L -12.5,0.0 L 5.0,5.0 L 0.0,0.0 z "
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+         transform="scale(0.4) rotate(180) translate(10,0)" />
+    </marker>
+    <linearGradient
+       inkscape:collect="always"
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+         offset="1"
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From 490943d79faedaa6c52527c8a1d4d74052f37c4e Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Fri, 27 Jan 2017 20:24:23 -0500
Subject: [PATCH 17/37] add HW2 figure png

---
 HW2/projectile.png | Bin 0 -> 14114 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 HW2/projectile.png

diff --git a/HW2/projectile.png b/HW2/projectile.png
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From 0156322d8f55ea69049fa7c8625207ca30425220 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Fri, 27 Jan 2017 20:25:33 -0500
Subject: [PATCH 18/37] add HW2 figure png

---
 HW2/projectile.png | Bin 14114 -> 10470 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/HW2/projectile.png b/HW2/projectile.png
index b4534b17138c418a104dc1a134e0efbd64ab239f..f54422403467fe703737b779cce6644e313cb47a 100644
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From f8b20dae6d8f0343708bf5df89b003ee4d8a3184 Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Fri, 27 Jan 2017 20:26:10 -0500
Subject: [PATCH 19/37] Update README.md

---
 HW2/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/HW2/README.md b/HW2/README.md
index 5f895e3..f74173b 100644
--- a/HW2/README.md
+++ b/HW2/README.md
@@ -13,7 +13,7 @@ script that will set default plotting parameters. In this file, add the followin
 
     Commit the changes to your repository. 
 
-![projectile(v_mag,theta) predicts the height of the projectile based upon initial
+    ![projectile(v_mag,theta) predicts the height of the projectile based upon initial
 velocity and position, as see in the Figure](projectile.png)
 
 2. Clone your 'homework_1' repository to your own computer. Now, we want to create a

From ae2b934970299bd0fe1fb053f048ba0d4695cd11 Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Fri, 27 Jan 2017 21:14:12 -0500
Subject: [PATCH 20/37] Update syllabus tools used

---
 README.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/README.md b/README.md
index eebd665..54fa117 100644
--- a/README.md
+++ b/README.md
@@ -30,6 +30,11 @@ matlab/octave functions and programming best practices.
 **Textbook:** Chapra, Steven, *Applied Numerical Methods with MATLAB for Engineers and
 Scientists* 3rd edition. 
 
+**Tools used:** Matlab, Octave, Github. 
+
+**Recommended tools:** Github Desktop, git, Atom (text editor), Vim (text editor), 
+Jupiter notebook (with matlab or octave kernel) 
+
 ## Grading
 
 | Item | Percent | Requirement |

From 436a6ba4a8f47c91c4a53fbf73d8a617561524c6 Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Fri, 27 Jan 2017 21:15:20 -0500
Subject: [PATCH 21/37] Update syllabus tools used and format

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 54fa117..25ca5bc 100644
--- a/README.md
+++ b/README.md
@@ -25,6 +25,7 @@ matlab/octave functions and programming best practices.
 - Graduate: Peiyu Zhang <peiyu.zhang@uconn.edu>
 - Office hours: 2 hours / week 
 
+## Course Information
 **Prerequisite:** CE 3110, MATH 2410Q 
 
 **Textbook:** Chapra, Steven, *Applied Numerical Methods with MATLAB for Engineers and

From ab777680a93a69b1da7979b36b8bbafed5d9030f Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Sat, 28 Jan 2017 10:17:01 -0500
Subject: [PATCH 22/37] Add matlab link

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 25ca5bc..f91ab85 100644
--- a/README.md
+++ b/README.md
@@ -31,7 +31,7 @@ matlab/octave functions and programming best practices.
 **Textbook:** Chapra, Steven, *Applied Numerical Methods with MATLAB for Engineers and
 Scientists* 3rd edition. 
 
-**Tools used:** Matlab, Octave, Github. 
+**Tools used:** [Matlab](https://www.mathworks.com/products/matlab.html), Octave, Github. 
 
 **Recommended tools:** Github Desktop, git, Atom (text editor), Vim (text editor), 
 Jupiter notebook (with matlab or octave kernel) 

From 517b20cf9ad01c00c978bab802408226ef6fcfd9 Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Sat, 28 Jan 2017 10:22:20 -0500
Subject: [PATCH 23/37] Add links for octave and github

---
 README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f91ab85..ac76991 100644
--- a/README.md
+++ b/README.md
@@ -31,7 +31,8 @@ matlab/octave functions and programming best practices.
 **Textbook:** Chapra, Steven, *Applied Numerical Methods with MATLAB for Engineers and
 Scientists* 3rd edition. 
 
-**Tools used:** [Matlab](https://www.mathworks.com/products/matlab.html), Octave, Github. 
+**Tools used:** [Matlab](https://www.mathworks.com/products/matlab.html), 
+[Octave](https://www.gnu.org/software/octave/) , [Github](https://github.com). 
 
 **Recommended tools:** Github Desktop, git, Atom (text editor), Vim (text editor), 
 Jupiter notebook (with matlab or octave kernel) 

From 561666b168b9979010a64534de21f682a2fa69f4 Mon Sep 17 00:00:00 2001
From: Peiyu Zhang <peiyu.zhang@uconn.edu>
Date: Mon, 30 Jan 2017 15:27:40 -0500
Subject: [PATCH 24/37] Peiyu's office hour is updated.

Peiyu's office hour is updated. Friday 9:00-11:00am in Engineering II room 315
---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index ac76991..8059993 100644
--- a/README.md
+++ b/README.md
@@ -23,7 +23,7 @@ matlab/octave functions and programming best practices.
 
 ## Teaching Assistants:
 - Graduate: Peiyu Zhang <peiyu.zhang@uconn.edu>
-- Office hours: 2 hours / week 
+- Office hours: Friday 9:00-11:00am in Engineering II room 315
 
 ## Course Information
 **Prerequisite:** CE 3110, MATH 2410Q 

From 67cefadaf84ccd19aaf0d78f40f9fb95987e8265 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Tue, 31 Jan 2017 14:41:31 -0500
Subject: [PATCH 25/37] updated lecture 05

---
 HW2/projectile.svg                            |   7 +-
 lecture_05/gp_image_01.png                    | Bin 0 -> 170 bytes
 lecture_05/lecture_05.ipynb                   | 389 +++++++++++++++++-
 lecture_05/lecture_05.md                      | 245 ++++++++++-
 lecture_05/lecture_05.pdf                     | Bin 28490 -> 133523 bytes
 .../lecture_05_files/lecture_05_11_0.png      | Bin 0 -> 19333 bytes
 .../lecture_05_files/lecture_05_25_0.png      | Bin 0 -> 29601 bytes
 lecture_05/my_caller.m                        |  23 ++
 lecture_05/my_function.m                      |  21 +
 lecture_05/nitrogen_pressure.m                |  10 +
 lecture_05/octave-workspace                   | Bin 158 -> 153 bytes
 lecture_05/q1.png                             | Bin 0 -> 38940 bytes
 lecture_05/q2.png                             | Bin 0 -> 40186 bytes
 lecture_05/setdefaults.m                      |   3 +
 14 files changed, 662 insertions(+), 36 deletions(-)
 create mode 100644 lecture_05/gp_image_01.png
 create mode 100644 lecture_05/lecture_05_files/lecture_05_11_0.png
 create mode 100644 lecture_05/lecture_05_files/lecture_05_25_0.png
 create mode 100644 lecture_05/my_caller.m
 create mode 100644 lecture_05/my_function.m
 create mode 100644 lecture_05/nitrogen_pressure.m
 create mode 100644 lecture_05/q1.png
 create mode 100644 lecture_05/q2.png
 create mode 100644 lecture_05/setdefaults.m

diff --git a/HW2/projectile.svg b/HW2/projectile.svg
index bb33043..dc73374 100644
--- a/HW2/projectile.svg
+++ b/HW2/projectile.svg
@@ -16,7 +16,10 @@
    id="svg2"
    version="1.1"
    inkscape:version="0.91 r13725"
-   sodipodi:docname="projectile.svg">
+   sodipodi:docname="projectile.svg"
+   inkscape:export-filename="/home/ryan/Documents/UConn/ME3255/me3255_S2017/course_git/HW2/projectile.png"
+   inkscape:export-xdpi="90"
+   inkscape:export-ydpi="90">
   <defs
      id="defs4">
     <marker
@@ -185,7 +188,7 @@
         <dc:format>image/svg+xml</dc:format>
         <dc:type
            rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
-        <dc:title></dc:title>
+        <dc:title />
       </cc:Work>
     </rdf:RDF>
   </metadata>
diff --git a/lecture_05/gp_image_01.png b/lecture_05/gp_image_01.png
new file mode 100644
index 0000000000000000000000000000000000000000..ef291b593f623b8b543ea653c733167f14e20882
GIT binary patch
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diff --git a/lecture_05/lecture_05.ipynb b/lecture_05/lecture_05.ipynb
index c04b9f5..66fcbe9 100644
--- a/lecture_05/lecture_05.ipynb
+++ b/lecture_05/lecture_05.ipynb
@@ -1,5 +1,303 @@
 {
  "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%plot --format svg"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Questions from last class"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "When you execute the given function \n",
+    "\n",
+    "my_function.m:\n",
+    "\n",
+    "```matlab\n",
+    "function [x,y] = my_function(max_time)\n",
+    "    N=100;\n",
+    "    t=linspace(0,max_time,N);\n",
+    "    x=t.^2;\n",
+    "    y=2*t;\n",
+    "end\n",
+    "```\n",
+    "\n",
+    "as \n",
+    "\n",
+    "```>> [x,y] = my_function(20);```\n",
+    "\n",
+    "What variables are saved to your workspace?\n",
+    "\n",
+    "![responses](q1.png)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "How do you write a help description for a function?\n",
+    "\n",
+    "![responses to question 2](q2.png)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " \n",
+    "How to keep our forked ME3255S page up to date with the original\n",
+    "pretty tired this morning\n",
+    "\n",
+    "How do I use the Github Desktop?\n",
+    "\n",
+    "whats your favorite football team?\n",
+    "\n",
+    "Will UConn's github get updated to the newest version of github?\n",
+    "As u said in class trail and error is the best way of learning.\n",
+    "\n",
+    "I believe the % is the same as matlab where it de-links your code into text\n",
+    "\n",
+    "Does the @ symbol designate a pointer? \n",
+    "\n",
+    "Given the change of air pressure as altitude increases, how fast would a frisbee have to travel (and spin) to hit an airplane?\n",
+    "\n",
+    "What is a gui?\n",
+    "\n",
+    "\n",
+    "could you go over a nested for loop example\n",
+    "\n",
+    "Can't seem to get this function to produce any graph and am not sure why\n",
+    "\n",
+    "When are these google forms due?\n",
+    "\n",
+    "how do I create a new function using Github on my desktop?\n",
+    "\n",
+    "Can you explain the first question more in class?\n",
+    "\n",
+    "What is the meaning of life?\n",
+    "\n",
+    "Should I just know how or what these topics are or will we learn them in the future?\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "f = \n",
+      "\n",
+      "    @(x)x.^2\n"
+     ]
+    }
+   ],
+   "source": [
+    "f =@(x) x.^2\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      "     1     9    25    49    81\n",
+      "\n",
+      "\n",
+      "ans =\n",
+      "\n",
+      "    16\n"
+     ]
+    }
+   ],
+   "source": [
+    "f([1:2:10])\n",
+    "f(4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "i=1 and j=1\n",
+      "i=1 and j=2\n",
+      "i=1 and j=3\n",
+      "i=2 and j=1\n",
+      "i=2 and j=2\n",
+      "i=2 and j=3\n",
+      "i=3 and j=1\n",
+      "i=3 and j=2\n",
+      "i=3 and j=3\n",
+      "i=4 and j=1\n",
+      "i=4 and j=2\n",
+      "i=4 and j=3\n",
+      "i=5 and j=1\n",
+      "i=5 and j=2\n",
+      "i=5 and j=3\n",
+      "i=6 and j=1\n",
+      "i=6 and j=2\n",
+      "i=6 and j=3\n"
+     ]
+    }
+   ],
+   "source": [
+    "% nested for loop example\n",
+    "for i = [1:6]\n",
+    "    for j = [1:3]\n",
+    "        fprintf('i=%i and j=%i\\n',i,j)\n",
+    "    end\n",
+    "end\n",
+    "        "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# From last class "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Help documentation of \"my_function\"\n",
+      "  This function computes the velocity in the x- and y-directions given\n",
+      "  three vectors of position in x- and y-directions as a function of time\n",
+      "  x = x-position\n",
+      "  y = y-position\n",
+      "  t = time\n",
+      "  output\n",
+      "  vx = velocity in x-direction\n",
+      "  vy = velocity in y-direction\n"
+     ]
+    }
+   ],
+   "source": [
+    "help my_function"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Help documentation of \"my_caller\"\n",
+      "  This function computes the acceleration in the x- and y-directions given\n",
+      "  three vectors of position in x- and y-directions as a function of time\n",
+      "  x = x-position\n",
+      "  y = y-position\n",
+      "  t = time\n",
+      "  output\n",
+      "  ax = acceleration in x-direction\n",
+      "  ay = acceleration in y-direction\n"
+     ]
+    }
+   ],
+   "source": [
+    "help my_caller"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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8H8sNnMXS2dF+qcrSZiAivnhQ64lD5x+fIJ547y0v/YOcmJCqGgy3vXXE0GHO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\nAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "t=linspace(0,10,100)'; \n",
+    "x=t.^3; % vx = 3*t^2\n",
+    "y=t.^2/2;  % vy = t\n",
+    "[vx,vy]=my_function(x,y,t);\n",
+    "[ax,ay]=my_caller(x,y,t);\n",
+    "yyaxis left\n",
+    "plot(t(1:10:end),ax(1:10:end),'o',t,6*t)\n",
+    "ylabel('a_{x}')\n",
+    "yyaxis right\n",
+    "plot(t(1:10:end),ay(1:10:end),'s',t, 1*t./t)\n",
+    "ylabel('a_{y}')\n",
+    "xlabel('time')\n",
+    "axis([0,10,0,3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\u001b[0;31mUndefined function 'diff_match_dims' for input arguments of type 'double'.\n",
+      "\u001b[0m"
+     ]
+    }
+   ],
+   "source": [
+    "diff_match_dims(x,t)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -36,11 +334,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\u001b[0;31mError: Function definitions are not permitted in this context.\n",
+      "\u001b[0m"
+     ]
+    }
+   ],
    "source": [
     "function i=code(j)\n",
     "    % Example of bad variable names and bad function name\n",
@@ -52,7 +359,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
@@ -61,18 +368,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "'code' is a command-line function\n",
-      "\n",
-      " Example of bad variable names and bad function name\n",
-      "\n",
+      "code not found.\n",
       "\n",
-      "Additional help for built-in functions and operators is\n",
-      "available in the online version of the manual.  Use the command\n",
-      "'doc <topic>' to search the manual index.\n",
-      "\n",
-      "Help and information about Octave is also available on the WWW\n",
-      "at http://www.octave.org and via the help@octave.org\n",
-      "mailing list.\n"
+      "Use the Help browser search field to search the documentation, or\n",
+      "type \"help help\" for help command options, such as help for methods.\n"
      ]
     }
    ],
@@ -89,9 +388,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 1,
    "metadata": {
-    "collapsed": true
+    "collapsed": false
    },
    "outputs": [],
    "source": [
@@ -108,7 +407,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
@@ -155,8 +454,8 @@
     "1. Clone your homework_1 to your computer\n",
     "2. open Matlab (cli, jupyter or gui)\n",
     "3. Change working directory to homework_1 *e.g.* Windows:`cd('C:\\Users\\rcc02007\\Documents\\Github\\homework_1')`, Mac: `cd('/Users/rcc02007/Documents/Github/homework_1')`\n",
-    "4. You have already created your first script `myscript.m` (if not see lecture_4)\n",
-    "5. Run `>> my_script.m`\n",
+    "4. You have already created your first script `setdefaults.m` (if not see lecture_4)\n",
+    "5. Run `>> setdefaults.m`\n",
     "6. Create a new m-file called nitrogen_pressure.m\n",
     "7. Create a function based upon the ideal gas law for nitrogen, Pv=RT\n",
     "    1. R=0.2968 kJ/(kg-K)\n",
@@ -174,6 +473,58 @@
     "   "
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "Now, use this function to plot the range of pressures that a pressure vessel would experience if it is 1000 gallons (3.79 m^3) with 10-20 kg of Nitrogen and temperatures range from -10 to 35 degrees C. \n",
+    "\n",
+    "```matlab\n",
+    "v=0.379/linspace(50,20,10);\n",
+    "T=273.15+linspace(-10,35,10);\n",
+    "[v_grid,T_grid]=meshgrid(v,T);\n",
+    "P = nitrogen_pressure(v,T);\n",
+    "pcolor(v_grid,T_grid,P)\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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T4sWLN2zYwOVyhULhwYMHU1JSuukb+D8KApKZmdmwYcNevXqFEPr++++///57e3v73bt3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\nONp5CLqPAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "setdefaults;\n",
+    "v=3.79./linspace(10,20,10);\n",
+    "T=273.15+linspace(-10,35,10);\n",
+    "[v_grid,T_grid]=meshgrid(v,T);\n",
+    "P = nitrogen_pressure(v_grid,T_grid);\n",
+    "pcolor(v_grid,T_grid-273.15,P-100)\n",
+    "xlabel('specific volume (m^3/kg)')\n",
+    "ylabel('Temperature (C)')\n",
+    "%zlabel('Pressure (kPa)')\n",
+    "\n",
+    "%colormap winter\n",
+    "%colormap summer\n",
+    "%colormap jet\n",
+    "colorbar()"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
diff --git a/lecture_05/lecture_05.md b/lecture_05/lecture_05.md
index e0bea24..11c2894 100644
--- a/lecture_05/lecture_05.md
+++ b/lecture_05/lecture_05.md
@@ -1,4 +1,193 @@
 
+
+```octave
+%plot --format svg
+```
+
+## Questions from last class
+
+When you execute the given function 
+
+my_function.m:
+
+```matlab
+function [x,y] = my_function(max_time)
+    N=100;
+    t=linspace(0,max_time,N);
+    x=t.^2;
+    y=2*t;
+end
+```
+
+as 
+
+```>> [x,y] = my_function(20);```
+
+What variables are saved to your workspace?
+
+![responses](q1.png)
+
+How do you write a help description for a function?
+
+![responses to question 2](q2.png)
+
+ 
+How to keep our forked ME3255S page up to date with the original
+pretty tired this morning
+
+How do I use the Github Desktop?
+
+whats your favorite football team?
+
+Will UConn's github get updated to the newest version of github?
+As u said in class trail and error is the best way of learning.
+
+I believe the % is the same as matlab where it de-links your code into text
+
+Does the @ symbol designate a pointer? 
+
+Given the change of air pressure as altitude increases, how fast would a frisbee have to travel (and spin) to hit an airplane?
+
+What is a gui?
+
+
+could you go over a nested for loop example
+
+Can't seem to get this function to produce any graph and am not sure why
+
+When are these google forms due?
+
+how do I create a new function using Github on my desktop?
+
+Can you explain the first question more in class?
+
+What is the meaning of life?
+
+Should I just know how or what these topics are or will we learn them in the future?
+
+
+
+```octave
+f =@(x) x.^2
+
+
+```
+
+    f = 
+    
+        @(x)x.^2
+
+
+
+```octave
+f([1:2:10])
+f(4)
+```
+
+    ans =
+    
+         1     9    25    49    81
+    
+    
+    ans =
+    
+        16
+
+
+
+```octave
+% nested for loop example
+for i = [1:6]
+    for j = [1:3]
+        fprintf('i=%i and j=%i\n',i,j)
+    end
+end
+        
+```
+
+    i=1 and j=1
+    i=1 and j=2
+    i=1 and j=3
+    i=2 and j=1
+    i=2 and j=2
+    i=2 and j=3
+    i=3 and j=1
+    i=3 and j=2
+    i=3 and j=3
+    i=4 and j=1
+    i=4 and j=2
+    i=4 and j=3
+    i=5 and j=1
+    i=5 and j=2
+    i=5 and j=3
+    i=6 and j=1
+    i=6 and j=2
+    i=6 and j=3
+
+
+# From last class 
+
+
+```octave
+help my_function
+```
+
+    Help documentation of "my_function"
+      This function computes the velocity in the x- and y-directions given
+      three vectors of position in x- and y-directions as a function of time
+      x = x-position
+      y = y-position
+      t = time
+      output
+      vx = velocity in x-direction
+      vy = velocity in y-direction
+
+
+
+```octave
+help my_caller
+```
+
+    Help documentation of "my_caller"
+      This function computes the acceleration in the x- and y-directions given
+      three vectors of position in x- and y-directions as a function of time
+      x = x-position
+      y = y-position
+      t = time
+      output
+      ax = acceleration in x-direction
+      ay = acceleration in y-direction
+
+
+
+```octave
+t=linspace(0,10,100)'; 
+x=t.^3; % vx = 3*t^2
+y=t.^2/2;  % vy = t
+[vx,vy]=my_function(x,y,t);
+[ax,ay]=my_caller(x,y,t);
+yyaxis left
+plot(t(1:10:end),ax(1:10:end),'o',t,6*t)
+ylabel('a_{x}')
+yyaxis right
+plot(t(1:10:end),ay(1:10:end),'s',t, 1*t./t)
+ylabel('a_{y}')
+xlabel('time')
+axis([0,10,0,3])
+```
+
+
+![png](lecture_05_files/lecture_05_11_0.png)
+
+
+
+```octave
+diff_match_dims(x,t)
+```
+
+    Undefined function 'diff_match_dims' for input arguments of type 'double'.
+    
+
 # Good coding habits
 ## naming folders and files
 
@@ -24,23 +213,18 @@ function i=code(j)
 end
 ```
 
+    Error: Function definitions are not permitted in this context.
+    
+
 
 ```octave
 help code
 ```
 
-    'code' is a command-line function
-    
-     Example of bad variable names and bad function name
-    
+    code not found.
     
-    Additional help for built-in functions and operators is
-    available in the online version of the manual.  Use the command
-    'doc <topic>' to search the manual index.
-    
-    Help and information about Octave is also available on the WWW
-    at http://www.octave.org and via the help@octave.org
-    mailing list.
+    Use the Help browser search field to search the documentation, or
+    type "help help" for help command options, such as help for methods.
 
 
 ## Choose variable names that describe the variable
@@ -85,8 +269,8 @@ help counting_function
 1. Clone your homework_1 to your computer
 2. open Matlab (cli, jupyter or gui)
 3. Change working directory to homework_1 *e.g.* Windows:`cd('C:\Users\rcc02007\Documents\Github\homework_1')`, Mac: `cd('/Users/rcc02007/Documents/Github/homework_1')`
-4. You have already created your first script `myscript.m` (if not see lecture_4)
-5. Run `>> my_script.m`
+4. You have already created your first script `setdefaults.m` (if not see lecture_4)
+5. Run `>> setdefaults.m`
 6. Create a new m-file called nitrogen_pressure.m
 7. Create a function based upon the ideal gas law for nitrogen, Pv=RT
     1. R=0.2968 kJ/(kg-K)
@@ -96,14 +280,45 @@ help counting_function
 9. After file is 'committed', 'push' the changes to your github account
 
 for the command-line git user, this is steps 8 and 9:
-
 1. `$ git add *`
 2. `$ git commit -m 'added file nitrogen_pressure.m'`
 3. `$ git push -u origin master
     Username for 'https://github.uconn.edu':rcc02007 <enter>
-    `
+    Password for 'https://rcc02007@github.uconn.edu': `
    
 
+Now, use this function to plot the range of pressures that a pressure vessel would experience if it is 1000 gallons (3.79 m^3) with 10-20 kg of Nitrogen and temperatures range from -10 to 35 degrees C. 
+
+```matlab
+v=0.379/linspace(50,20,10);
+T=273.15+linspace(-10,35,10);
+[v_grid,T_grid]=meshgrid(v,T);
+P = nitrogen_pressure(v,T);
+pcolor(v_grid,T_grid,P)
+```
+
+
+```octave
+setdefaults;
+v=3.79./linspace(10,20,10);
+T=273.15+linspace(-10,35,10);
+[v_grid,T_grid]=meshgrid(v,T);
+P = nitrogen_pressure(v_grid,T_grid);
+pcolor(v_grid,T_grid-273.15,P-100)
+xlabel('specific volume (m^3/kg)')
+ylabel('Temperature (C)')
+%zlabel('Pressure (kPa)')
+
+%colormap winter
+%colormap summer
+%colormap jet
+colorbar()
+```
+
+
+![png](lecture_05_files/lecture_05_25_0.png)
+
+
 
 ```octave
 
diff --git a/lecture_05/lecture_05.pdf b/lecture_05/lecture_05.pdf
index b12565972dde9f1c8eb63539b25a1aa1ea4c4127..589a8543a277078c257f8aae0319eb69448e4e09 100644
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literal 0
HcmV?d00001

diff --git a/lecture_05/my_caller.m b/lecture_05/my_caller.m
new file mode 100644
index 0000000..f0cd536
--- /dev/null
+++ b/lecture_05/my_caller.m
@@ -0,0 +1,23 @@
+function [ax,ay]=my_caller(x,y,t)
+    % Help documentation of "my_caller"
+    % This function computes the acceleration in the x- and y-directions given
+    % three vectors of position in x- and y-directions as a function of time
+    % x = x-position
+    % y = y-position
+    % t = time
+    % output
+    % ax = acceleration in x-direction
+    % ay = acceleration in y-direction
+
+    function v=diff_match_dims(x,t)
+      v=zeros(length(t),1);
+      v(1:end-1)=diff(x)./diff(t);
+      v(end)=v(end-1);
+    end
+
+    [vx,vy]=my_function(x,y,t);
+
+    ax = diff_match_dims(vx,t);
+    ay = diff_match_dims(vy,t);
+
+end
diff --git a/lecture_05/my_function.m b/lecture_05/my_function.m
new file mode 100644
index 0000000..5953061
--- /dev/null
+++ b/lecture_05/my_function.m
@@ -0,0 +1,21 @@
+function [vx,vy] = my_function(x,y,t)
+    % Help documentation of "my_function"
+    % This function computes the velocity in the x- and y-directions given
+    % three vectors of position in x- and y-directions as a function of time
+    % x = x-position
+    % y = y-position
+    % t = time
+    % output
+    % vx = velocity in x-direction
+    % vy = velocity in y-direction
+
+    vx=zeros(length(t),1);
+    vy=zeros(length(t),1);
+
+    vx(1:end-1) = diff(x)./diff(t); % calculate vx as delta x/delta t
+    vy(1:end-1) = diff(y)./diff(t); % calculate vy as delta y/delta t
+
+    vx(end) = vx(end-1);
+    vy(end) = vy(end-1);
+
+end
diff --git a/lecture_05/nitrogen_pressure.m b/lecture_05/nitrogen_pressure.m
new file mode 100644
index 0000000..a76abf3
--- /dev/null
+++ b/lecture_05/nitrogen_pressure.m
@@ -0,0 +1,10 @@
+function P=nitrogen_pressure(v,T)
+  % function to calculate Pressure of Nitrogen using ideal gas law given the specific
+  % volume, v (m^3/kg), and temperature, T (K)
+  % Pv = RT
+  %  R=0.2968; % kJ/kg-K
+  % P [in kPa] = nitrogen_pressure(v [in m^3/kg], T[in K])
+  R=0.2968; % kJ/kg-K
+  P=R*T./v;
+end
+
diff --git a/lecture_05/octave-workspace b/lecture_05/octave-workspace
index 1ca4b384c522da4846a7bfe4aa26132bc70dc92b..8c437bb6e55a5d1b6115661b3a20e86870909d32 100644
GIT binary patch
delta 90
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delta 118
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diff --git a/lecture_05/q1.png b/lecture_05/q1.png
new file mode 100644
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diff --git a/lecture_05/setdefaults.m b/lecture_05/setdefaults.m
new file mode 100644
index 0000000..8c3c5c8
--- /dev/null
+++ b/lecture_05/setdefaults.m
@@ -0,0 +1,3 @@
+set(0, 'defaultAxesFontSize', 16)
+set(0,'defaultTextFontSize',14)
+set(0,'defaultLineLineWidth',3)

From 908bbf1e62e5b4fad1685c9e0921313fb305b061 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Thu, 2 Feb 2017 09:30:03 -0500
Subject: [PATCH 26/37] updated lecture 06

---
 lecture_06/bisect.m                           |  37 +
 lecture_06/falsepos.m                         |  39 +
 lecture_06/incsearch.m                        |  37 +
 lecture_06/lecture_06.ipynb                   | 834 ++++++++++++++++++
 lecture_06/lecture_06.md                      | 373 ++++++++
 .../lecture_06_files/lecture_06_18_0.svg      | 144 +++
 .../lecture_06_files/lecture_06_5_0.svg       | 145 +++
 7 files changed, 1609 insertions(+)
 create mode 100644 lecture_06/bisect.m
 create mode 100644 lecture_06/falsepos.m
 create mode 100644 lecture_06/incsearch.m
 create mode 100644 lecture_06/lecture_06.ipynb
 create mode 100644 lecture_06/lecture_06.md
 create mode 100644 lecture_06/lecture_06_files/lecture_06_18_0.svg
 create mode 100644 lecture_06/lecture_06_files/lecture_06_5_0.svg

diff --git a/lecture_06/bisect.m b/lecture_06/bisect.m
new file mode 100644
index 0000000..c09ffbf
--- /dev/null
+++ b/lecture_06/bisect.m
@@ -0,0 +1,37 @@
+function [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es | iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});
\ No newline at end of file
diff --git a/lecture_06/falsepos.m b/lecture_06/falsepos.m
new file mode 100644
index 0000000..0a3477c
--- /dev/null
+++ b/lecture_06/falsepos.m
@@ -0,0 +1,39 @@
+function [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  % xr = (xl + xu)/2; % bisect method
+  xr=xu - (f_m(xu)*(xl-xu))/(f_m(xl)-f_m(xu)); % false position method
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es | iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});
diff --git a/lecture_06/incsearch.m b/lecture_06/incsearch.m
new file mode 100644
index 0000000..bd82554
--- /dev/null
+++ b/lecture_06/incsearch.m
@@ -0,0 +1,37 @@
+function xb = incsearch(func,xmin,xmax,ns)
+% incsearch: incremental search root locator
+%   xb = incsearch(func,xmin,xmax,ns):
+%     finds brackets of x that contain sign changes
+%     of a function on an interval
+% input:
+%   func = name of function
+%   xmin, xmax = endpoints of interval
+%   ns = number of subintervals (default = 50)
+% output:
+%   xb(k,1) is the lower bound of the kth sign change
+%   xb(k,2) is the upper bound of the kth sign change
+%   If no brackets found, xb = [].
+if nargin < 3, error('at least 3 arguments required'), end
+if nargin < 4, ns = 50; end %if ns blank set to 50
+% Incremental search
+x = linspace(xmin,xmax,ns);
+f = func(x);
+nb = 0; xb = []; %xb is null unless sign change detected
+%for k = 1:length(x)-1
+%  if sign(f(k)) ~= sign(f(k+1)) %check for sign change
+%    nb = nb + 1;
+%    xb(nb,1) = x(k);
+%    xb(nb,2) = x(k+1);
+%  end
+%end
+sign_change = diff(sign(f));
+[~,i_change] = find(sign_change~=0);
+nb=length(i_change);
+xb=[x(i_change)',x(i_change+1)'];
+
+if isempty(xb) %display that no brackets were found
+  fprintf('no brackets found\n')
+  fprintf('check interval or increase ns\n')
+else
+  fprintf('number of brackets: %i\n',nb) %display number of brackets
+end
diff --git a/lecture_06/lecture_06.ipynb b/lecture_06/lecture_06.ipynb
new file mode 100644
index 0000000..f44f84c
--- /dev/null
+++ b/lecture_06/lecture_06.ipynb
@@ -0,0 +1,834 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%plot --format svg"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "my_caller.m\n",
+    "```matlab\n",
+    "function [vx,vy] = my_caller(max_time)\n",
+    "    N=100;\n",
+    "    t=linspace(0,max_time,N);\n",
+    "    [x,y]=my_function(max_time);\n",
+    "    vx=diff(x)./diff(t);\n",
+    "    vy=diff(y)./diff(t);\n",
+    "end\n",
+    "```\n",
+    "\n",
+    "my_function.m\n",
+    "```matlab\n",
+    "function [x,y] = my_function(max_time)\n",
+    "    N=100;\n",
+    "    t=linspace(0,max_time,N);\n",
+    "    x=t.^2;\n",
+    "    y=2*t;\n",
+    "end\n",
+    "```\n",
+    "\n",
+    "In order to use `my_caller.m` where does `my_function.m` need to be saved?\n",
+    "![responses](q1.png)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "What cool personal projects are you working on?\n",
+    "While we delve deeper into Matlab functions, could we review some of the basic logic\n",
+    "operators it uses and command codes. \n",
+    "\n",
+    "I still dont know when these forms are technically due. \n",
+    "    \n",
+    "    -by the following lecture\n",
+    "\n",
+    "I'm having trouble interfacing Atom with GitHub. Is there a simple tutorial for this?\n",
+    "    \n",
+    "    -Mac? Seems there could be a bug that folks are working on\n",
+    "\n",
+    "What are the bear necessities of life? \n",
+    "please go over how to \"submit\" the homeworks because it is still confusing\n",
+    "\n",
+    "Do you prefer Matlab or Octave?\n",
+    "    \n",
+    "    -octave is my preference, but Matlab has some benefits\n",
+    "\n",
+    "Would you consider a country to be open-source?\n",
+    "    \n",
+    "    -??\n",
+    "\n",
+    "Is there a way to download matlab for free?\n",
+    "    \n",
+    "    -not legally\n",
+    "\n",
+    "how do you add files to current folder in matlab?\n",
+    "    \n",
+    "    -you can do this either through a file browser or cli\n",
+    "\n",
+    "How should Homework 2 be submitted?  By simply putting the function into the homework_1\n",
+    "repository?\n",
+    "    \n",
+    "    -yes\n",
+    "    \n",
+    "How can we tell that these forms are being received?\n",
+    "    \n",
+    "    -when you hit submit, the form says \"form received\"\n",
+    "    \n",
+    "can you save scripted outputs from matlab/octave as an excel file?\n",
+    "    \n",
+    "    -yes, easy way is open a file with a .csv extension then fprintf and separate everything with commas, harder way is to use the `xlswrite`\n",
+    "    \n",
+    "\n",
+    "Also, can you update your notes to show what happens when these things are run, as you do\n",
+    "in class?\"\n",
+    "    \n",
+    "    -I always update the lecture notes after class so they should display what we did in class\n",
+    "    \n",
+    "I have a little difficulty following along in class on my laptop when you have programs\n",
+    "pre-written.  Maybe if you posted those codes on Github so I could copy them when you\n",
+    "switch to different desktops I would be able to follow along better.\n",
+    "\n",
+    "Kirk or Picard?\n",
+    "    \n",
+    "    -Kirk\n",
+    "    \n",
+    "Who is our TA?\n",
+    "    \n",
+    "    -Peiyu Zhang peiyu.zhang@uconn.edu\n",
+    "\n",
+    "Can we download libraries of data like thermodynamic tables into matlab?\n",
+    "    \n",
+    "-YES! [Matlab Steam Tables](http://bit.ly/2kZygu8)\n",
+    "\n",
+    "Will we use the Simulink addition to Matlab? I found it interesting and useful for\n",
+    "evaluating ODEs in Linear systems.\n",
+    "    \n",
+    "    -not in this class, everything in simulink has a matlab script/function that can be substituted, but many times its hidden by the gui. Here we want to look directly at our solvers\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Roots and Optimization\n",
+    "## Bracketing ch. 5"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "When you are given a function, numerical or analytical, it's not always possible to solve directly for a given variable. \n",
+    "\n",
+    "Even for the freefall example we first explored, \n",
+    "\n",
+    "$v(t)=\\sqrt{\\frac{gm}{c_{d}}}\\tanh(\\sqrt{\\frac{gc_{d}}{m}}t)$\n",
+    "\n",
+    "There is no way to solve for m in terms of the other variables. \n",
+    "\n",
+    "Instead, we can solve the problem by creating a new function f(m) where\n",
+    "\n",
+    "$f(m)=\\sqrt{\\frac{gm}{c_{d}}}\\tanh(\\sqrt{\\frac{gc_{d}}{m}}t)-v(t)$. \n",
+    "\n",
+    "When f(m) = 0, we have solved for m in terms of the other variables (e.g. for a given time, velocity, drag coefficient and acceleration due to gravity)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
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+       "</g>\n",
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+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "setdefaults\n",
+    "g=9.81; % acceleration due to gravity\n",
+    "m=linspace(50, 200,100); % possible values for mass 50 to 200 kg\n",
+    "c_d=0.25; % drag coefficient\n",
+    "t=4; % at time = 4 seconds\n",
+    "v=36; % speed must be 36 m/s\n",
+    "f_m = @(m) sqrt(g*m/c_d).*tanh(sqrt(g*c_d./m)*t)-v; % anonymous function f_m\n",
+    "\n",
+    "plot(m,f_m(m),m,zeros(length(m),1))\n",
+    "axis([45 200 -5 1])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  0.045626\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "f_m(145)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Brute force method is plot f_m vs m and with smaller and smaller steps until f_m ~ 0\n",
+    "\n",
+    "Better methods are the \n",
+    "1. Bracketing methods\n",
+    "2. Open methods\n",
+    "\n",
+    "Both need an initial guess. \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Incremental method (Brute force)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "You know that for one value, m_lower, f_m is negative and for another value, m_upper, f_m is positive. \n",
+    "\n",
+    "```matlab\n",
+    "function xb = incsearch(func,xmin,xmax,ns)\n",
+    "% incsearch: incremental search root locator\n",
+    "%   xb = incsearch(func,xmin,xmax,ns):\n",
+    "%     finds brackets of x that contain sign changes\n",
+    "%     of a function on an interval\n",
+    "% input:\n",
+    "%   func = name of function\n",
+    "%   xmin, xmax = endpoints of interval\n",
+    "%   ns = number of subintervals (default = 50)\n",
+    "% output:\n",
+    "%   xb(k,1) is the lower bound of the kth sign change\n",
+    "%   xb(k,2) is the upper bound of the kth sign change\n",
+    "%   If no brackets found, xb = [].\n",
+    "if nargin < 3, error('at least 3 arguments required'), end\n",
+    "if nargin < 4, ns = 50; end %if ns blank set to 50\n",
+    "% Incremental search\n",
+    "x = linspace(xmin,xmax,ns);\n",
+    "f = func(x);\n",
+    "nb = 0; xb = []; %xb is null unless sign change detected\n",
+    "for k = 1:length(x)-1\n",
+    "  if sign(f(k)) ~= sign(f(k+1)) %check for sign change\n",
+    "    nb = nb + 1;\n",
+    "    xb(nb,1) = x(k);\n",
+    "    xb(nb,2) = x(k+1);\n",
+    "  end\n",
+    "end\n",
+    "if isempty(xb) %display that no brackets were found\n",
+    "  fprintf('no brackets found\\n')\n",
+    "  fprintf('check interval or increase ns\\n')\n",
+    "else\n",
+    "  fprintf('number of brackets: %i\\n',nb) %display number of brackets\n",
+    "end\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "'incsearch' is a function from the file /home/ryan/Documents/UConn/ME3255/me3255_S2017/lecture_06/incsearch.m\n",
+      "\n",
+      " incsearch: incremental search root locator\n",
+      "   xb = incsearch(func,xmin,xmax,ns):\n",
+      "     finds brackets of x that contain sign changes\n",
+      "     of a function on an interval\n",
+      " input:\n",
+      "   func = name of function\n",
+      "   xmin, xmax = endpoints of interval\n",
+      "   ns = number of subintervals (default = 50)\n",
+      " output:\n",
+      "   xb(k,1) is the lower bound of the kth sign change\n",
+      "   xb(k,2) is the upper bound of the kth sign change\n",
+      "   If no brackets found, xb = [].\n",
+      "\n",
+      "\n",
+      "Additional help for built-in functions and operators is\n",
+      "available in the online version of the manual.  Use the command\n",
+      "'doc <topic>' to search the manual index.\n",
+      "\n",
+      "Help and information about Octave is also available on the WWW\n",
+      "at http://www.octave.org and via the help@octave.org\n",
+      "mailing list.\n"
+     ]
+    }
+   ],
+   "source": [
+    "help incsearch"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "no brackets found\n",
+      "check interval or increase ns\n",
+      "ans = [](1x0)\n"
+     ]
+    }
+   ],
+   "source": [
+    "incsearch(f_m,50, 200,55)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "## Bisection method"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Divide interval in half until error is reduced to some level\n",
+    "\n",
+    "in previous example of freefall, choose x_l=50, x_u=200\n",
+    "\n",
+    "x_r = (50+200)/2 = 125\n",
+    "\n",
+    "f_m(125) = -0.408\n",
+    "\n",
+    "x_r= (125+200)/2 = 162.5\n",
+    "\n",
+    "f_m(162.5) = 0.3594\n",
+    "\n",
+    "x_r = (125+162.5)/2=143.75\n",
+    "\n",
+    "f_m(143.75)= 0.0206"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  0.020577\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "f_m(143.75)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Much better root locator, with 4 iterations, our function is already close to zero\n",
+    "\n",
+    "Automate this with a function:\n",
+    "`bisect.m`\n",
+    "\n",
+    "```matlab\n",
+    "function [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,varargin)\n",
+    "% bisect: root location zeroes\n",
+    "% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):\n",
+    "% uses bisection method to find the root of func\n",
+    "% input:\n",
+    "% func = name of function\n",
+    "% xl, xu = lower and upper guesses\n",
+    "% es = desired relative error (default = 0.0001%)\n",
+    "% maxit = maximum allowable iterations (default = 50)\n",
+    "% p1,p2,... = additional parameters used by func\n",
+    "% output:\n",
+    "% root = real root\n",
+    "% fx = function value at root\n",
+    "% ea = approximate relative error (%)\n",
+    "% iter = number of iterations\n",
+    "if nargin<3,error('at least 3 input arguments required'),end\n",
+    "test = func(xl,varargin{:})*func(xu,varargin{:});\n",
+    "if test>0,error('no sign change'),end\n",
+    "if nargin<4|isempty(es), es=0.0001;end\n",
+    "if nargin<5|isempty(maxit), maxit=50;end\n",
+    "iter = 0; xr = xl; ea = 100;\n",
+    "while (1)\n",
+    "  xrold = xr;\n",
+    "  xr = (xl + xu)/2;\n",
+    "  iter = iter + 1;\n",
+    "  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end\n",
+    "  test = func(xl,varargin{:})*func(xr,varargin{:});\n",
+    "  if test < 0\n",
+    "    xu = xr;\n",
+    "  elseif test > 0\n",
+    "    xl = xr;\n",
+    "  else\n",
+    "    ea = 0;\n",
+    "  end\n",
+    "  if ea <= es | iter >= maxit,break,end\n",
+    "end\n",
+    "root = xr; fx = func(xr, varargin{:});\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## False position (linear interpolation)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Rather than bisecting each bracket (1/2 each time) we can calculate the slope between the two points and update the xr position in this manner\n",
+    "\n",
+    "$ x_{r} = x_{u} - \\frac{f(x_{u})(x_{l}-x_{u})}{f(x_{l})-f(x_{u})}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
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+       "</g>\n",
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+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "xl=50; xu=200; \n",
+    "xr=xu - (f_m(xu)*(xl-xu))/(f_m(xl)-f_m(xu));\n",
+    "\n",
+    "plot(m,f_m(m),xl,f_m(xl),'s',xu,f_m(xu),'s',xr,0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Much better root locator, with 4 iterations, our function is already close to zero\n",
+    "\n",
+    "Automate this with a function:\n",
+    "`falsepos.m`\n",
+    "\n",
+    "```matlab\n",
+    "function [root,fx,ea,iter]=falsepos(func,xl,xu,es,maxit,varargin)\n",
+    "% falsepos: root location zeroes\n",
+    "% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):\n",
+    "% uses false position method to find the root of func\n",
+    "% input:\n",
+    "% func = name of function\n",
+    "% xl, xu = lower and upper guesses\n",
+    "% es = desired relative error (default = 0.0001%)\n",
+    "% maxit = maximum allowable iterations (default = 50)\n",
+    "% p1,p2,... = additional parameters used by func\n",
+    "% output:\n",
+    "% root = real root\n",
+    "% fx = function value at root\n",
+    "% ea = approximate relative error (%)\n",
+    "% iter = number of iterations\n",
+    "if nargin<3,error('at least 3 input arguments required'),end\n",
+    "test = func(xl,varargin{:})*func(xu,varargin{:});\n",
+    "if test>0,error('no sign change'),end\n",
+    "if nargin<4|isempty(es), es=0.0001;end\n",
+    "if nargin<5|isempty(maxit), maxit=50;end\n",
+    "iter = 0; xr = xl; ea = 100;\n",
+    "while (1)\n",
+    "  xrold = xr;\n",
+    "  % xr = (xl + xu)/2; % bisect method\n",
+    "  xr=xu - (f_m(xu)*(xl-xu))/(f_m(xl)-f_m(xu)); % false position method\n",
+    "  iter = iter + 1;\n",
+    "  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end\n",
+    "  test = func(xl,varargin{:})*func(xr,varargin{:});\n",
+    "  if test < 0\n",
+    "    xu = xr;\n",
+    "  elseif test > 0\n",
+    "    xl = xr;\n",
+    "  else\n",
+    "    ea = 0;\n",
+    "  end\n",
+    "  if ea <= es | iter >= maxit,break,end\n",
+    "end\n",
+    "root = xr; fx = func(xr, varargin{:});\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Octave",
+   "language": "octave",
+   "name": "octave"
+  },
+  "language_info": {
+   "file_extension": ".m",
+   "help_links": [
+    {
+     "text": "MetaKernel Magics",
+     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+    }
+   ],
+   "mimetype": "text/x-octave",
+   "name": "octave",
+   "version": "0.19.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/lecture_06/lecture_06.md b/lecture_06/lecture_06.md
new file mode 100644
index 0000000..b3d2266
--- /dev/null
+++ b/lecture_06/lecture_06.md
@@ -0,0 +1,373 @@
+
+
+```octave
+%plot --format svg
+```
+
+my_caller.m
+```matlab
+function [vx,vy] = my_caller(max_time)
+    N=100;
+    t=linspace(0,max_time,N);
+    [x,y]=my_function(max_time);
+    vx=diff(x)./diff(t);
+    vy=diff(y)./diff(t);
+end
+```
+
+my_function.m
+```matlab
+function [x,y] = my_function(max_time)
+    N=100;
+    t=linspace(0,max_time,N);
+    x=t.^2;
+    y=2*t;
+end
+```
+
+In order to use `my_caller.m` where does `my_function.m` need to be saved?
+![responses](q1.png)
+
+
+What cool personal projects are you working on?
+While we delve deeper into Matlab functions, could we review some of the basic logic
+operators it uses and command codes. 
+
+I still dont know when these forms are technically due. 
+    
+    -by the following lecture
+
+I'm having trouble interfacing Atom with GitHub. Is there a simple tutorial for this?
+    
+    -Mac? Seems there could be a bug that folks are working on
+
+What are the bear necessities of life? 
+please go over how to "submit" the homeworks because it is still confusing
+
+Do you prefer Matlab or Octave?
+    
+    -octave is my preference, but Matlab has some benefits
+
+Would you consider a country to be open-source?
+    
+    -??
+
+Is there a way to download matlab for free?
+    
+    -not legally
+
+how do you add files to current folder in matlab?
+    
+    -you can do this either through a file browser or cli
+
+How should Homework 2 be submitted?  By simply putting the function into the homework_1
+repository?
+    
+    -yes
+    
+How can we tell that these forms are being received?
+    
+    -when you hit submit, the form says "form received"
+    
+can you save scripted outputs from matlab/octave as an excel file?
+    
+    -yes, easy way is open a file with a .csv extension then fprintf and separate everything with commas, harder way is to use the `xlswrite`
+    
+
+Also, can you update your notes to show what happens when these things are run, as you do
+in class?"
+    
+    -I always update the lecture notes after class so they should display what we did in class
+    
+I have a little difficulty following along in class on my laptop when you have programs
+pre-written.  Maybe if you posted those codes on Github so I could copy them when you
+switch to different desktops I would be able to follow along better.
+
+Kirk or Picard?
+    
+    -Kirk
+    
+Who is our TA?
+    
+    -Peiyu Zhang peiyu.zhang@uconn.edu
+
+Can we download libraries of data like thermodynamic tables into matlab?
+    
+-YES! [Matlab Steam Tables](http://bit.ly/2kZygu8)
+
+Will we use the Simulink addition to Matlab? I found it interesting and useful for
+evaluating ODEs in Linear systems.
+    
+    -not in this class, everything in simulink has a matlab script/function that can be substituted, but many times its hidden by the gui. Here we want to look directly at our solvers
+
+
+# Roots and Optimization
+## Bracketing ch. 5
+
+When you are given a function, numerical or analytical, it's not always possible to solve directly for a given variable. 
+
+Even for the freefall example we first explored, 
+
+$v(t)=\sqrt{\frac{gm}{c_{d}}}\tanh(\sqrt{\frac{gc_{d}}{m}}t)$
+
+There is no way to solve for m in terms of the other variables. 
+
+Instead, we can solve the problem by creating a new function f(m) where
+
+$f(m)=\sqrt{\frac{gm}{c_{d}}}\tanh(\sqrt{\frac{gc_{d}}{m}}t)-v(t)$. 
+
+When f(m) = 0, we have solved for m in terms of the other variables (e.g. for a given time, velocity, drag coefficient and acceleration due to gravity)
+
+
+```octave
+setdefaults
+g=9.81; % acceleration due to gravity
+m=linspace(50, 200,100); % possible values for mass 50 to 200 kg
+c_d=0.25; % drag coefficient
+t=4; % at time = 4 seconds
+v=36; % speed must be 36 m/s
+f_m = @(m) sqrt(g*m/c_d).*tanh(sqrt(g*c_d./m)*t)-v; % anonymous function f_m
+
+plot(m,f_m(m),m,zeros(length(m),1))
+axis([45 200 -5 1])
+```
+
+
+![svg](lecture_06_files/lecture_06_5_0.svg)
+
+
+
+```octave
+f_m(145)
+```
+
+    ans =  0.045626
+
+
+Brute force method is plot f_m vs m and with smaller and smaller steps until f_m ~ 0
+
+Better methods are the 
+1. Bracketing methods
+2. Open methods
+
+Both need an initial guess. 
+
+
+## Incremental method (Brute force)
+
+You know that for one value, m_lower, f_m is negative and for another value, m_upper, f_m is positive. 
+
+```matlab
+function xb = incsearch(func,xmin,xmax,ns)
+% incsearch: incremental search root locator
+%   xb = incsearch(func,xmin,xmax,ns):
+%     finds brackets of x that contain sign changes
+%     of a function on an interval
+% input:
+%   func = name of function
+%   xmin, xmax = endpoints of interval
+%   ns = number of subintervals (default = 50)
+% output:
+%   xb(k,1) is the lower bound of the kth sign change
+%   xb(k,2) is the upper bound of the kth sign change
+%   If no brackets found, xb = [].
+if nargin < 3, error('at least 3 arguments required'), end
+if nargin < 4, ns = 50; end %if ns blank set to 50
+% Incremental search
+x = linspace(xmin,xmax,ns);
+f = func(x);
+nb = 0; xb = []; %xb is null unless sign change detected
+for k = 1:length(x)-1
+  if sign(f(k)) ~= sign(f(k+1)) %check for sign change
+    nb = nb + 1;
+    xb(nb,1) = x(k);
+    xb(nb,2) = x(k+1);
+  end
+end
+if isempty(xb) %display that no brackets were found
+  fprintf('no brackets found\n')
+  fprintf('check interval or increase ns\n')
+else
+  fprintf('number of brackets: %i\n',nb) %display number of brackets
+end
+```
+
+
+```octave
+help incsearch
+```
+
+    'incsearch' is a function from the file /home/ryan/Documents/UConn/ME3255/me3255_S2017/lecture_06/incsearch.m
+    
+     incsearch: incremental search root locator
+       xb = incsearch(func,xmin,xmax,ns):
+         finds brackets of x that contain sign changes
+         of a function on an interval
+     input:
+       func = name of function
+       xmin, xmax = endpoints of interval
+       ns = number of subintervals (default = 50)
+     output:
+       xb(k,1) is the lower bound of the kth sign change
+       xb(k,2) is the upper bound of the kth sign change
+       If no brackets found, xb = [].
+    
+    
+    Additional help for built-in functions and operators is
+    available in the online version of the manual.  Use the command
+    'doc <topic>' to search the manual index.
+    
+    Help and information about Octave is also available on the WWW
+    at http://www.octave.org and via the help@octave.org
+    mailing list.
+
+
+
+```octave
+incsearch(f_m,50, 200,55)
+```
+
+    no brackets found
+    check interval or increase ns
+    ans = [](1x0)
+
+
+## Bisection method
+
+Divide interval in half until error is reduced to some level
+
+in previous example of freefall, choose x_l=50, x_u=200
+
+x_r = (50+200)/2 = 125
+
+f_m(125) = -0.408
+
+x_r= (125+200)/2 = 162.5
+
+f_m(162.5) = 0.3594
+
+x_r = (125+162.5)/2=143.75
+
+f_m(143.75)= 0.0206
+
+
+```octave
+f_m(143.75)
+```
+
+    ans =  0.020577
+
+
+Much better root locator, with 4 iterations, our function is already close to zero
+
+Automate this with a function:
+`bisect.m`
+
+```matlab
+function [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es | iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});
+```
+
+## False position (linear interpolation)
+
+Rather than bisecting each bracket (1/2 each time) we can calculate the slope between the two points and update the xr position in this manner
+
+$ x_{r} = x_{u} - \frac{f(x_{u})(x_{l}-x_{u})}{f(x_{l})-f(x_{u})}$
+
+
+```octave
+xl=50; xu=200; 
+xr=xu - (f_m(xu)*(xl-xu))/(f_m(xl)-f_m(xu));
+
+plot(m,f_m(m),xl,f_m(xl),'s',xu,f_m(xu),'s',xr,0)
+```
+
+
+![svg](lecture_06_files/lecture_06_18_0.svg)
+
+
+Much better root locator, with 4 iterations, our function is already close to zero
+
+Automate this with a function:
+`falsepos.m`
+
+```matlab
+function [root,fx,ea,iter]=falsepos(func,xl,xu,es,maxit,varargin)
+% falsepos: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses false position method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  % xr = (xl + xu)/2; % bisect method
+  xr=xu - (f_m(xu)*(xl-xu))/(f_m(xl)-f_m(xu)); % false position method
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es | iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});
+```
+
+
+```octave
+
+```
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From 2ce5ca32f0eeb211bb368079c412aabf8646d33b Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Mon, 6 Feb 2017 23:06:31 -0500
Subject: [PATCH 27/37] updated lecture 07

---
 lecture_07/bisect.m                           |   37 +
 lecture_07/car_payments.m                     |   17 +
 lecture_07/falsepos.m                         |   39 +
 lecture_07/fzerosimp.m                        |   41 +
 lecture_07/incsearch.m                        |   37 +
 lecture_07/lecture_07.ipynb                   | 1195 +++++++++++++++++
 lecture_07/lecture_07.md                      |  388 ++++++
 lecture_07/lecture_07.pdf                     |  Bin 0 -> 68853 bytes
 .../lecture_07_files/lecture_07_14_1.svg      |  146 ++
 .../lecture_07_files/lecture_07_22_1.svg      |  197 +++
 .../lecture_07_files/lecture_07_24_1.svg      |  182 +++
 lecture_07/mod_secant.m                       |   31 +
 lecture_07/newtraph.m                         |   29 +
 13 files changed, 2339 insertions(+)
 create mode 100644 lecture_07/bisect.m
 create mode 100644 lecture_07/car_payments.m
 create mode 100644 lecture_07/falsepos.m
 create mode 100644 lecture_07/fzerosimp.m
 create mode 100644 lecture_07/incsearch.m
 create mode 100644 lecture_07/lecture_07.ipynb
 create mode 100644 lecture_07/lecture_07.md
 create mode 100644 lecture_07/lecture_07.pdf
 create mode 100644 lecture_07/lecture_07_files/lecture_07_14_1.svg
 create mode 100644 lecture_07/lecture_07_files/lecture_07_22_1.svg
 create mode 100644 lecture_07/lecture_07_files/lecture_07_24_1.svg
 create mode 100644 lecture_07/mod_secant.m
 create mode 100644 lecture_07/newtraph.m

diff --git a/lecture_07/bisect.m b/lecture_07/bisect.m
new file mode 100644
index 0000000..9f696a0
--- /dev/null
+++ b/lecture_07/bisect.m
@@ -0,0 +1,37 @@
+function [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4||isempty(es), es=0.0001;end
+if nargin<5||isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es || iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});
diff --git a/lecture_07/car_payments.m b/lecture_07/car_payments.m
new file mode 100644
index 0000000..9d5b2a5
--- /dev/null
+++ b/lecture_07/car_payments.m
@@ -0,0 +1,17 @@
+function amount_left = car_payments(monthly_payment,price,apr,no_of_years,plot_bool)
+  interest_per_month = apr/12;
+  number_of_months = no_of_years*12;
+  principle=price;
+  P_vector=zeros(1,number_of_months);
+  for i = 1:number_of_months
+    principle=principle-monthly_payment;
+    principle=(1+interest_per_month)*principle;
+    P_vector(i)=principle;
+  end
+  amount_left=principle;
+  if plot_bool
+    plot([1:number_of_months]/12, P_vector)
+    xlabel('time (years)')
+    ylabel('principle amount left ($)')
+  end
+end
diff --git a/lecture_07/falsepos.m b/lecture_07/falsepos.m
new file mode 100644
index 0000000..d5575d5
--- /dev/null
+++ b/lecture_07/falsepos.m
@@ -0,0 +1,39 @@
+function [root,fx,ea,iter]=falsepos(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4||isempty(es), es=0.0001;end
+if nargin<5||isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  % xr = (xl + xu)/2; % bisect method
+  xr=xu - (func(xu)*(xl-xu))/(func(xl)-func(xu)); % false position method
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es || iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});
diff --git a/lecture_07/fzerosimp.m b/lecture_07/fzerosimp.m
new file mode 100644
index 0000000..05c7a9b
--- /dev/null
+++ b/lecture_07/fzerosimp.m
@@ -0,0 +1,41 @@
+function b = fzerosimp(xl,xu)
+a = xl; b = xu; fa = f(a); fb = f(b);
+c = a; fc = fa; d = b - c; e = d;
+while (1)
+  if fb == 0, break, end
+  if sign(fa) == sign(fb) %If needed, rearrange points
+    a = c; fa = fc; d = b - c; e = d;
+  end
+  if abs(fa) < abs(fb)
+    c = b; b = a; a = c;
+    fc = fb; fb = fa; fa = fc;
+  end
+  m = 0.5*(a - b); %Termination test and possible exit
+  tol = 2 * eps * max(abs(b), 1);
+  if abs(m) <= tol | fb == 0.
+    break
+  end
+  %Choose open methods or bisection
+  if abs(e) >= tol & abs(fc) > abs(fb)
+    s = fb/fc;
+    if a == c %Secant method
+      p = 2*m*s;
+      q = 1 - s;
+    else %Inverse quadratic interpolation
+      q = fc/fa; r = fb/fa;
+      p = s * (2*m*q * (q - r) - (b - c)*(r - 1));
+      q = (q - 1)*(r - 1)*(s - 1);
+    end
+    if p > 0, q = -q; else p = -p; end;
+    if 2*p < 3*m*q - abs(tol*q) & p < abs(0.5*e*q)
+      e = d; d = p/q;
+    else
+      d = m; e = m;
+    end
+  else %Bisection
+    d = m; e = m;
+  end
+  c = b; fc = fb;
+  if abs(d) > tol, b=b+d; else b=b-sign(b-a)*tol; end
+  fb = f(b);
+end
\ No newline at end of file
diff --git a/lecture_07/incsearch.m b/lecture_07/incsearch.m
new file mode 100644
index 0000000..bd82554
--- /dev/null
+++ b/lecture_07/incsearch.m
@@ -0,0 +1,37 @@
+function xb = incsearch(func,xmin,xmax,ns)
+% incsearch: incremental search root locator
+%   xb = incsearch(func,xmin,xmax,ns):
+%     finds brackets of x that contain sign changes
+%     of a function on an interval
+% input:
+%   func = name of function
+%   xmin, xmax = endpoints of interval
+%   ns = number of subintervals (default = 50)
+% output:
+%   xb(k,1) is the lower bound of the kth sign change
+%   xb(k,2) is the upper bound of the kth sign change
+%   If no brackets found, xb = [].
+if nargin < 3, error('at least 3 arguments required'), end
+if nargin < 4, ns = 50; end %if ns blank set to 50
+% Incremental search
+x = linspace(xmin,xmax,ns);
+f = func(x);
+nb = 0; xb = []; %xb is null unless sign change detected
+%for k = 1:length(x)-1
+%  if sign(f(k)) ~= sign(f(k+1)) %check for sign change
+%    nb = nb + 1;
+%    xb(nb,1) = x(k);
+%    xb(nb,2) = x(k+1);
+%  end
+%end
+sign_change = diff(sign(f));
+[~,i_change] = find(sign_change~=0);
+nb=length(i_change);
+xb=[x(i_change)',x(i_change+1)'];
+
+if isempty(xb) %display that no brackets were found
+  fprintf('no brackets found\n')
+  fprintf('check interval or increase ns\n')
+else
+  fprintf('number of brackets: %i\n',nb) %display number of brackets
+end
diff --git a/lecture_07/lecture_07.ipynb b/lecture_07/lecture_07.ipynb
new file mode 100644
index 0000000..0c3c2ca
--- /dev/null
+++ b/lecture_07/lecture_07.ipynb
@@ -0,0 +1,1195 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%plot --format svg"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "setdefaults"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Roots: Open methods\n",
+    "## Newton-Raphson"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First-order approximation for the location of the root (i.e. assume the slope at the given point is constant, what is the solution when f(x)=0)\n",
+    "\n",
+    "$f'(x_{i})=\\frac{f(x_{i})-0}{x_{i}-x_{i+1}}$\n",
+    "\n",
+    "$x_{i+1}=x_{i}-\\frac{f(x_{i})}{f'(x_{i})}$\n",
+    "\n",
+    "Use Newton-Raphson to find solution when $e^{x}=x$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "error: 'c' undefined near line 1 column 1\n",
+      "error: 'x_r' undefined near line 1 column 21\n",
+      "error: evaluating argument list element number 1\n",
+      "error: 'x_r' undefined near line 1 column 5\n"
+     ]
+    }
+   ],
+   "source": [
+    "f= @(x) exp(-x)-x;\n",
+    "df= @(x) -exp(-x)-1;\n",
+    "\n",
+    "x_i= 0;\n",
+    "c\n",
+    "error_approx = abs((x_r-x_i)/x_r)\n",
+    "x_i=x_r;\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x_r =  0.50000\n",
+      "error_approx =  1\n"
+     ]
+    }
+   ],
+   "source": [
+    "x_r = x_i-f(x_i)/df(x_i)\n",
+    "error_approx = abs((x_r-x_i)/x_r)\n",
+    "x_i=x_r;"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x_r =  0.56631\n",
+      "error_approx =  0.11709\n"
+     ]
+    }
+   ],
+   "source": [
+    "x_r = x_i-f(x_i)/df(x_i)\n",
+    "error_approx = abs((x_r-x_i)/x_r)\n",
+    "x_i=x_r;"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x_r =  0.56714\n",
+      "error_approx =  0.0014673\n"
+     ]
+    }
+   ],
+   "source": [
+    "x_r = x_i-f(x_i)/df(x_i)\n",
+    "error_approx = abs((x_r-x_i)/x_r)\n",
+    "x_i=x_r;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In the bungee jumper example, we created a function f(m) that when f(m)=0, then the mass had been chosen such that at t=4 s, the velocity is 36 m/s. \n",
+    "\n",
+    "$f(m)=\\sqrt{\\frac{gm}{c_{d}}}\\tanh(\\sqrt{\\frac{gc_{d}}{m}}t)-v(t)$.\n",
+    "\n",
+    "to use the Newton-Raphson method, we need the derivative $\\frac{df}{dm}$\n",
+    "\n",
+    "$\\frac{df}{dm}=\\frac{1}{2}\\sqrt{\\frac{g}{mc_{d}}}\\tanh(\\sqrt{\\frac{gc_{d}}{m}}t)-\n",
+    "\\frac{g}{2m}\\mathrm{sech}^{2}(\\sqrt{\\frac{gc_{d}}{m}}t)$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "setdefaults\n",
+    "g=9.81; % acceleration due to gravity\n",
+    "m=linspace(50, 200,100); % possible values for mass 50 to 200 kg\n",
+    "c_d=0.25; % drag coefficient\n",
+    "t=4; % at time = 4 seconds\n",
+    "v=36; % speed must be 36 m/s\n",
+    "f_m = @(m) sqrt(g*m/c_d).*tanh(sqrt(g*c_d./m)*t)-v; % anonymous function f_m\n",
+    "df_m = @(m) 1/2*sqrt(g./m/c_d).*tanh(sqrt(g*c_d./m)*t)-g/2./m*sech(sqrt(g*c_d./m)*t).^2;"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  142.74\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "newtraph(f_m,df_m,140,0.00001)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Secant Methods"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Not always able to evaluate the derivative. Approximation of derivative:\n",
+    "\n",
+    "$f'(x_{i})=\\frac{f(x_{i-1})-f(x_{i})}{x_{i-1}-x_{i}}$\n",
+    "\n",
+    "$x_{i+1}=x_{i}-\\frac{f(x_{i})}{f'(x_{i})}$\n",
+    "\n",
+    "$x_{i+1}=x_{i}-\\frac{f(x_{i})}{\\frac{f(x_{i-1})-f(x_{i})}{x_{i-1}-x_{i}}}=\n",
+    "    x_{i}-\\frac{f(x_{i})(x_{i-1}-x_{i})}{f(x_{i-1})-f(x_{i})}$\n",
+    "    \n",
+    "What values should $x_{i}$ and $x_{i-1}$ take?\n",
+    "\n",
+    "To reduce arbitrary selection of variables, use the\n",
+    "\n",
+    "## Modified Secant method\n",
+    "\n",
+    "Change the x evaluations to a perturbation $\\delta$. \n",
+    "\n",
+    "$x_{i+1}=x_{i}-\\frac{f(x_{i})(\\delta x_{i})}{f(x_{i}+\\delta x_{i})-f(x_{i})}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  142.74\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "mod_secant(f_m,1e-6,50,0.00001)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Amt_numerical =  563.79\n",
+      "ans = -160.42\n"
+     ]
+    },
+    {
+     "data": {
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+       "\t\t<text><tspan font-family=\"{}\">5</tspan></text>\n",
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+       "\t<path d=\"M80.2,16.7 L80.2,362.4 L535.0,362.4 L535.0,16.7 L80.2,16.7 Z  \" stroke=\"black\"/></g>\n",
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+       "\t\t<text><tspan font-family=\"{}\">principle amount left ($)</tspan></text>\n",
+       "\t</g>\n",
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+       "\t\t<text><tspan font-family=\"{}\">time (years)</tspan></text>\n",
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+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "Amt_numerical=mod_secant(@(A) car_payments(A,30000,0.05,5),1e-6,50,0.001)\n",
+    "car_payments(Amt,30000,0.05,5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =    3.3968e+04\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "Amt*12*5"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Amortization calculation makes the same calculation for the monthly payment amount, A, paying off the principle amount, P, over n pay periods with monthly interest rate, r. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Amt =  566.14\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "% Amortization calculation\n",
+    "A  = @(P,r,n) P*(r*(1+r)^n)./((1+r)^n-1);\n",
+    "Amt=A(30000,0.05/12,5*12)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Matlab's function\n",
+    "\n",
+    "Matlab and Octave combine bracketing and open methods in the `fzero` function. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "'fzero' is a function from the file /usr/share/octave/4.0.0/m/optimization/fzero.m\n",
+      "\n",
+      " -- Function File: fzero (FUN, X0)\n",
+      " -- Function File: fzero (FUN, X0, OPTIONS)\n",
+      " -- Function File: [X, FVAL, INFO, OUTPUT] = fzero (...)\n",
+      "     Find a zero of a univariate function.\n",
+      "\n",
+      "     FUN is a function handle, inline function, or string containing the\n",
+      "     name of the function to evaluate.\n",
+      "\n",
+      "     X0 should be a two-element vector specifying two points which\n",
+      "     bracket a zero.  In other words, there must be a change in sign of\n",
+      "     the function between X0(1) and X0(2).  More mathematically, the\n",
+      "     following must hold\n",
+      "\n",
+      "          sign (FUN(X0(1))) * sign (FUN(X0(2))) <= 0\n",
+      "\n",
+      "     If X0 is a single scalar then several nearby and distant values are\n",
+      "     probed in an attempt to obtain a valid bracketing.  If this is not\n",
+      "     successful, the function fails.\n",
+      "\n",
+      "     OPTIONS is a structure specifying additional options.  Currently,\n",
+      "     'fzero' recognizes these options: \"FunValCheck\", \"OutputFcn\",\n",
+      "     \"TolX\", \"MaxIter\", \"MaxFunEvals\".  For a description of these\n",
+      "     options, see *note optimset: XREFoptimset.\n",
+      "\n",
+      "     On exit, the function returns X, the approximate zero point and\n",
+      "     FVAL, the function value thereof.\n",
+      "\n",
+      "     INFO is an exit flag that can have these values:\n",
+      "\n",
+      "        * 1 The algorithm converged to a solution.\n",
+      "\n",
+      "        * 0 Maximum number of iterations or function evaluations has\n",
+      "          been reached.\n",
+      "\n",
+      "        * -1 The algorithm has been terminated from user output\n",
+      "          function.\n",
+      "\n",
+      "        * -5 The algorithm may have converged to a singular point.\n",
+      "\n",
+      "     OUTPUT is a structure containing runtime information about the\n",
+      "     'fzero' algorithm.  Fields in the structure are:\n",
+      "\n",
+      "        * iterations Number of iterations through loop.\n",
+      "\n",
+      "        * nfev Number of function evaluations.\n",
+      "\n",
+      "        * bracketx A two-element vector with the final bracketing of the\n",
+      "          zero along the x-axis.\n",
+      "\n",
+      "        * brackety A two-element vector with the final bracketing of the\n",
+      "          zero along the y-axis.\n",
+      "\n",
+      "     See also: optimset, fsolve.\n",
+      "\n",
+      "Additional help for built-in functions and operators is\n",
+      "available in the online version of the manual.  Use the command\n",
+      "'doc <topic>' to search the manual index.\n",
+      "\n",
+      "Help and information about Octave is also available on the WWW\n",
+      "at http://www.octave.org and via the help@octave.org\n",
+      "mailing list.\n"
+     ]
+    }
+   ],
+   "source": [
+    "help fzero"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  563.79\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "fzero(@(A) car_payments(A,30000,0.05,5,0),500)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Comparison of Solvers\n",
+    "\n",
+    "It's helpful to compare to the convergence of different routines to see how quickly you find a solution. \n",
+    "\n",
+    "Comparing the freefall example\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 84,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: called from\n",
+      "    __line__ at line 120 column 16\n",
+      "    line at line 56 column 8\n",
+      "    __plt__>__plt2vv__ at line 500 column 10\n",
+      "    __plt__>__plt2__ at line 246 column 14\n",
+      "    __plt__ at line 133 column 15\n",
+      "    semilogy at line 60 column 10\n",
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: axis: omitting non-positive data in log plot\n"
+     ]
+    },
+    {
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+       "\t<g id=\"gnuplot_plot_1a\"><title>newton-raphson</title>\n",
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+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "N=20;\n",
+    "iterations = linspace(1,400,N);\n",
+    "ea_nr=zeros(1,N); % appr error Newton-Raphson\n",
+    "ea_ms=zeros(1,N); % appr error Modified Secant\n",
+    "ea_fp=zeros(1,N); % appr error false point method\n",
+    "ea_bs=zeros(1,N); % appr error bisect method\n",
+    "for i=1:length(iterations)\n",
+    "    [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,200,0,iterations(i));\n",
+    "    [root_ms,ea_ms(i),iter_ms]=mod_secant(f_m,1e-6,300,0,iterations(i));\n",
+    "    [root_fp,ea_fp(i),iter_fp]=falsepos(f_m,1,300,0,iterations(i));\n",
+    "    [root_bs,ea_bs(i),iter_bs]=bisect(f_m,1,300,0,iterations(i));\n",
+    "end\n",
+    "        \n",
+    "semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))\n",
+    "legend('newton-raphson','mod-secant','false point','bisection')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 75,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ea_ms =\n",
+      "\n",
+      " Columns 1 through 7:\n",
+      "\n",
+      "   43.43883    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000\n",
+      "\n",
+      " Columns 8 through 14:\n",
+      "\n",
+      "    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000\n",
+      "\n",
+      " Columns 15 through 20:\n",
+      "\n",
+      "    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "ea_ms"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 101,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: called from\n",
+      "    __line__ at line 120 column 16\n",
+      "    line at line 56 column 8\n",
+      "    __plt__>__plt2vv__ at line 500 column 10\n",
+      "    __plt__>__plt2__ at line 246 column 14\n",
+      "    __plt__ at line 133 column 15\n",
+      "    semilogy at line 60 column 10\n",
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: axis: omitting non-positive data in log plot\n"
+     ]
+    },
+    {
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+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<path d=\"M304.9,193.7 L358.7,193.7 M63.5,17.1 L88.3,100.3 L113.2,107.1 L138.0,117.6 L162.8,144.5 L187.6,156.2   L212.4,164.4 L237.2,191.1 L262.0,202.7 L286.9,211.0 L311.7,222.6 L336.5,249.3 L361.3,260.9 L386.1,269.1   L410.9,295.8 L435.7,307.5 L460.6,315.7 L485.4,327.3 L510.2,354.0 L535.0,365.7  \" stroke=\"rgb(  0, 191, 191)\"/></g>\n",
+       "\t</g>\n",
+       "<g color=\"white\" fill=\"none\" stroke=\"rgb(  0, 191, 191)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "N=20;\n",
+    "f= @(x) x^10-1;\n",
+    "df=@(x) 10*x^9;\n",
+    "iterations = linspace(1,50,N);\n",
+    "ea_nr=zeros(1,N); % appr error Newton-Raphson\n",
+    "ea_ms=zeros(1,N); % appr error Modified Secant\n",
+    "ea_fp=zeros(1,N); % appr error false point method\n",
+    "ea_bs=zeros(1,N); % appr error bisect method\n",
+    "for i=1:length(iterations)\n",
+    "    [root_nr,ea_nr(i),iter_nr]=newtraph(f,df,0.5,0,iterations(i));\n",
+    "    [root_ms,ea_ms(i),iter_ms]=mod_secant(f,1e-6,0.5,0,iterations(i));\n",
+    "    [root_fp,ea_fp(i),iter_fp]=falsepos(f,0,5,0,iterations(i));\n",
+    "    [root_bs,ea_bs(i),iter_bs]=bisect(f,0,5,0,iterations(i));\n",
+    "end\n",
+    "        \n",
+    "semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))\n",
+    "legend('newton-raphson','mod-secant','false point','bisection')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 102,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ea_bs =\n",
+      "\n",
+      " Columns 1 through 6:\n",
+      "\n",
+      "   9.5357e+03  -4.7554e-01  -2.1114e-01   6.0163e-02  -2.4387e-03   6.1052e-04\n",
+      "\n",
+      " Columns 7 through 12:\n",
+      "\n",
+      "   2.2891e-04  -9.5367e-06   2.3842e-06   8.9407e-07  -2.2352e-07   9.3132e-09\n",
+      "\n",
+      " Columns 13 through 18:\n",
+      "\n",
+      "  -2.3283e-09  -8.7311e-10   3.6380e-11  -9.0949e-12  -3.4106e-12   8.5265e-13\n",
+      "\n",
+      " Columns 19 and 20:\n",
+      "\n",
+      "  -3.5527e-14   8.8818e-15\n",
+      "\n",
+      "ans =  16.208\n"
+     ]
+    }
+   ],
+   "source": [
+    "ea_bs\n",
+    "newtraph(f,df,0.5,0,12)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =    1.9683e+23\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "df(300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Octave",
+   "language": "octave",
+   "name": "octave"
+  },
+  "language_info": {
+   "file_extension": ".m",
+   "help_links": [
+    {
+     "text": "MetaKernel Magics",
+     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+    }
+   ],
+   "mimetype": "text/x-octave",
+   "name": "octave",
+   "version": "0.19.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/lecture_07/lecture_07.md b/lecture_07/lecture_07.md
new file mode 100644
index 0000000..020699b
--- /dev/null
+++ b/lecture_07/lecture_07.md
@@ -0,0 +1,388 @@
+
+
+```octave
+%plot --format svg
+```
+
+
+```octave
+setdefaults
+```
+
+# Roots: Open methods
+## Newton-Raphson
+
+First-order approximation for the location of the root (i.e. assume the slope at the given point is constant, what is the solution when f(x)=0)
+
+$f'(x_{i})=\frac{f(x_{i})-0}{x_{i}-x_{i+1}}$
+
+$x_{i+1}=x_{i}-\frac{f(x_{i})}{f'(x_{i})}$
+
+Use Newton-Raphson to find solution when $e^{x}=x$
+
+
+```octave
+f= @(x) exp(-x)-x;
+df= @(x) -exp(-x)-1;
+
+x_i= 0;
+c
+error_approx = abs((x_r-x_i)/x_r)
+x_i=x_r;
+
+```
+
+    error: 'c' undefined near line 1 column 1
+    error: 'x_r' undefined near line 1 column 21
+    error: evaluating argument list element number 1
+    error: 'x_r' undefined near line 1 column 5
+
+
+
+```octave
+x_r = x_i-f(x_i)/df(x_i)
+error_approx = abs((x_r-x_i)/x_r)
+x_i=x_r;
+```
+
+    x_r =  0.50000
+    error_approx =  1
+
+
+
+```octave
+x_r = x_i-f(x_i)/df(x_i)
+error_approx = abs((x_r-x_i)/x_r)
+x_i=x_r;
+```
+
+    x_r =  0.56631
+    error_approx =  0.11709
+
+
+
+```octave
+x_r = x_i-f(x_i)/df(x_i)
+error_approx = abs((x_r-x_i)/x_r)
+x_i=x_r;
+```
+
+    x_r =  0.56714
+    error_approx =  0.0014673
+
+
+In the bungee jumper example, we created a function f(m) that when f(m)=0, then the mass had been chosen such that at t=4 s, the velocity is 36 m/s. 
+
+$f(m)=\sqrt{\frac{gm}{c_{d}}}\tanh(\sqrt{\frac{gc_{d}}{m}}t)-v(t)$.
+
+to use the Newton-Raphson method, we need the derivative $\frac{df}{dm}$
+
+$\frac{df}{dm}=\frac{1}{2}\sqrt{\frac{g}{mc_{d}}}\tanh(\sqrt{\frac{gc_{d}}{m}}t)-
+\frac{g}{2m}\mathrm{sech}^{2}(\sqrt{\frac{gc_{d}}{m}}t)$
+
+
+```octave
+setdefaults
+g=9.81; % acceleration due to gravity
+m=linspace(50, 200,100); % possible values for mass 50 to 200 kg
+c_d=0.25; % drag coefficient
+t=4; % at time = 4 seconds
+v=36; % speed must be 36 m/s
+f_m = @(m) sqrt(g*m/c_d).*tanh(sqrt(g*c_d./m)*t)-v; % anonymous function f_m
+df_m = @(m) 1/2*sqrt(g./m/c_d).*tanh(sqrt(g*c_d./m)*t)-g/2./m*sech(sqrt(g*c_d./m)*t).^2;
+```
+
+
+```octave
+newtraph(f_m,df_m,140,0.00001)
+```
+
+    ans =  142.74
+
+
+## Secant Methods
+
+Not always able to evaluate the derivative. Approximation of derivative:
+
+$f'(x_{i})=\frac{f(x_{i-1})-f(x_{i})}{x_{i-1}-x_{i}}$
+
+$x_{i+1}=x_{i}-\frac{f(x_{i})}{f'(x_{i})}$
+
+$x_{i+1}=x_{i}-\frac{f(x_{i})}{\frac{f(x_{i-1})-f(x_{i})}{x_{i-1}-x_{i}}}=
+    x_{i}-\frac{f(x_{i})(x_{i-1}-x_{i})}{f(x_{i-1})-f(x_{i})}$
+    
+What values should $x_{i}$ and $x_{i-1}$ take?
+
+To reduce arbitrary selection of variables, use the
+
+## Modified Secant method
+
+Change the x evaluations to a perturbation $\delta$. 
+
+$x_{i+1}=x_{i}-\frac{f(x_{i})(\delta x_{i})}{f(x_{i}+\delta x_{i})-f(x_{i})}$
+
+
+```octave
+mod_secant(f_m,1e-6,50,0.00001)
+```
+
+    ans =  142.74
+
+
+
+```octave
+Amt_numerical=mod_secant(@(A) car_payments(A,30000,0.05,5),1e-6,50,0.001)
+car_payments(Amt,30000,0.05,5)
+```
+
+    Amt_numerical =  563.79
+    ans = -160.42
+
+
+
+![svg](lecture_07_files/lecture_07_14_1.svg)
+
+
+
+```octave
+Amt*12*5
+```
+
+    ans =    3.3968e+04
+
+
+Amortization calculation makes the same calculation for the monthly payment amount, A, paying off the principle amount, P, over n pay periods with monthly interest rate, r. 
+
+
+```octave
+% Amortization calculation
+A  = @(P,r,n) P*(r*(1+r)^n)./((1+r)^n-1);
+Amt=A(30000,0.05/12,5*12)
+```
+
+    Amt =  566.14
+
+
+## Matlab's function
+
+Matlab and Octave combine bracketing and open methods in the `fzero` function. 
+
+
+```octave
+help fzero
+```
+
+    'fzero' is a function from the file /usr/share/octave/4.0.0/m/optimization/fzero.m
+    
+     -- Function File: fzero (FUN, X0)
+     -- Function File: fzero (FUN, X0, OPTIONS)
+     -- Function File: [X, FVAL, INFO, OUTPUT] = fzero (...)
+         Find a zero of a univariate function.
+    
+         FUN is a function handle, inline function, or string containing the
+         name of the function to evaluate.
+    
+         X0 should be a two-element vector specifying two points which
+         bracket a zero.  In other words, there must be a change in sign of
+         the function between X0(1) and X0(2).  More mathematically, the
+         following must hold
+    
+              sign (FUN(X0(1))) * sign (FUN(X0(2))) <= 0
+    
+         If X0 is a single scalar then several nearby and distant values are
+         probed in an attempt to obtain a valid bracketing.  If this is not
+         successful, the function fails.
+    
+         OPTIONS is a structure specifying additional options.  Currently,
+         'fzero' recognizes these options: "FunValCheck", "OutputFcn",
+         "TolX", "MaxIter", "MaxFunEvals".  For a description of these
+         options, see *note optimset: XREFoptimset.
+    
+         On exit, the function returns X, the approximate zero point and
+         FVAL, the function value thereof.
+    
+         INFO is an exit flag that can have these values:
+    
+            * 1 The algorithm converged to a solution.
+    
+            * 0 Maximum number of iterations or function evaluations has
+              been reached.
+    
+            * -1 The algorithm has been terminated from user output
+              function.
+    
+            * -5 The algorithm may have converged to a singular point.
+    
+         OUTPUT is a structure containing runtime information about the
+         'fzero' algorithm.  Fields in the structure are:
+    
+            * iterations Number of iterations through loop.
+    
+            * nfev Number of function evaluations.
+    
+            * bracketx A two-element vector with the final bracketing of the
+              zero along the x-axis.
+    
+            * brackety A two-element vector with the final bracketing of the
+              zero along the y-axis.
+    
+         See also: optimset, fsolve.
+    
+    Additional help for built-in functions and operators is
+    available in the online version of the manual.  Use the command
+    'doc <topic>' to search the manual index.
+    
+    Help and information about Octave is also available on the WWW
+    at http://www.octave.org and via the help@octave.org
+    mailing list.
+
+
+
+```octave
+fzero(@(A) car_payments(A,30000,0.05,5,0),500)
+```
+
+    ans =  563.79
+
+
+## Comparison of Solvers
+
+It's helpful to compare to the convergence of different routines to see how quickly you find a solution. 
+
+Comparing the freefall example
+
+
+
+```octave
+N=20;
+iterations = linspace(1,400,N);
+ea_nr=zeros(1,N); % appr error Newton-Raphson
+ea_ms=zeros(1,N); % appr error Modified Secant
+ea_fp=zeros(1,N); % appr error false point method
+ea_bs=zeros(1,N); % appr error bisect method
+for i=1:length(iterations)
+    [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,200,0,iterations(i));
+    [root_ms,ea_ms(i),iter_ms]=mod_secant(f_m,1e-6,300,0,iterations(i));
+    [root_fp,ea_fp(i),iter_fp]=falsepos(f_m,1,300,0,iterations(i));
+    [root_bs,ea_bs(i),iter_bs]=bisect(f_m,1,300,0,iterations(i));
+end
+        
+semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))
+legend('newton-raphson','mod-secant','false point','bisection')
+```
+
+    warning: axis: omitting non-positive data in log plot
+    warning: called from
+        __line__ at line 120 column 16
+        line at line 56 column 8
+        __plt__>__plt2vv__ at line 500 column 10
+        __plt__>__plt2__ at line 246 column 14
+        __plt__ at line 133 column 15
+        semilogy at line 60 column 10
+    warning: axis: omitting non-positive data in log plot
+    warning: axis: omitting non-positive data in log plot
+    warning: axis: omitting non-positive data in log plot
+
+
+
+![svg](lecture_07_files/lecture_07_22_1.svg)
+
+
+
+```octave
+ea_ms
+```
+
+    ea_ms =
+    
+     Columns 1 through 7:
+    
+       43.43883    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
+    
+     Columns 8 through 14:
+    
+        0.00000    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
+    
+     Columns 15 through 20:
+    
+        0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
+    
+
+
+
+```octave
+N=20;
+f= @(x) x^10-1;
+df=@(x) 10*x^9;
+iterations = linspace(1,50,N);
+ea_nr=zeros(1,N); % appr error Newton-Raphson
+ea_ms=zeros(1,N); % appr error Modified Secant
+ea_fp=zeros(1,N); % appr error false point method
+ea_bs=zeros(1,N); % appr error bisect method
+for i=1:length(iterations)
+    [root_nr,ea_nr(i),iter_nr]=newtraph(f,df,0.5,0,iterations(i));
+    [root_ms,ea_ms(i),iter_ms]=mod_secant(f,1e-6,0.5,0,iterations(i));
+    [root_fp,ea_fp(i),iter_fp]=falsepos(f,0,5,0,iterations(i));
+    [root_bs,ea_bs(i),iter_bs]=bisect(f,0,5,0,iterations(i));
+end
+        
+semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))
+legend('newton-raphson','mod-secant','false point','bisection')
+```
+
+    warning: axis: omitting non-positive data in log plot
+    warning: called from
+        __line__ at line 120 column 16
+        line at line 56 column 8
+        __plt__>__plt2vv__ at line 500 column 10
+        __plt__>__plt2__ at line 246 column 14
+        __plt__ at line 133 column 15
+        semilogy at line 60 column 10
+    warning: axis: omitting non-positive data in log plot
+    warning: axis: omitting non-positive data in log plot
+    warning: axis: omitting non-positive data in log plot
+
+
+
+![svg](lecture_07_files/lecture_07_24_1.svg)
+
+
+
+```octave
+ea_bs
+newtraph(f,df,0.5,0,12)
+```
+
+    ea_bs =
+    
+     Columns 1 through 6:
+    
+       9.5357e+03  -4.7554e-01  -2.1114e-01   6.0163e-02  -2.4387e-03   6.1052e-04
+    
+     Columns 7 through 12:
+    
+       2.2891e-04  -9.5367e-06   2.3842e-06   8.9407e-07  -2.2352e-07   9.3132e-09
+    
+     Columns 13 through 18:
+    
+      -2.3283e-09  -8.7311e-10   3.6380e-11  -9.0949e-12  -3.4106e-12   8.5265e-13
+    
+     Columns 19 and 20:
+    
+      -3.5527e-14   8.8818e-15
+    
+    ans =  16.208
+
+
+
+```octave
+df(300)
+```
+
+    ans =    1.9683e+23
+
+
+
+```octave
+
+```
diff --git a/lecture_07/lecture_07.pdf b/lecture_07/lecture_07.pdf
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+		<text><tspan font-family="{}">20000</tspan></text>
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+		<text><tspan font-family="{}">30000</tspan></text>
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+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+		<text><tspan font-family="{}">0</tspan></text>
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+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+		<text><tspan font-family="{}">1</tspan></text>
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+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M262.1,362.4 L262.1,349.9 M262.1,16.7 L262.1,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(262.1,386.4)">
+		<text><tspan font-family="{}">2</tspan></text>
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+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M353.1,362.4 L353.1,349.9 M353.1,16.7 L353.1,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(353.1,386.4)">
+		<text><tspan font-family="{}">3</tspan></text>
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+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M444.0,362.4 L444.0,349.9 M444.0,16.7 L444.0,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(444.0,386.4)">
+		<text><tspan font-family="{}">4</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M535.0,362.4 L535.0,349.9 M535.0,16.7 L535.0,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(535.0,386.4)">
+		<text><tspan font-family="{}">5</tspan></text>
+	</g>
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+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M80.2,16.7 L80.2,362.4 L535.0,362.4 L535.0,16.7 L80.2,16.7 Z  " stroke="black"/></g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(19.1,189.6) rotate(-90)">
+		<text><tspan font-family="{}">principle amount left ($)</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(307.6,413.4)">
+		<text><tspan font-family="{}">time (years)</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+	<g id="gnuplot_plot_1a"><title>gnuplot_plot_1a</title>
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new file mode 100644
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+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M53.9,16.7 L60.1,16.7 M535.0,16.7 L528.8,16.7 M53.9,16.7 L66.4,16.7 M535.0,16.7 L522.5,16.7    " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(45.6,22.7)">
+		<text><tspan font-family="{}">10</tspan><tspan dy="-8.00px" font-family="{}" font-size="12.8">4</tspan><tspan dy="8.00" font-size="16.0"/></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M53.9,384.0 L53.9,371.5 M53.9,16.7 L53.9,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(53.9,408.0)">
+		<text><tspan font-family="{}">0</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M150.1,384.0 L150.1,371.5 M150.1,16.7 L150.1,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(150.1,408.0)">
+		<text><tspan font-family="{}">10</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M246.3,384.0 L246.3,371.5 M246.3,16.7 L246.3,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(246.3,408.0)">
+		<text><tspan font-family="{}">20</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M342.6,384.0 L342.6,371.5 M342.6,16.7 L342.6,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(342.6,408.0)">
+		<text><tspan font-family="{}">30</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M438.8,384.0 L438.8,371.5 M438.8,16.7 L438.8,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(438.8,408.0)">
+		<text><tspan font-family="{}">40</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M535.0,384.0 L535.0,371.5 M535.0,16.7 L535.0,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(535.0,408.0)">
+		<text><tspan font-family="{}">50</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M53.9,16.7 L53.9,384.0 L535.0,384.0 L535.0,16.7 L53.9,16.7 Z  " stroke="black"/></g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="black" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="1.00">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="1.00">
+	<path d="M293.7,217.7 L293.7,25.7 L526.7,25.7 L526.7,217.7 L293.7,217.7 Z  " stroke="black"/></g>
+	<g id="gnuplot_plot_1a"><title>newton-raphson</title>
+<g color="white" fill="none" stroke="black" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(526.7,55.7)">
+		<text><tspan font-family="{}">newton-raphson</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<path d="M304.9,49.7 L358.7,49.7 M63.5,55.4 L88.3,73.8 L113.2,73.8 L138.0,73.8 L162.8,73.8 L187.6,73.8   L212.4,73.8 L237.2,73.8 L262.0,73.8 L286.9,73.8 L311.7,73.8 L336.5,73.8 L361.3,73.8 L386.1,73.9   L410.9,75.8 L435.7,87.7 L460.6,221.4  " stroke="rgb(  0,   0, 255)"/></g>
+	</g>
+	<g id="gnuplot_plot_2a"><title>mod-secant</title>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(526.7,103.7)">
+		<text><tspan font-family="{}">mod-secant</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<path d="M304.9,97.7 L358.7,97.7 M63.5,55.4 L88.3,73.8 L113.2,73.8 L138.0,73.8 L162.8,73.8 L187.6,73.8   L212.4,73.8 L237.2,73.8 L262.0,73.8 L286.9,73.8 L311.7,73.8 L336.5,73.8 L361.3,73.8 L386.1,73.9   L410.9,75.8 L435.7,87.7 L460.6,221.0  " stroke="rgb(  0, 128,   0)"/></g>
+	</g>
+	<g id="gnuplot_plot_3a"><title>false point</title>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(526.7,151.7)">
+		<text><tspan font-family="{}">false point</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<path d="M304.9,145.7 L358.7,145.7 M63.5,94.0 L88.3,94.0 L113.2,94.0 L138.0,94.0 L162.8,94.0 L187.6,94.0   L212.4,94.0 L237.2,94.0 L262.0,94.0 L286.9,94.0 L311.7,94.0 L336.5,94.0 L361.3,94.0 L386.1,94.0   L410.9,94.0 L435.7,94.0 L460.6,94.0 L485.4,94.0 L510.2,94.0 L535.0,94.0  " stroke="rgb(255,   0,   0)"/></g>
+	</g>
+	<g id="gnuplot_plot_4a"><title>bisection</title>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(526.7,199.7)">
+		<text><tspan font-family="{}">bisection</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<path d="M304.9,193.7 L358.7,193.7 M63.5,17.1 L88.3,100.3 L113.2,107.1 L138.0,117.6 L162.8,144.5 L187.6,156.2   L212.4,164.4 L237.2,191.1 L262.0,202.7 L286.9,211.0 L311.7,222.6 L336.5,249.3 L361.3,260.9 L386.1,269.1   L410.9,295.8 L435.7,307.5 L460.6,315.7 L485.4,327.3 L510.2,354.0 L535.0,365.7  " stroke="rgb(  0, 191, 191)"/></g>
+	</g>
+<g color="white" fill="none" stroke="rgb(  0, 191, 191)" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="2.00">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="2.00">
+</g>
+<g color="black" fill="none" stroke="black" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+</g>
+</svg>
\ No newline at end of file
diff --git a/lecture_07/mod_secant.m b/lecture_07/mod_secant.m
new file mode 100644
index 0000000..a3caa10
--- /dev/null
+++ b/lecture_07/mod_secant.m
@@ -0,0 +1,31 @@
+function [root,ea,iter]=mod_secant(func,dx,xr,es,maxit,varargin)
+% newtraph: Modified secant root location zeroes
+% [root,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):
+%   uses modified secant method to find the root of func
+% input:
+%   func = name of function
+%   dx = perturbation fraction
+%   xr = initial guess
+%   es = desired relative error (default = 0.0001%)
+%   maxit = maximum allowable iterations (default = 50)
+%   p1,p2,... = additional parameters used by function
+% output:
+%   root = real root
+%   ea = approximate relative error (%)
+%   iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+if nargin<4 || isempty(es),es=0.0001;end
+if nargin<5 || isempty(maxit),maxit=50;end
+iter = 0;
+while (1)
+  xrold = xr;
+  dfunc=(func(xr+dx)-func(xr))./dx;
+  xr = xr - func(xr)/dfunc;
+  iter = iter + 1;
+  if xr ~= 0 
+    ea = abs((xr - xrold)/xr) * 100;
+  end
+  if ea <= es || iter >= maxit, break, end
+end
+root = xr;
+
diff --git a/lecture_07/newtraph.m b/lecture_07/newtraph.m
new file mode 100644
index 0000000..94ca667
--- /dev/null
+++ b/lecture_07/newtraph.m
@@ -0,0 +1,29 @@
+function [root,ea,iter]=newtraph(func,dfunc,xr,es,maxit,varargin)
+% newtraph: Newton-Raphson root location zeroes
+% [root,ea,iter]=newtraph(func,dfunc,xr,es,maxit,p1,p2,...):
+%   uses Newton-Raphson method to find the root of func
+% input:
+%   func = name of function
+%   dfunc = name of derivative of function
+%   xr = initial guess
+%   es = desired relative error (default = 0.0001%)
+%   maxit = maximum allowable iterations (default = 50)
+%   p1,p2,... = additional parameters used by function
+% output:
+%   root = real root
+%   ea = approximate relative error (%)
+%   iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+if nargin<4 || isempty(es),es=0.0001;end
+if nargin<5 || isempty(maxit),maxit=50;end
+iter = 0;
+while (1)
+  xrold = xr;
+  xr = xr - func(xr)/dfunc(xr);
+  iter = iter + 1;
+  if xr ~= 0 
+    ea = abs((xr - xrold)/xr) * 100;
+  end
+  if ea <= es || iter >= maxit, break, end
+end
+root = xr;

From 128293527542aee47063ab0300509de8f9ae9967 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Mon, 6 Feb 2017 23:09:42 -0500
Subject: [PATCH 28/37] updated lecture 07 output

---
 .../lecture_07-checkpoint.ipynb               | 1042 +++++++++++++++++
 lecture_07/lecture_07.ipynb                   |  229 +---
 lecture_07/octave-workspace                   |  Bin 0 -> 3219 bytes
 3 files changed, 1080 insertions(+), 191 deletions(-)
 create mode 100644 lecture_07/.ipynb_checkpoints/lecture_07-checkpoint.ipynb
 create mode 100644 lecture_07/octave-workspace

diff --git a/lecture_07/.ipynb_checkpoints/lecture_07-checkpoint.ipynb b/lecture_07/.ipynb_checkpoints/lecture_07-checkpoint.ipynb
new file mode 100644
index 0000000..d7ff495
--- /dev/null
+++ b/lecture_07/.ipynb_checkpoints/lecture_07-checkpoint.ipynb
@@ -0,0 +1,1042 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%plot --format svg"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "setdefaults"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Roots: Open methods\n",
+    "## Newton-Raphson"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First-order approximation for the location of the root (i.e. assume the slope at the given point is constant, what is the solution when f(x)=0)\n",
+    "\n",
+    "$f'(x_{i})=\\frac{f(x_{i})-0}{x_{i}-x_{i+1}}$\n",
+    "\n",
+    "$x_{i+1}=x_{i}-\\frac{f(x_{i})}{f'(x_{i})}$\n",
+    "\n",
+    "Use Newton-Raphson to find solution when $e^{x}=x$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "error_approx =  1\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "f= @(x) exp(-x)-x;\n",
+    "df= @(x) -exp(-x)-1;\n",
+    "\n",
+    "x_i= 0;\n",
+    "error_approx = abs((x_r-x_i)/x_r)\n",
+    "x_r=x_i;\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x_r =  0.50000\n",
+      "error_approx =  1\n"
+     ]
+    }
+   ],
+   "source": [
+    "x_r = x_i-f(x_i)/df(x_i)\n",
+    "error_approx = abs((x_r-x_i)/x_r)\n",
+    "x_i=x_r;"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x_r =  0.56631\n",
+      "error_approx =  0.11709\n"
+     ]
+    }
+   ],
+   "source": [
+    "x_r = x_i-f(x_i)/df(x_i)\n",
+    "error_approx = abs((x_r-x_i)/x_r)\n",
+    "x_i=x_r;"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x_r =  0.56714\n",
+      "error_approx =  0.0014673\n"
+     ]
+    }
+   ],
+   "source": [
+    "x_r = x_i-f(x_i)/df(x_i)\n",
+    "error_approx = abs((x_r-x_i)/x_r)\n",
+    "x_i=x_r;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In the bungee jumper example, we created a function f(m) that when f(m)=0, then the mass had been chosen such that at t=4 s, the velocity is 36 m/s. \n",
+    "\n",
+    "$f(m)=\\sqrt{\\frac{gm}{c_{d}}}\\tanh(\\sqrt{\\frac{gc_{d}}{m}}t)-v(t)$.\n",
+    "\n",
+    "to use the Newton-Raphson method, we need the derivative $\\frac{df}{dm}$\n",
+    "\n",
+    "$\\frac{df}{dm}=\\frac{1}{2}\\sqrt{\\frac{g}{mc_{d}}}\\tanh(\\sqrt{\\frac{gc_{d}}{m}}t)-\n",
+    "\\frac{g}{2m}\\mathrm{sech}^{2}(\\sqrt{\\frac{gc_{d}}{m}}t)$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "setdefaults\n",
+    "g=9.81; % acceleration due to gravity\n",
+    "m=linspace(50, 200,100); % possible values for mass 50 to 200 kg\n",
+    "c_d=0.25; % drag coefficient\n",
+    "t=4; % at time = 4 seconds\n",
+    "v=36; % speed must be 36 m/s\n",
+    "f_m = @(m) sqrt(g*m/c_d).*tanh(sqrt(g*c_d./m)*t)-v; % anonymous function f_m\n",
+    "df_m = @(m) 1/2*sqrt(g./m/c_d).*tanh(sqrt(g*c_d./m)*t)-g/2./m*sech(sqrt(g*c_d./m)*t).^2;"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  142.74\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "newtraph(f_m,df_m,140,0.00001)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Secant Methods"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Not always able to evaluate the derivative. Approximation of derivative:\n",
+    "\n",
+    "$f'(x_{i})=\\frac{f(x_{i-1})-f(x_{i})}{x_{i-1}-x_{i}}$\n",
+    "\n",
+    "$x_{i+1}=x_{i}-\\frac{f(x_{i})}{f'(x_{i})}$\n",
+    "\n",
+    "$x_{i+1}=x_{i}-\\frac{f(x_{i})}{\\frac{f(x_{i-1})-f(x_{i})}{x_{i-1}-x_{i}}}=\n",
+    "    x_{i}-\\frac{f(x_{i})(x_{i-1}-x_{i})}{f(x_{i-1})-f(x_{i})}$\n",
+    "    \n",
+    "What values should $x_{i}$ and $x_{i-1}$ take?\n",
+    "\n",
+    "To reduce arbitrary selection of variables, use the\n",
+    "\n",
+    "## Modified Secant method\n",
+    "\n",
+    "Change the x evaluations to a perturbation $\\delta$. \n",
+    "\n",
+    "$x_{i+1}=x_{i}-\\frac{f(x_{i})(\\delta x_{i})}{f(x_{i}+\\delta x_{i})-f(x_{i})}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  142.74\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "mod_secant(f_m,1e-6,50,0.00001)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "error: 'plot_bool' undefined near line 12 column 6\n",
+      "error: called from\n",
+      "    car_payments at line 12 column 3\n",
+      "    mod_secant at line 22 column 8\n",
+      "error: 'Amt' undefined near line 1 column 14\n",
+      "error: evaluating argument list element number 1\n"
+     ]
+    }
+   ],
+   "source": [
+    "Amt_numerical=mod_secant(@(A) car_payments(A,30000,0.05,5),1e-6,50,0.001)\n",
+    "car_payments(Amt,30000,0.05,5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "error: 'Amt' undefined near line 1 column 1\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "Amt*12*5"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Amortization calculation makes the same calculation for the monthly payment amount, A, paying off the principle amount, P, over n pay periods with monthly interest rate, r. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Amt =  566.14\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "% Amortization calculation\n",
+    "A  = @(P,r,n) P*(r*(1+r)^n)./((1+r)^n-1);\n",
+    "Amt=A(30000,0.05/12,5*12)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Matlab's function\n",
+    "\n",
+    "Matlab and Octave combine bracketing and open methods in the `fzero` function. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "'fzero' is a function from the file /usr/share/octave/4.0.0/m/optimization/fzero.m\n",
+      "\n",
+      " -- Function File: fzero (FUN, X0)\n",
+      " -- Function File: fzero (FUN, X0, OPTIONS)\n",
+      " -- Function File: [X, FVAL, INFO, OUTPUT] = fzero (...)\n",
+      "     Find a zero of a univariate function.\n",
+      "\n",
+      "     FUN is a function handle, inline function, or string containing the\n",
+      "     name of the function to evaluate.\n",
+      "\n",
+      "     X0 should be a two-element vector specifying two points which\n",
+      "     bracket a zero.  In other words, there must be a change in sign of\n",
+      "     the function between X0(1) and X0(2).  More mathematically, the\n",
+      "     following must hold\n",
+      "\n",
+      "          sign (FUN(X0(1))) * sign (FUN(X0(2))) <= 0\n",
+      "\n",
+      "     If X0 is a single scalar then several nearby and distant values are\n",
+      "     probed in an attempt to obtain a valid bracketing.  If this is not\n",
+      "     successful, the function fails.\n",
+      "\n",
+      "     OPTIONS is a structure specifying additional options.  Currently,\n",
+      "     'fzero' recognizes these options: \"FunValCheck\", \"OutputFcn\",\n",
+      "     \"TolX\", \"MaxIter\", \"MaxFunEvals\".  For a description of these\n",
+      "     options, see *note optimset: XREFoptimset.\n",
+      "\n",
+      "     On exit, the function returns X, the approximate zero point and\n",
+      "     FVAL, the function value thereof.\n",
+      "\n",
+      "     INFO is an exit flag that can have these values:\n",
+      "\n",
+      "        * 1 The algorithm converged to a solution.\n",
+      "\n",
+      "        * 0 Maximum number of iterations or function evaluations has\n",
+      "          been reached.\n",
+      "\n",
+      "        * -1 The algorithm has been terminated from user output\n",
+      "          function.\n",
+      "\n",
+      "        * -5 The algorithm may have converged to a singular point.\n",
+      "\n",
+      "     OUTPUT is a structure containing runtime information about the\n",
+      "     'fzero' algorithm.  Fields in the structure are:\n",
+      "\n",
+      "        * iterations Number of iterations through loop.\n",
+      "\n",
+      "        * nfev Number of function evaluations.\n",
+      "\n",
+      "        * bracketx A two-element vector with the final bracketing of the\n",
+      "          zero along the x-axis.\n",
+      "\n",
+      "        * brackety A two-element vector with the final bracketing of the\n",
+      "          zero along the y-axis.\n",
+      "\n",
+      "     See also: optimset, fsolve.\n",
+      "\n",
+      "Additional help for built-in functions and operators is\n",
+      "available in the online version of the manual.  Use the command\n",
+      "'doc <topic>' to search the manual index.\n",
+      "\n",
+      "Help and information about Octave is also available on the WWW\n",
+      "at http://www.octave.org and via the help@octave.org\n",
+      "mailing list.\n"
+     ]
+    }
+   ],
+   "source": [
+    "help fzero"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  563.79\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "fzero(@(A) car_payments(A,30000,0.05,5,0),500)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Comparison of Solvers\n",
+    "\n",
+    "It's helpful to compare to the convergence of different routines to see how quickly you find a solution. \n",
+    "\n",
+    "Comparing the freefall example\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: called from\n",
+      "    __line__ at line 120 column 16\n",
+      "    line at line 56 column 8\n",
+      "    __plt__>__plt2vv__ at line 500 column 10\n",
+      "    __plt__>__plt2__ at line 246 column 14\n",
+      "    __plt__ at line 133 column 15\n",
+      "    semilogy at line 60 column 10\n",
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: axis: omitting non-positive data in log plot\n"
+     ]
+    },
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+   ],
+   "source": [
+    "N=20;\n",
+    "iterations = linspace(1,400,N);\n",
+    "ea_nr=zeros(1,N); % appr error Newton-Raphson\n",
+    "ea_ms=zeros(1,N); % appr error Modified Secant\n",
+    "ea_fp=zeros(1,N); % appr error false point method\n",
+    "ea_bs=zeros(1,N); % appr error bisect method\n",
+    "for i=1:length(iterations)\n",
+    "    [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,200,0,iterations(i));\n",
+    "    [root_ms,ea_ms(i),iter_ms]=mod_secant(f_m,1e-6,300,0,iterations(i));\n",
+    "    [root_fp,ea_fp(i),iter_fp]=falsepos(f_m,1,300,0,iterations(i));\n",
+    "    [root_bs,ea_bs(i),iter_bs]=bisect(f_m,1,300,0,iterations(i));\n",
+    "end\n",
+    "        \n",
+    "semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))\n",
+    "legend('newton-raphson','mod-secant','false point','bisection')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ea_ms =\n",
+      "\n",
+      " Columns 1 through 6:\n",
+      "\n",
+      "   2.3382e+03   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14\n",
+      "\n",
+      " Columns 7 through 12:\n",
+      "\n",
+      "   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14\n",
+      "\n",
+      " Columns 13 through 18:\n",
+      "\n",
+      "   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14\n",
+      "\n",
+      " Columns 19 and 20:\n",
+      "\n",
+      "   1.9171e-14   1.9171e-14\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "ea_ms"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: called from\n",
+      "    __line__ at line 120 column 16\n",
+      "    line at line 56 column 8\n",
+      "    __plt__>__plt2vv__ at line 500 column 10\n",
+      "    __plt__>__plt2__ at line 246 column 14\n",
+      "    __plt__ at line 133 column 15\n",
+      "    semilogy at line 60 column 10\n",
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: axis: omitting non-positive data in log plot\n",
+      "warning: axis: omitting non-positive data in log plot\n"
+     ]
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+       "\t\t<text><tspan font-family=\"{}\">10</tspan><tspan dy=\"-8.00px\" font-family=\"{}\" font-size=\"12.8\">-8</tspan><tspan dy=\"8.00\" font-size=\"16.0\"/></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M53.9,210.0 L60.1,210.0 M535.0,210.0 L528.8,210.0 M53.9,171.4 L60.1,171.4 M535.0,171.4 L528.8,171.4   M53.9,132.7 L60.1,132.7 M535.0,132.7 L528.8,132.7 M53.9,94.0 L60.1,94.0 M535.0,94.0 L528.8,94.0   M53.9,55.4 L60.1,55.4 M535.0,55.4 L528.8,55.4 M53.9,16.7 L60.1,16.7 M535.0,16.7 L528.8,16.7   M53.9,210.0 L66.4,210.0 M535.0,210.0 L522.5,210.0  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(45.6,216.0)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">10</tspan><tspan dy=\"-8.00px\" font-family=\"{}\" font-size=\"12.8\">-6</tspan><tspan dy=\"8.00\" font-size=\"16.0\"/></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M53.9,171.4 L60.1,171.4 M535.0,171.4 L528.8,171.4 M53.9,132.7 L60.1,132.7 M535.0,132.7 L528.8,132.7   M53.9,94.0 L60.1,94.0 M535.0,94.0 L528.8,94.0 M53.9,55.4 L60.1,55.4 M535.0,55.4 L528.8,55.4   M53.9,16.7 L60.1,16.7 M535.0,16.7 L528.8,16.7 M53.9,171.4 L66.4,171.4 M535.0,171.4 L522.5,171.4    \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(45.6,177.4)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">10</tspan><tspan dy=\"-8.00px\" font-family=\"{}\" font-size=\"12.8\">-4</tspan><tspan dy=\"8.00\" font-size=\"16.0\"/></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M53.9,132.7 L60.1,132.7 M535.0,132.7 L528.8,132.7 M53.9,94.0 L60.1,94.0 M535.0,94.0 L528.8,94.0   M53.9,55.4 L60.1,55.4 M535.0,55.4 L528.8,55.4 M53.9,16.7 L60.1,16.7 M535.0,16.7 L528.8,16.7   M53.9,132.7 L66.4,132.7 M535.0,132.7 L522.5,132.7  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(45.6,138.7)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">10</tspan><tspan dy=\"-8.00px\" font-family=\"{}\" font-size=\"12.8\">-2</tspan><tspan dy=\"8.00\" font-size=\"16.0\"/></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M53.9,94.0 L60.1,94.0 M535.0,94.0 L528.8,94.0 M53.9,55.4 L60.1,55.4 M535.0,55.4 L528.8,55.4   M53.9,16.7 L60.1,16.7 M535.0,16.7 L528.8,16.7 M53.9,94.0 L66.4,94.0 M535.0,94.0 L522.5,94.0    \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(45.6,100.0)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">10</tspan><tspan dy=\"-8.00px\" font-family=\"{}\" font-size=\"12.8\">0</tspan><tspan dy=\"8.00\" font-size=\"16.0\"/></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M53.9,55.4 L60.1,55.4 M535.0,55.4 L528.8,55.4 M53.9,16.7 L60.1,16.7 M535.0,16.7 L528.8,16.7   M53.9,55.4 L66.4,55.4 M535.0,55.4 L522.5,55.4  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(45.6,61.4)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">10</tspan><tspan dy=\"-8.00px\" font-family=\"{}\" font-size=\"12.8\">2</tspan><tspan dy=\"8.00\" font-size=\"16.0\"/></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M53.9,16.7 L60.1,16.7 M535.0,16.7 L528.8,16.7 M53.9,16.7 L66.4,16.7 M535.0,16.7 L522.5,16.7    \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(45.6,22.7)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">10</tspan><tspan dy=\"-8.00px\" font-family=\"{}\" font-size=\"12.8\">4</tspan><tspan dy=\"8.00\" font-size=\"16.0\"/></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M53.9,384.0 L53.9,371.5 M53.9,16.7 L53.9,29.2  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(53.9,408.0)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">0</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M150.1,384.0 L150.1,371.5 M150.1,16.7 L150.1,29.2  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(150.1,408.0)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">10</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M246.3,384.0 L246.3,371.5 M246.3,16.7 L246.3,29.2  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(246.3,408.0)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">20</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M342.6,384.0 L342.6,371.5 M342.6,16.7 L342.6,29.2  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(342.6,408.0)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">30</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M438.8,384.0 L438.8,371.5 M438.8,16.7 L438.8,29.2  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(438.8,408.0)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">40</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M535.0,384.0 L535.0,371.5 M535.0,16.7 L535.0,29.2  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(535.0,408.0)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">50</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<path d=\"M53.9,16.7 L53.9,384.0 L535.0,384.0 L535.0,16.7 L53.9,16.7 Z  \" stroke=\"black\"/></g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"1.00\">\n",
+       "\t<path d=\"M293.7,217.7 L293.7,25.7 L526.7,25.7 L526.7,217.7 L293.7,217.7 Z  \" stroke=\"black\"/></g>\n",
+       "\t<g id=\"gnuplot_plot_1a\"><title>newton-raphson</title>\n",
+       "<g color=\"white\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(526.7,55.7)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">newton-raphson</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<path d=\"M304.9,49.7 L358.7,49.7 M63.5,55.4 L88.3,73.8 L113.2,73.8 L138.0,73.8 L162.8,73.8 L187.6,73.8   L212.4,73.8 L237.2,73.8 L262.0,73.8 L286.9,73.8 L311.7,73.8 L336.5,73.8 L361.3,73.8 L386.1,73.9   L410.9,75.8 L435.7,87.7 L460.6,221.4  \" stroke=\"rgb(  0,   0, 255)\"/></g>\n",
+       "\t</g>\n",
+       "\t<g id=\"gnuplot_plot_2a\"><title>mod-secant</title>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(526.7,103.7)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">mod-secant</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<path d=\"M304.9,97.7 L358.7,97.7 M63.5,55.4 L88.3,73.8 L113.2,73.8 L138.0,73.8 L162.8,73.8 L187.6,73.8   L212.4,73.8 L237.2,73.8 L262.0,73.8 L286.9,73.8 L311.7,73.8 L336.5,73.8 L361.3,73.8 L386.1,73.9   L410.9,75.8 L435.7,87.7 L460.6,221.0  \" stroke=\"rgb(  0, 128,   0)\"/></g>\n",
+       "\t</g>\n",
+       "\t<g id=\"gnuplot_plot_3a\"><title>false point</title>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(526.7,151.7)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">false point</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<path d=\"M304.9,145.7 L358.7,145.7 M63.5,94.0 L88.3,94.0 L113.2,94.0 L138.0,94.0 L162.8,94.0 L187.6,94.0   L212.4,94.0 L237.2,94.0 L262.0,94.0 L286.9,94.0 L311.7,94.0 L336.5,94.0 L361.3,94.0 L386.1,94.0   L410.9,94.0 L435.7,94.0 L460.6,94.0 L485.4,94.0 L510.2,94.0 L535.0,94.0  \" stroke=\"rgb(255,   0,   0)\"/></g>\n",
+       "\t</g>\n",
+       "\t<g id=\"gnuplot_plot_4a\"><title>bisection</title>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(526.7,199.7)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">bisection</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<path d=\"M304.9,193.7 L358.7,193.7 M63.5,17.1 L88.3,100.3 L113.2,107.1 L138.0,117.6 L162.8,144.5 L187.6,156.2   L212.4,164.4 L237.2,191.1 L262.0,202.7 L286.9,211.0 L311.7,222.6 L336.5,249.3 L361.3,260.9 L386.1,269.1   L410.9,295.8 L435.7,307.5 L460.6,315.7 L485.4,327.3 L510.2,354.0 L535.0,365.7  \" stroke=\"rgb(  0, 191, 191)\"/></g>\n",
+       "\t</g>\n",
+       "<g color=\"white\" fill=\"none\" stroke=\"rgb(  0, 191, 191)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "N=20;\n",
+    "f= @(x) x^10-1;\n",
+    "df=@(x) 10*x^9;\n",
+    "iterations = linspace(1,50,N);\n",
+    "ea_nr=zeros(1,N); % appr error Newton-Raphson\n",
+    "ea_ms=zeros(1,N); % appr error Modified Secant\n",
+    "ea_fp=zeros(1,N); % appr error false point method\n",
+    "ea_bs=zeros(1,N); % appr error bisect method\n",
+    "for i=1:length(iterations)\n",
+    "    [root_nr,ea_nr(i),iter_nr]=newtraph(f,df,0.5,0,iterations(i));\n",
+    "    [root_ms,ea_ms(i),iter_ms]=mod_secant(f,1e-6,0.5,0,iterations(i));\n",
+    "    [root_fp,ea_fp(i),iter_fp]=falsepos(f,0,5,0,iterations(i));\n",
+    "    [root_bs,ea_bs(i),iter_bs]=bisect(f,0,5,0,iterations(i));\n",
+    "end\n",
+    "        \n",
+    "semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))\n",
+    "legend('newton-raphson','mod-secant','false point','bisection')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ea_bs =\n",
+      "\n",
+      " Columns 1 through 6:\n",
+      "\n",
+      "   9.5357e+03  -4.7554e-01  -2.1114e-01   6.0163e-02  -2.4387e-03   6.1052e-04\n",
+      "\n",
+      " Columns 7 through 12:\n",
+      "\n",
+      "   2.2891e-04  -9.5367e-06   2.3842e-06   8.9407e-07  -2.2352e-07   9.3132e-09\n",
+      "\n",
+      " Columns 13 through 18:\n",
+      "\n",
+      "  -2.3283e-09  -8.7311e-10   3.6380e-11  -9.0949e-12  -3.4106e-12   8.5265e-13\n",
+      "\n",
+      " Columns 19 and 20:\n",
+      "\n",
+      "  -3.5527e-14   8.8818e-15\n",
+      "\n",
+      "ans =  16.208\n"
+     ]
+    }
+   ],
+   "source": [
+    "ea_bs\n",
+    "newtraph(f,df,0.5,0,12)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =    1.9683e+23\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "df(300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Octave",
+   "language": "octave",
+   "name": "octave"
+  },
+  "language_info": {
+   "file_extension": ".m",
+   "help_links": [
+    {
+     "text": "MetaKernel Magics",
+     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+    }
+   ],
+   "mimetype": "text/x-octave",
+   "name": "octave",
+   "version": "0.19.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/lecture_07/lecture_07.ipynb b/lecture_07/lecture_07.ipynb
index 0c3c2ca..d7ff495 100644
--- a/lecture_07/lecture_07.ipynb
+++ b/lecture_07/lecture_07.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 1,
    "metadata": {
     "collapsed": true
    },
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 2,
    "metadata": {
     "collapsed": true
    },
@@ -45,7 +45,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false
    },
@@ -54,10 +54,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "error: 'c' undefined near line 1 column 1\n",
-      "error: 'x_r' undefined near line 1 column 21\n",
-      "error: evaluating argument list element number 1\n",
-      "error: 'x_r' undefined near line 1 column 5\n"
+      "error_approx =  1\r\n"
      ]
     }
    ],
@@ -66,14 +63,13 @@
     "df= @(x) -exp(-x)-1;\n",
     "\n",
     "x_i= 0;\n",
-    "c\n",
     "error_approx = abs((x_r-x_i)/x_r)\n",
-    "x_i=x_r;\n"
+    "x_r=x_i;\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 21,
    "metadata": {
     "collapsed": false
    },
@@ -95,7 +91,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 22,
    "metadata": {
     "collapsed": false
    },
@@ -117,7 +113,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 23,
    "metadata": {
     "collapsed": false
    },
@@ -153,7 +149,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {
     "collapsed": true
    },
@@ -171,7 +167,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
@@ -221,7 +217,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
@@ -240,7 +236,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
@@ -249,166 +245,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Amt_numerical =  563.79\n",
-      "ans = -160.42\n"
+      "error: 'plot_bool' undefined near line 12 column 6\n",
+      "error: called from\n",
+      "    car_payments at line 12 column 3\n",
+      "    mod_secant at line 22 column 8\n",
+      "error: 'Amt' undefined near line 1 column 14\n",
+      "error: evaluating argument list element number 1\n"
      ]
-    },
-    {
-     "data": {
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-       "\n",
-       "<title>Gnuplot</title>\n",
-       "<desc>Produced by GNUPLOT 5.0 patchlevel 3 </desc>\n",
-       "\n",
-       "<g id=\"gnuplot_canvas\">\n",
-       "\n",
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-       "\n",
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-       "\t\t<text><tspan font-family=\"{}\">-5000</tspan></text>\n",
-       "\t</g>\n",
-       "</g>\n",
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-       "\t\t<text><tspan font-family=\"{}\">1</tspan></text>\n",
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-       "</g>\n",
-       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
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-       "\t<path d=\"M80.2,16.7 L80.2,362.4 L535.0,362.4 L535.0,16.7 L80.2,16.7 Z  \" stroke=\"black\"/></g>\n",
-       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
-       "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(19.1,189.6) rotate(-90)\">\n",
-       "\t\t<text><tspan font-family=\"{}\">principle amount left ($)</tspan></text>\n",
-       "\t</g>\n",
-       "</g>\n",
-       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
-       "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(307.6,413.4)\">\n",
-       "\t\t<text><tspan font-family=\"{}\">time (years)</tspan></text>\n",
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-       "</g>\n",
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-       "</g>\n",
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-       "\t</g>\n",
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-       "</g>\n",
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-       "</g>\n",
-       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
-       "</g>\n",
-       "</g>\n",
-       "</svg>"
-      ],
-      "text/plain": [
-       "<IPython.core.display.SVG object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -418,7 +261,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
@@ -427,7 +270,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ans =    3.3968e+04\r\n"
+      "error: 'Amt' undefined near line 1 column 1\r\n"
      ]
     }
    ],
@@ -444,7 +287,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
@@ -474,7 +317,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
@@ -555,7 +398,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
@@ -585,7 +428,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 84,
+   "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
@@ -836,7 +679,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 16,
    "metadata": {
     "collapsed": false
    },
@@ -847,17 +690,21 @@
      "text": [
       "ea_ms =\n",
       "\n",
-      " Columns 1 through 7:\n",
+      " Columns 1 through 6:\n",
+      "\n",
+      "   2.3382e+03   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14\n",
       "\n",
-      "   43.43883    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000\n",
+      " Columns 7 through 12:\n",
+      "\n",
+      "   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14\n",
       "\n",
-      " Columns 8 through 14:\n",
+      " Columns 13 through 18:\n",
       "\n",
-      "    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000\n",
+      "   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14\n",
       "\n",
-      " Columns 15 through 20:\n",
+      " Columns 19 and 20:\n",
       "\n",
-      "    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000\n",
+      "   1.9171e-14   1.9171e-14\n",
       "\n"
      ]
     }
@@ -868,7 +715,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 101,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false
    },
@@ -1106,7 +953,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 102,
+   "execution_count": 18,
    "metadata": {
     "collapsed": false
    },
@@ -1144,7 +991,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 93,
+   "execution_count": 19,
    "metadata": {
     "collapsed": false
    },
diff --git a/lecture_07/octave-workspace b/lecture_07/octave-workspace
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From 3bfd22acff1a9199c077ad72a0bfa9b3c56ed021 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Mon, 6 Feb 2017 23:10:39 -0500
Subject: [PATCH 29/37] updated lecture 07 pdf and markdown

---
 lecture_07/lecture_07.md  |  38 +++++++++++++++++++-------------------
 lecture_07/lecture_07.pdf | Bin 68853 -> 61249 bytes
 2 files changed, 19 insertions(+), 19 deletions(-)

diff --git a/lecture_07/lecture_07.md b/lecture_07/lecture_07.md
index 020699b..ffdc48d 100644
--- a/lecture_07/lecture_07.md
+++ b/lecture_07/lecture_07.md
@@ -26,16 +26,12 @@ f= @(x) exp(-x)-x;
 df= @(x) -exp(-x)-1;
 
 x_i= 0;
-c
 error_approx = abs((x_r-x_i)/x_r)
-x_i=x_r;
+x_r=x_i;
 
 ```
 
-    error: 'c' undefined near line 1 column 1
-    error: 'x_r' undefined near line 1 column 21
-    error: evaluating argument list element number 1
-    error: 'x_r' undefined near line 1 column 5
+    error_approx =  1
 
 
 
@@ -135,12 +131,12 @@ Amt_numerical=mod_secant(@(A) car_payments(A,30000,0.05,5),1e-6,50,0.001)
 car_payments(Amt,30000,0.05,5)
 ```
 
-    Amt_numerical =  563.79
-    ans = -160.42
-
-
-
-![svg](lecture_07_files/lecture_07_14_1.svg)
+    error: 'plot_bool' undefined near line 12 column 6
+    error: called from
+        car_payments at line 12 column 3
+        mod_secant at line 22 column 8
+    error: 'Amt' undefined near line 1 column 14
+    error: evaluating argument list element number 1
 
 
 
@@ -148,7 +144,7 @@ car_payments(Amt,30000,0.05,5)
 Amt*12*5
 ```
 
-    ans =    3.3968e+04
+    error: 'Amt' undefined near line 1 column 1
 
 
 Amortization calculation makes the same calculation for the monthly payment amount, A, paying off the principle amount, P, over n pay periods with monthly interest rate, r. 
@@ -295,17 +291,21 @@ ea_ms
 
     ea_ms =
     
-     Columns 1 through 7:
+     Columns 1 through 6:
+    
+       2.3382e+03   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14
+    
+     Columns 7 through 12:
     
-       43.43883    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
+       1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14
     
-     Columns 8 through 14:
+     Columns 13 through 18:
     
-        0.00000    0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
+       1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14
     
-     Columns 15 through 20:
+     Columns 19 and 20:
     
-        0.00000    0.00000    0.00000    0.00000    0.00000    0.00000
+       1.9171e-14   1.9171e-14
     
 
 
diff --git a/lecture_07/lecture_07.pdf b/lecture_07/lecture_07.pdf
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From 3519f1bfbda115e72a58482e7476c05bb3087b78 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Tue, 7 Feb 2017 20:46:45 -0500
Subject: [PATCH 30/37] added HW3

---
 HW3/README.html                               |  60 ++
 HW3/README.md                                 |  74 +++
 lecture_07/.newtraph.m.swp                    | Bin 0 -> 12288 bytes
 lecture_07/lecture_07.ipynb                   | 544 +++++++++++++++---
 lecture_07/lecture_07.md                      | 160 ++++--
 lecture_07/lecture_07.pdf                     | Bin 61249 -> 79416 bytes
 .../lecture_07_files/lecture_07_15_1.svg      | 131 +++++
 .../lecture_07_files/lecture_07_16_1.svg      | 151 +++++
 .../lecture_07_files/lecture_07_24_1.svg      |  59 +-
 .../lecture_07_files/lecture_07_26_1.svg      | 182 ++++++
 10 files changed, 1225 insertions(+), 136 deletions(-)
 create mode 100644 HW3/README.html
 create mode 100644 HW3/README.md
 create mode 100644 lecture_07/.newtraph.m.swp
 create mode 100644 lecture_07/lecture_07_files/lecture_07_15_1.svg
 create mode 100644 lecture_07/lecture_07_files/lecture_07_16_1.svg
 create mode 100644 lecture_07/lecture_07_files/lecture_07_26_1.svg

diff --git a/HW3/README.html b/HW3/README.html
new file mode 100644
index 0000000..950e6d3
--- /dev/null
+++ b/HW3/README.html
@@ -0,0 +1,60 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+  <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+  <meta http-equiv="Content-Style-Type" content="text/css" />
+  <meta name="generator" content="pandoc" />
+  <title></title>
+  <style type="text/css">code{white-space: pre;}</style>
+</head>
+<body>
+<h1 id="homework-3">Homework #3</h1>
+<h2 id="due-21517-by-1159pm">due 2/15/17 by 11:59pm</h2>
+<ol style="list-style-type: decimal">
+<li><p>Create a new github repository called ‘roots_and_optimization’.</p>
+<ol style="list-style-type: lower-alpha">
+<li><p>Add rcc02007 and pez16103 as collaborators.</p></li>
+<li><p>Clone the repository to your computer.</p></li>
+<li><p>Copy your <code>projectile.m</code> function into the ‘roots_and_optimization’ folder. <em>Disable the plotting routine for the solvers</em></p></li>
+<li><p>Use the four solvers <code>falsepos.m</code>, <code>incsearch.m</code>, <code>newtraph.m</code> and <code>mod_secant.m</code> to solve for the angle needed to reach h=1.72, with an initial speed of 1.5 m/s.</p></li>
+<li><p>The <code>newtraph.m</code> function needs a derivative, calculate the derivative of your function with respect to theta, <code>dprojectile_dtheta.m</code>. This function should output d(h)/d(theta).</p></li>
+<li><p>In your <code>README.md</code> file, you will document the following under the heading <code># Homework #3</code>:</p>
+<ol style="list-style-type: lower-roman">
+<li>Compare the number of iterations that each function needed to reach an accuracy of 0.00001%. Include a table in your README.md with:</li>
+</ol>
+<pre><code>| solver | initial guess(es) | ea | number of iterations|
+| --- | --- | --- | --- |
+|falsepos   |  |  |  |
+|incsearch  |  |  |  |
+|newtraph   |  |  |  |
+|mod_secant |  |  |  |</code></pre>
+<ol start="2" style="list-style-type: lower-roman">
+<li>Compare the convergence of the 4 methods. Plot the approximate error vs the number of iterations that the solver has calculated. Save the plot as <code>convergence.png</code> and display the plot in your <code>README.md</code> with:</li>
+</ol>
+<p><code>![Plot of convergence for four numerical solvers.](convergence.png)</code></p>
+<ol start="3" style="list-style-type: lower-roman">
+<li>In the <code>README.md</code> provide a description of the files used to create the table and the convergence plot.</li>
+</ol></li>
+</ol></li>
+<li><p>The Newton-Raphson method and the modified secant method do not always converge to a solution. One simple example is the function f(x) = x*exp(-x^2). The root is at 0, but using the numerical solvers, <code>newtraph.m</code> and <code>mod_secant.m</code>, there are certain initial guesses that do not converge.</p>
+<ol style="list-style-type: lower-alpha">
+<li><p>Calculate the first 5 iterations for the Newton-Raphson method with an initial guess of x_i=2.</p></li>
+<li><p>Add the results to a table in the <code>README.md</code> with:</p></li>
+</ol>
+<pre><code>### divergence of Newton-Raphson method
+
+| iteration | x_i | approx error |
+| --- | --- | --- |
+| 0 | 2 | n/a |
+| 1 |   |     |
+| 2 |   |     |
+| 3 |   |     |
+| 4 |   |     |
+| 5 |   |     |</code></pre>
+<ol start="3" style="list-style-type: lower-alpha">
+<li>Repeat steps a-b for an initial guess of 0.2. (But change the heading from ‘divergence’ to ‘convergence’)</li>
+</ol></li>
+<li><p>Commit your changes to your repository. Sync your local repository with github. Then copy and paste the “clone URL” into the following Google Form <a href="https://goo.gl/forms/UJBGwp0fQcSxImkq2">Homework #3</a></p></li>
+</ol>
+</body>
+</html>
diff --git a/HW3/README.md b/HW3/README.md
new file mode 100644
index 0000000..494e0d5
--- /dev/null
+++ b/HW3/README.md
@@ -0,0 +1,74 @@
+# Homework #3
+## due 2/15/17 by 11:59pm
+
+
+1. Create a new github repository called 'roots_and_optimization'. 
+
+    a. Add rcc02007 and pez16103 as collaborators.
+
+    b. Clone the repository to your computer.
+
+    c. Copy your `projectile.m` function into the 'roots_and_optimization' folder.
+    *Disable the plotting routine for the solvers*
+
+    d. Use the four solvers `falsepos.m`, `incsearch.m`, `newtraph.m` and `mod_secant.m`
+    to solve for the angle needed to reach h=1.72 m, with an initial speed of 1.5 m/s. 
+
+    e. The `newtraph.m` function needs a derivative, calculate the derivative of your
+    function with respect to theta, `dprojectile_dtheta.m`. This function should
+    output d(h)/d(theta). 
+
+
+    f. In your `README.md` file, document the following under the heading `#
+    Homework #3`:
+
+        i. Compare the number of iterations that each function needed to reach an
+        accuracy of 0.00001%. Include a table in your README.md with:
+
+        ```
+        | solver | initial guess(es) | ea | number of iterations|
+        | --- | --- | --- | --- |
+        |falsepos   |  |  |  |
+        |incsearch  |  |  |  |
+        |newtraph   |  |  |  |
+        |mod_secant |  |  |  |
+        ```
+
+        ii. Compare the convergence of the 4 methods. Plot the approximate error vs the
+        number of iterations that the solver has calculated. Save the plot as
+        `convergence.png` and display the plot in your `README.md` with:
+
+        `![Plot of convergence for four numerical solvers.](convergence.png)`
+
+        iii. In the `README.md` provide a description of the files used to create the
+        table and the convergence plot. 
+
+2. The Newton-Raphson method and the modified secant method do not always converge to a
+solution. One simple example is the function f(x) = x*exp(-x^2). The root is at 0, but
+using the numerical solvers, `newtraph.m` and `mod_secant.m`, there are certain initial
+guesses that do not converge. 
+
+    a. Calculate the first 5 iterations for the Newton-Raphson method with an initial
+    guess of x_i=2. 
+
+    b. Add the results to a table in the `README.md` with:
+
+    ```
+    ### divergence of Newton-Raphson method
+
+    | iteration | x_i | approx error |
+    | --- | --- | --- |
+    | 0 | 2 | n/a |
+    | 1 |   |     |
+    | 2 |   |     |
+    | 3 |   |     |
+    | 4 |   |     |
+    | 5 |   |     |
+    ```
+
+    c. Repeat steps a-b for an initial guess of 0.2. (But change the heading from
+    'divergence' to 'convergence')
+
+3. Commit your changes to your repository. Sync your local repository with github. Then
+copy and paste the "clone URL" into the following Google Form [Homework
+#3](https://goo.gl/forms/UJBGwp0fQcSxImkq2)
diff --git a/lecture_07/.newtraph.m.swp b/lecture_07/.newtraph.m.swp
new file mode 100644
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diff --git a/lecture_07/lecture_07.ipynb b/lecture_07/lecture_07.ipynb
index d7ff495..08d29c4 100644
--- a/lecture_07/lecture_07.ipynb
+++ b/lecture_07/lecture_07.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 13,
    "metadata": {
     "collapsed": true
    },
@@ -40,12 +40,12 @@
     "\n",
     "$x_{i+1}=x_{i}-\\frac{f(x_{i})}{f'(x_{i})}$\n",
     "\n",
-    "Use Newton-Raphson to find solution when $e^{x}=x$"
+    "Use Newton-Raphson to find solution when $e^{-x}=x$"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
@@ -54,7 +54,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "error_approx =  1\r\n"
+      "x_r =  0.50000\n",
+      "error_approx =  1\n"
      ]
     }
    ],
@@ -63,13 +64,14 @@
     "df= @(x) -exp(-x)-1;\n",
     "\n",
     "x_i= 0;\n",
+    "x_r = x_i-f(x_i)/df(x_i)\n",
     "error_approx = abs((x_r-x_i)/x_r)\n",
-    "x_r=x_i;\n"
+    "x_i=x_r;\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
@@ -78,8 +80,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "x_r =  0.50000\n",
-      "error_approx =  1\n"
+      "x_r =  0.56631\n",
+      "error_approx =  0.11709\n"
      ]
     }
    ],
@@ -91,7 +93,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
@@ -100,8 +102,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "x_r =  0.56631\n",
-      "error_approx =  0.11709\n"
+      "x_r =  0.56714\n",
+      "error_approx =  0.0014673\n"
      ]
     }
    ],
@@ -113,7 +115,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -123,7 +125,7 @@
      "output_type": "stream",
      "text": [
       "x_r =  0.56714\n",
-      "error_approx =  0.0014673\n"
+      "error_approx =    2.2106e-07\n"
      ]
     }
    ],
@@ -149,7 +151,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {
     "collapsed": true
    },
@@ -176,12 +178,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ans =  142.74\r\n"
+      "root =  142.74\n",
+      "ea =    8.0930e-06\n",
+      "iter =  48\n"
      ]
     }
    ],
    "source": [
-    "newtraph(f_m,df_m,140,0.00001)"
+    "[root,ea,iter]=newtraph(f_m,df_m,140,0.00001)"
    ]
   },
   {
@@ -217,7 +221,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
@@ -226,17 +230,24 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ans =  142.74\r\n"
+      "root =  142.74\n",
+      "ea =    3.0615e-07\n",
+      "iter =  7\n"
      ]
     }
    ],
    "source": [
-    "mod_secant(f_m,1e-6,50,0.00001)"
+    "[root,ea,iter]=mod_secant(f_m,1,50,0.00001)"
    ]
   },
+  {
+   "cell_type": "raw",
+   "metadata": {},
+   "source": []
+  },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
@@ -245,23 +256,159 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "error: 'plot_bool' undefined near line 12 column 6\n",
-      "error: called from\n",
-      "    car_payments at line 12 column 3\n",
-      "    mod_secant at line 22 column 8\n",
-      "error: 'Amt' undefined near line 1 column 14\n",
-      "error: evaluating argument list element number 1\n"
+      "ans =    1.1185e+04\r\n"
      ]
+    },
+    {
+     "data": {
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+       "\t\t<text><tspan font-family=\"{}\">5</tspan></text>\n",
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+       "\t<path d=\"M80.2,16.7 L80.2,362.4 L535.0,362.4 L535.0,16.7 L80.2,16.7 Z  \" stroke=\"black\"/></g>\n",
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+       "\t\t<text><tspan font-family=\"{}\">principle amount left ($)</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
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+       "\t\t<text><tspan font-family=\"{}\">time (years)</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
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+       "\t</g>\n",
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+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
-    "Amt_numerical=mod_secant(@(A) car_payments(A,30000,0.05,5),1e-6,50,0.001)\n",
-    "car_payments(Amt,30000,0.05,5)"
+    "car_payments(400,30000,0.05,5,1)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false
    },
@@ -270,12 +417,195 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "error: 'Amt' undefined near line 1 column 1\r\n"
+      "Amt_numerical =  5467.0\n",
+      "ans =    3.9755e-04\n"
+     ]
+    },
+    {
+     "data": {
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+       "<title>Gnuplot</title>\n",
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+       "</g>\n",
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+       "\t<path d=\"M88.5,362.4 L101.0,362.4 M535.0,362.4 L522.5,362.4  \" stroke=\"black\"/>\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"end\" transform=\"translate(80.2,368.4)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">0</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
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+       "\t\t<text><tspan font-family=\"{}\">100000</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
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+       "\t\t<text><tspan font-family=\"{}\">300000</tspan></text>\n",
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+       "\t\t<text><tspan font-family=\"{}\">400000</tspan></text>\n",
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+       "\t\t<text><tspan font-family=\"{}\">500000</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
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+       "\t\t<text><tspan font-family=\"{}\">600000</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
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+       "\t\t<text><tspan font-family=\"{}\">700000</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
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+       "\t\t<text><tspan font-family=\"{}\">5</tspan></text>\n",
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+       "</g>\n",
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+       "\t\t<text><tspan font-family=\"{}\">20</tspan></text>\n",
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+       "</g>\n",
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+       "</g>\n",
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+       "\t\t<text><tspan font-family=\"{}\">30</tspan></text>\n",
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+       "</g>\n",
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+       "\t<path d=\"M88.5,16.7 L88.5,362.4 L535.0,362.4 L535.0,16.7 L88.5,16.7 Z  \" stroke=\"black\"/></g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(19.1,189.6) rotate(-90)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">principle amount left ($)</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "\t<g fill=\"rgb(0,0,0)\" font-family=\"{}\" font-size=\"16.00\" stroke=\"none\" text-anchor=\"middle\" transform=\"translate(311.7,413.4)\">\n",
+       "\t\t<text><tspan font-family=\"{}\">time (years)</tspan></text>\n",
+       "\t</g>\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "\t<g id=\"gnuplot_plot_1a\"><title>gnuplot_plot_1a</title>\n",
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+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<path d=\"M89.7,16.9 L91.0,17.1 L92.2,17.3 L93.5,17.5 L94.7,17.7 L95.9,17.9 L97.2,18.1 L98.4,18.3   L99.7,18.5 L100.9,18.8 L102.1,19.0 L103.4,19.2 L104.6,19.4 L105.9,19.6 L107.1,19.8 L108.3,20.1   L109.6,20.3 L110.8,20.5 L112.1,20.7 L113.3,21.0 L114.5,21.2 L115.8,21.4 L117.0,21.7 L118.3,21.9   L119.5,22.1 L120.7,22.4 L122.0,22.6 L123.2,22.9 L124.5,23.1 L125.7,23.3 L126.9,23.6 L128.2,23.8   L129.4,24.1 L130.7,24.3 L131.9,24.6 L133.2,24.9 L134.4,25.1 L135.6,25.4 L136.9,25.6 L138.1,25.9   L139.4,26.2 L140.6,26.4 L141.8,26.7 L143.1,27.0 L144.3,27.2 L145.6,27.5 L146.8,27.8 L148.0,28.1   L149.3,28.4 L150.5,28.6 L151.8,28.9 L153.0,29.2 L154.2,29.5 L155.5,29.8 L156.7,30.1 L158.0,30.4   L159.2,30.7 L160.4,31.0 L161.7,31.3 L162.9,31.6 L164.2,31.9 L165.4,32.2 L166.6,32.5 L167.9,32.8   L169.1,33.2 L170.4,33.5 L171.6,33.8 L172.8,34.1 L174.1,34.5 L175.3,34.8 L176.6,35.1 L177.8,35.4   L179.0,35.8 L180.3,36.1 L181.5,36.5 L182.8,36.8 L184.0,37.1 L185.2,37.5 L186.5,37.8 L187.7,38.2   L189.0,38.6 L190.2,38.9 L191.4,39.3 L192.7,39.6 L193.9,40.0 L195.2,40.4 L196.4,40.7 L197.6,41.1   L198.9,41.5 L200.1,41.9 L201.4,42.3 L202.6,42.6 L203.8,43.0 L205.1,43.4 L206.3,43.8 L207.6,44.2   L208.8,44.6 L210.0,45.0 L211.3,45.4 L212.5,45.8 L213.8,46.2 L215.0,46.7 L216.2,47.1 L217.5,47.5   L218.7,47.9 L220.0,48.3 L221.2,48.8 L222.5,49.2 L223.7,49.6 L224.9,50.1 L226.2,50.5 L227.4,51.0   L228.7,51.4 L229.9,51.9 L231.1,52.3 L232.4,52.8 L233.6,53.2 L234.9,53.7 L236.1,54.2 L237.3,54.6   L238.6,55.1 L239.8,55.6 L241.1,56.1 L242.3,56.6 L243.5,57.1 L244.8,57.6 L246.0,58.1 L247.3,58.6   L248.5,59.1 L249.7,59.6 L251.0,60.1 L252.2,60.6 L253.5,61.1 L254.7,61.6 L255.9,62.2 L257.2,62.7   L258.4,63.2 L259.7,63.8 L260.9,64.3 L262.1,64.9 L263.4,65.4 L264.6,66.0 L265.9,66.5 L267.1,67.1   L268.3,67.6 L269.6,68.2 L270.8,68.8 L272.1,69.4 L273.3,69.9 L274.5,70.5 L275.8,71.1 L277.0,71.7   L278.3,72.3 L279.5,72.9 L280.7,73.5 L282.0,74.1 L283.2,74.8 L284.5,75.4 L285.7,76.0 L286.9,76.6   L288.2,77.3 L289.4,77.9 L290.7,78.6 L291.9,79.2 L293.1,79.9 L294.4,80.5 L295.6,81.2 L296.9,81.9   L298.1,82.5 L299.3,83.2 L300.6,83.9 L301.8,84.6 L303.1,85.3 L304.3,86.0 L305.5,86.7 L306.8,87.4   L308.0,88.1 L309.3,88.8 L310.5,89.6 L311.8,90.3 L313.0,91.0 L314.2,91.8 L315.5,92.5 L316.7,93.3   L318.0,94.0 L319.2,94.8 L320.4,95.5 L321.7,96.3 L322.9,97.1 L324.2,97.9 L325.4,98.7 L326.6,99.5   L327.9,100.3 L329.1,101.1 L330.4,101.9 L331.6,102.7 L332.8,103.5 L334.1,104.4 L335.3,105.2 L336.6,106.1   L337.8,106.9 L339.0,107.8 L340.3,108.6 L341.5,109.5 L342.8,110.4 L344.0,111.3 L345.2,112.1 L346.5,113.0   L347.7,113.9 L349.0,114.9 L350.2,115.8 L351.4,116.7 L352.7,117.6 L353.9,118.5 L355.2,119.5 L356.4,120.4   L357.6,121.4 L358.9,122.4 L360.1,123.3 L361.4,124.3 L362.6,125.3 L363.8,126.3 L365.1,127.3 L366.3,128.3   L367.6,129.3 L368.8,130.3 L370.0,131.3 L371.3,132.4 L372.5,133.4 L373.8,134.5 L375.0,135.5 L376.2,136.6   L377.5,137.7 L378.7,138.7 L380.0,139.8 L381.2,140.9 L382.4,142.0 L383.7,143.1 L384.9,144.3 L386.2,145.4   L387.4,146.5 L388.6,147.7 L389.9,148.8 L391.1,150.0 L392.4,151.2 L393.6,152.3 L394.8,153.5 L396.1,154.7   L397.3,155.9 L398.6,157.2 L399.8,158.4 L401.1,159.6 L402.3,160.8 L403.5,162.1 L404.8,163.4 L406.0,164.6   L407.3,165.9 L408.5,167.2 L409.7,168.5 L411.0,169.8 L412.2,171.1 L413.5,172.4 L414.7,173.8 L415.9,175.1   L417.2,176.5 L418.4,177.8 L419.7,179.2 L420.9,180.6 L422.1,182.0 L423.4,183.4 L424.6,184.8 L425.9,186.2   L427.1,187.7 L428.3,189.1 L429.6,190.6 L430.8,192.0 L432.1,193.5 L433.3,195.0 L434.5,196.5 L435.8,198.0   L437.0,199.5 L438.3,201.1 L439.5,202.6 L440.7,204.1 L442.0,205.7 L443.2,207.3 L444.5,208.9 L445.7,210.5   L446.9,212.1 L448.2,213.7 L449.4,215.4 L450.7,217.0 L451.9,218.7 L453.1,220.3 L454.4,222.0 L455.6,223.7   L456.9,225.4 L458.1,227.1 L459.3,228.9 L460.6,230.6 L461.8,232.4 L463.1,234.1 L464.3,235.9 L465.5,237.7   L466.8,239.5 L468.0,241.4 L469.3,243.2 L470.5,245.1 L471.7,246.9 L473.0,248.8 L474.2,250.7 L475.5,252.6   L476.7,254.5 L477.9,256.4 L479.2,258.4 L480.4,260.3 L481.7,262.3 L482.9,264.3 L484.1,266.3 L485.4,268.3   L486.6,270.4 L487.9,272.4 L489.1,274.5 L490.4,276.6 L491.6,278.7 L492.8,280.8 L494.1,282.9 L495.3,285.0   L496.6,287.2 L497.8,289.4 L499.0,291.5 L500.3,293.7 L501.5,296.0 L502.8,298.2 L504.0,300.5 L505.2,302.7   L506.5,305.0 L507.7,307.3 L509.0,309.6 L510.2,312.0 L511.4,314.3 L512.7,316.7 L513.9,319.1 L515.2,321.5   L516.4,323.9 L517.6,326.3 L518.9,328.8 L520.1,331.3 L521.4,333.8 L522.6,336.3 L523.8,338.8 L525.1,341.3   L526.3,343.9 L527.6,346.5 L528.8,349.1 L530.0,351.7 L531.3,354.4 L532.5,357.0 L533.8,359.7 L535.0,362.4    \" stroke=\"rgb(  0,   0, 255)\"/></g>\n",
+       "\t</g>\n",
+       "<g color=\"white\" fill=\"none\" stroke=\"rgb(  0,   0, 255)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "Amt_numerical=mod_secant(@(A) car_payments(A,700000,0.0875,30,0),1e-6,50,0.001)\n",
+    "car_payments(Amt_numerical,700000,0.0875,30,1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =    1.9681e+06\r\n"
      ]
     }
    ],
    "source": [
-    "Amt*12*5"
+    "Amt_numerical*12*30"
    ]
   },
   {
@@ -287,7 +617,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 19,
    "metadata": {
     "collapsed": false
    },
@@ -398,7 +728,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false
    },
@@ -428,7 +758,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 23,
    "metadata": {
     "collapsed": false
    },
@@ -611,7 +941,7 @@
        "\t</g>\n",
        "</g>\n",
        "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
-       "\t<path d=\"M304.9,49.7 L358.7,49.7 M55.1,81.9 L80.4,122.6 L105.6,165.4 L130.9,208.1 L156.1,250.8 L181.4,293.6   L206.6,336.0  \" stroke=\"rgb(  0,   0, 255)\"/></g>\n",
+       "\t<path d=\"M304.9,49.7 L358.7,49.7 M55.1,75.9 L80.4,114.0 L105.6,156.7 L130.9,199.4 L156.1,242.2 L181.4,284.9   L206.6,327.6  \" stroke=\"rgb(  0,   0, 255)\"/></g>\n",
        "\t</g>\n",
        "\t<g id=\"gnuplot_plot_2a\"><title>mod-secant</title>\n",
        "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
@@ -667,19 +997,20 @@
     "ea_fp=zeros(1,N); % appr error false point method\n",
     "ea_bs=zeros(1,N); % appr error bisect method\n",
     "for i=1:length(iterations)\n",
-    "    [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,200,0,iterations(i));\n",
+    "    [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,300,0,iterations(i));\n",
     "    [root_ms,ea_ms(i),iter_ms]=mod_secant(f_m,1e-6,300,0,iterations(i));\n",
     "    [root_fp,ea_fp(i),iter_fp]=falsepos(f_m,1,300,0,iterations(i));\n",
     "    [root_bs,ea_bs(i),iter_bs]=bisect(f_m,1,300,0,iterations(i));\n",
     "end\n",
-    "        \n",
+    "\n",
+    "setdefaults\n",
     "semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))\n",
     "legend('newton-raphson','mod-secant','false point','bisection')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 22,
    "metadata": {
     "collapsed": false
    },
@@ -688,34 +1019,30 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ea_ms =\n",
-      "\n",
-      " Columns 1 through 6:\n",
+      "ea_nr =\n",
       "\n",
-      "   2.3382e+03   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14\n",
+      " Columns 1 through 8:\n",
       "\n",
-      " Columns 7 through 12:\n",
+      "   6.36591   0.06436   0.00052   0.00000   0.00000   0.00000   0.00000   0.00000\n",
       "\n",
-      "   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14\n",
+      " Columns 9 through 16:\n",
       "\n",
-      " Columns 13 through 18:\n",
+      "   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000\n",
       "\n",
-      "   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14\n",
+      " Columns 17 through 20:\n",
       "\n",
-      " Columns 19 and 20:\n",
-      "\n",
-      "   1.9171e-14   1.9171e-14\n",
+      "   0.00000   0.00000   0.00000   0.00000\n",
       "\n"
      ]
     }
    ],
    "source": [
-    "ea_ms"
+    "ea_nr"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 26,
    "metadata": {
     "collapsed": false
    },
@@ -953,7 +1280,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 27,
    "metadata": {
     "collapsed": false
    },
@@ -962,30 +1289,26 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ea_bs =\n",
+      "ea_nr =\n",
       "\n",
-      " Columns 1 through 6:\n",
+      " Columns 1 through 7:\n",
       "\n",
-      "   9.5357e+03  -4.7554e-01  -2.1114e-01   6.0163e-02  -2.4387e-03   6.1052e-04\n",
+      "   99.03195   11.11111   11.11111   11.11111   11.11111   11.11111   11.11111\n",
       "\n",
-      " Columns 7 through 12:\n",
+      " Columns 8 through 14:\n",
       "\n",
-      "   2.2891e-04  -9.5367e-06   2.3842e-06   8.9407e-07  -2.2352e-07   9.3132e-09\n",
+      "   11.11111   11.11111   11.11111   11.11109   11.11052   11.10624   10.99684\n",
       "\n",
-      " Columns 13 through 18:\n",
+      " Columns 15 through 20:\n",
       "\n",
-      "  -2.3283e-09  -8.7311e-10   3.6380e-11  -9.0949e-12  -3.4106e-12   8.5265e-13\n",
-      "\n",
-      " Columns 19 and 20:\n",
-      "\n",
-      "  -3.5527e-14   8.8818e-15\n",
+      "    8.76956    2.12993    0.00000    0.00000    0.00000    0.00000\n",
       "\n",
       "ans =  16.208\n"
      ]
     }
    ],
    "source": [
-    "ea_bs\n",
+    "ea_nr\n",
     "newtraph(f,df,0.5,0,12)"
    ]
   },
@@ -1008,6 +1331,99 @@
     "df(300)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "f =\n",
+      "\n",
+      "@(x) tan (x) - (x - 1) .^ 2\n",
+      "\n",
+      "ans =  0.37375\n"
+     ]
+    }
+   ],
+   "source": [
+    "% our class function\n",
+    "f= @(x) tan(x)-(x-1).^2\n",
+    "mod_secant(f,1e-3,1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =   -3.5577e-13\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "f(ans)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  0.39218\n",
+      "ans =  0.39219\n"
+     ]
+    }
+   ],
+   "source": [
+    "tan(0.37375)\n",
+    "(0.37375-1)^2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =\n",
+      "\n",
+      " Columns 1 through 8:\n",
+      "\n",
+      "   -1.0000    1.5574   -3.1850   -4.1425   -7.8422  -19.3805  -25.2910  -35.1286\n",
+      "\n",
+      " Columns 9 through 11:\n",
+      "\n",
+      "  -55.7997  -64.4523  -80.3516\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "f([0:10])"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
diff --git a/lecture_07/lecture_07.md b/lecture_07/lecture_07.md
index ffdc48d..3aacefb 100644
--- a/lecture_07/lecture_07.md
+++ b/lecture_07/lecture_07.md
@@ -18,7 +18,7 @@ $f'(x_{i})=\frac{f(x_{i})-0}{x_{i}-x_{i+1}}$
 
 $x_{i+1}=x_{i}-\frac{f(x_{i})}{f'(x_{i})}$
 
-Use Newton-Raphson to find solution when $e^{x}=x$
+Use Newton-Raphson to find solution when $e^{-x}=x$
 
 
 ```octave
@@ -26,12 +26,14 @@ f= @(x) exp(-x)-x;
 df= @(x) -exp(-x)-1;
 
 x_i= 0;
+x_r = x_i-f(x_i)/df(x_i)
 error_approx = abs((x_r-x_i)/x_r)
-x_r=x_i;
+x_i=x_r;
 
 ```
 
-    error_approx =  1
+    x_r =  0.50000
+    error_approx =  1
 
 
 
@@ -41,8 +43,8 @@ error_approx = abs((x_r-x_i)/x_r)
 x_i=x_r;
 ```
 
-    x_r =  0.50000
-    error_approx =  1
+    x_r =  0.56631
+    error_approx =  0.11709
 
 
 
@@ -52,8 +54,8 @@ error_approx = abs((x_r-x_i)/x_r)
 x_i=x_r;
 ```
 
-    x_r =  0.56631
-    error_approx =  0.11709
+    x_r =  0.56714
+    error_approx =  0.0014673
 
 
 
@@ -64,7 +66,7 @@ x_i=x_r;
 ```
 
     x_r =  0.56714
-    error_approx =  0.0014673
+    error_approx =    2.2106e-07
 
 
 In the bungee jumper example, we created a function f(m) that when f(m)=0, then the mass had been chosen such that at t=4 s, the velocity is 36 m/s. 
@@ -90,10 +92,12 @@ df_m = @(m) 1/2*sqrt(g./m/c_d).*tanh(sqrt(g*c_d./m)*t)-g/2./m*sech(sqrt(g*c_d./m
 
 
 ```octave
-newtraph(f_m,df_m,140,0.00001)
+[root,ea,iter]=newtraph(f_m,df_m,140,0.00001)
 ```
 
-    ans =  142.74
+    root =  142.74
+    ea =    8.0930e-06
+    iter =  48
 
 
 ## Secant Methods
@@ -119,32 +123,46 @@ $x_{i+1}=x_{i}-\frac{f(x_{i})(\delta x_{i})}{f(x_{i}+\delta x_{i})-f(x_{i})}$
 
 
 ```octave
-mod_secant(f_m,1e-6,50,0.00001)
+[root,ea,iter]=mod_secant(f_m,1,50,0.00001)
 ```
 
-    ans =  142.74
+    root =  142.74
+    ea =    3.0615e-07
+    iter =  7
 
 
 
 ```octave
-Amt_numerical=mod_secant(@(A) car_payments(A,30000,0.05,5),1e-6,50,0.001)
-car_payments(Amt,30000,0.05,5)
+car_payments(400,30000,0.05,5,1)
 ```
 
-    error: 'plot_bool' undefined near line 12 column 6
-    error: called from
-        car_payments at line 12 column 3
-        mod_secant at line 22 column 8
-    error: 'Amt' undefined near line 1 column 14
-    error: evaluating argument list element number 1
+    ans =    1.1185e+04
+
+
+
+![svg](lecture_07_files/lecture_07_15_1.svg)
 
 
 
 ```octave
-Amt*12*5
+Amt_numerical=mod_secant(@(A) car_payments(A,700000,0.0875,30,0),1e-6,50,0.001)
+car_payments(Amt_numerical,700000,0.0875,30,1)
 ```
 
-    error: 'Amt' undefined near line 1 column 1
+    Amt_numerical =  5467.0
+    ans =    3.9755e-04
+
+
+
+![svg](lecture_07_files/lecture_07_16_1.svg)
+
+
+
+```octave
+Amt_numerical*12*30
+```
+
+    ans =    1.9681e+06
 
 
 Amortization calculation makes the same calculation for the monthly payment amount, A, paying off the principle amount, P, over n pay periods with monthly interest rate, r. 
@@ -257,12 +275,13 @@ ea_ms=zeros(1,N); % appr error Modified Secant
 ea_fp=zeros(1,N); % appr error false point method
 ea_bs=zeros(1,N); % appr error bisect method
 for i=1:length(iterations)
-    [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,200,0,iterations(i));
+    [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,300,0,iterations(i));
     [root_ms,ea_ms(i),iter_ms]=mod_secant(f_m,1e-6,300,0,iterations(i));
     [root_fp,ea_fp(i),iter_fp]=falsepos(f_m,1,300,0,iterations(i));
     [root_bs,ea_bs(i),iter_bs]=bisect(f_m,1,300,0,iterations(i));
 end
-        
+
+setdefaults
 semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))
 legend('newton-raphson','mod-secant','false point','bisection')
 ```
@@ -281,31 +300,27 @@ legend('newton-raphson','mod-secant','false point','bisection')
 
 
 
-![svg](lecture_07_files/lecture_07_22_1.svg)
+![svg](lecture_07_files/lecture_07_24_1.svg)
 
 
 
 ```octave
-ea_ms
+ea_nr
 ```
 
-    ea_ms =
+    ea_nr =
     
-     Columns 1 through 6:
+     Columns 1 through 8:
     
-       2.3382e+03   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14
+       6.36591   0.06436   0.00052   0.00000   0.00000   0.00000   0.00000   0.00000
     
-     Columns 7 through 12:
+     Columns 9 through 16:
     
-       1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14
+       0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
     
-     Columns 13 through 18:
+     Columns 17 through 20:
     
-       1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14   1.9171e-14
-    
-     Columns 19 and 20:
-    
-       1.9171e-14   1.9171e-14
+       0.00000   0.00000   0.00000   0.00000
     
 
 
@@ -344,32 +359,28 @@ legend('newton-raphson','mod-secant','false point','bisection')
 
 
 
-![svg](lecture_07_files/lecture_07_24_1.svg)
+![svg](lecture_07_files/lecture_07_26_1.svg)
 
 
 
 ```octave
-ea_bs
+ea_nr
 newtraph(f,df,0.5,0,12)
 ```
 
-    ea_bs =
-    
-     Columns 1 through 6:
+    ea_nr =
     
-       9.5357e+03  -4.7554e-01  -2.1114e-01   6.0163e-02  -2.4387e-03   6.1052e-04
+     Columns 1 through 7:
     
-     Columns 7 through 12:
+       99.03195   11.11111   11.11111   11.11111   11.11111   11.11111   11.11111
     
-       2.2891e-04  -9.5367e-06   2.3842e-06   8.9407e-07  -2.2352e-07   9.3132e-09
+     Columns 8 through 14:
     
-     Columns 13 through 18:
+       11.11111   11.11111   11.11111   11.11109   11.11052   11.10624   10.99684
     
-      -2.3283e-09  -8.7311e-10   3.6380e-11  -9.0949e-12  -3.4106e-12   8.5265e-13
+     Columns 15 through 20:
     
-     Columns 19 and 20:
-    
-      -3.5527e-14   8.8818e-15
+        8.76956    2.12993    0.00000    0.00000    0.00000    0.00000
     
     ans =  16.208
 
@@ -383,6 +394,55 @@ df(300)
 
 
 
+```octave
+% our class function
+f= @(x) tan(x)-(x-1).^2
+mod_secant(f,1e-3,1)
+```
+
+    f =
+    
+    @(x) tan (x) - (x - 1) .^ 2
+    
+    ans =  0.37375
+
+
+
+```octave
+f(ans)
+```
+
+    ans =   -3.5577e-13
+
+
+
+```octave
+tan(0.37375)
+(0.37375-1)^2
+```
+
+    ans =  0.39218
+    ans =  0.39219
+
+
+
+```octave
+f([0:10])
+```
+
+    ans =
+    
+     Columns 1 through 8:
+    
+       -1.0000    1.5574   -3.1850   -4.1425   -7.8422  -19.3805  -25.2910  -35.1286
+    
+     Columns 9 through 11:
+    
+      -55.7997  -64.4523  -80.3516
+    
+
+
+
 ```octave
 
 ```
diff --git a/lecture_07/lecture_07.pdf b/lecture_07/lecture_07.pdf
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+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M262.1,362.4 L262.1,349.9 M262.1,16.7 L262.1,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(262.1,386.4)">
+		<text><tspan font-family="{}">2</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M353.1,362.4 L353.1,349.9 M353.1,16.7 L353.1,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(353.1,386.4)">
+		<text><tspan font-family="{}">3</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M444.0,362.4 L444.0,349.9 M444.0,16.7 L444.0,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(444.0,386.4)">
+		<text><tspan font-family="{}">4</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M535.0,362.4 L535.0,349.9 M535.0,16.7 L535.0,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(535.0,386.4)">
+		<text><tspan font-family="{}">5</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M80.2,16.7 L80.2,362.4 L535.0,362.4 L535.0,16.7 L80.2,16.7 Z  " stroke="black"/></g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(19.1,189.6) rotate(-90)">
+		<text><tspan font-family="{}">principle amount left ($)</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(307.6,413.4)">
+		<text><tspan font-family="{}">time (years)</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+	<g id="gnuplot_plot_1a"><title>gnuplot_plot_1a</title>
+<g color="white" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
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+	</g>
+<g color="white" fill="none" stroke="rgb(  0,   0, 255)" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="2.00">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="2.00">
+</g>
+<g color="black" fill="none" stroke="black" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+</g>
+</svg>
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new file mode 100644
index 0000000..a3a2125
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+	<use id="gpPt9" stroke="currentColor" transform="rotate(180)" xlink:href="#gpPt7"/>
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+<g color="white" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="1.00">
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+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="1.00">
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+		<polygon fill="rgb(255, 255, 255)" points="88.5,362.4 534.9,362.4 534.9,16.8 88.5,16.8 "/>
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+</g>
+<g color="black" fill="none" stroke="rgb(255, 255, 255)" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M88.5,362.4 L101.0,362.4 M535.0,362.4 L522.5,362.4  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(80.2,368.4)">
+		<text><tspan font-family="{}">0</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M88.5,313.0 L101.0,313.0 M535.0,313.0 L522.5,313.0  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(80.2,319.0)">
+		<text><tspan font-family="{}">100000</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M88.5,263.6 L101.0,263.6 M535.0,263.6 L522.5,263.6  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(80.2,269.6)">
+		<text><tspan font-family="{}">200000</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M88.5,214.2 L101.0,214.2 M535.0,214.2 L522.5,214.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(80.2,220.2)">
+		<text><tspan font-family="{}">300000</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+		<text><tspan font-family="{}">400000</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M88.5,115.5 L101.0,115.5 M535.0,115.5 L522.5,115.5  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(80.2,121.5)">
+		<text><tspan font-family="{}">500000</tspan></text>
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+</g>
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+		<text><tspan font-family="{}">600000</tspan></text>
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+		<text><tspan font-family="{}">700000</tspan></text>
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+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M88.5,362.4 L88.5,349.9 M88.5,16.7 L88.5,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(88.5,386.4)">
+		<text><tspan font-family="{}">0</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M162.9,362.4 L162.9,349.9 M162.9,16.7 L162.9,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(162.9,386.4)">
+		<text><tspan font-family="{}">5</tspan></text>
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+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M237.3,362.4 L237.3,349.9 M237.3,16.7 L237.3,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(237.3,386.4)">
+		<text><tspan font-family="{}">10</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M311.8,362.4 L311.8,349.9 M311.8,16.7 L311.8,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(311.8,386.4)">
+		<text><tspan font-family="{}">15</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M386.2,362.4 L386.2,349.9 M386.2,16.7 L386.2,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(386.2,386.4)">
+		<text><tspan font-family="{}">20</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M460.6,362.4 L460.6,349.9 M460.6,16.7 L460.6,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(460.6,386.4)">
+		<text><tspan font-family="{}">25</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M535.0,362.4 L535.0,349.9 M535.0,16.7 L535.0,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(535.0,386.4)">
+		<text><tspan font-family="{}">30</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M88.5,16.7 L88.5,362.4 L535.0,362.4 L535.0,16.7 L88.5,16.7 Z  " stroke="black"/></g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(19.1,189.6) rotate(-90)">
+		<text><tspan font-family="{}">principle amount left ($)</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(311.7,413.4)">
+		<text><tspan font-family="{}">time (years)</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+	<g id="gnuplot_plot_1a"><title>gnuplot_plot_1a</title>
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index a8b614c..b511b10 100644
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+	</g>
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+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+		<text><tspan font-family="{}">10</tspan><tspan dy="-8.00px" font-family="{}" font-size="12.8">-4</tspan><tspan dy="8.00" font-size="16.0"/></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+		<text><tspan font-family="{}">10</tspan><tspan dy="-8.00px" font-family="{}" font-size="12.8">2</tspan><tspan dy="8.00" font-size="16.0"/></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
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+		<text><tspan font-family="{}">10</tspan><tspan dy="-8.00px" font-family="{}" font-size="12.8">4</tspan><tspan dy="8.00" font-size="16.0"/></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M53.9,384.0 L53.9,371.5 M53.9,16.7 L53.9,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(53.9,408.0)">
+		<text><tspan font-family="{}">0</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M150.1,384.0 L150.1,371.5 M150.1,16.7 L150.1,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(150.1,408.0)">
+		<text><tspan font-family="{}">10</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M246.3,384.0 L246.3,371.5 M246.3,16.7 L246.3,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(246.3,408.0)">
+		<text><tspan font-family="{}">20</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M342.6,384.0 L342.6,371.5 M342.6,16.7 L342.6,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(342.6,408.0)">
+		<text><tspan font-family="{}">30</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M438.8,384.0 L438.8,371.5 M438.8,16.7 L438.8,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(438.8,408.0)">
+		<text><tspan font-family="{}">40</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M535.0,384.0 L535.0,371.5 M535.0,16.7 L535.0,29.2  " stroke="black"/>	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="middle" transform="translate(535.0,408.0)">
+		<text><tspan font-family="{}">50</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+	<path d="M53.9,16.7 L53.9,384.0 L535.0,384.0 L535.0,16.7 L53.9,16.7 Z  " stroke="black"/></g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="black" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="1.00">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="1.00">
+	<path d="M293.7,217.7 L293.7,25.7 L526.7,25.7 L526.7,217.7 L293.7,217.7 Z  " stroke="black"/></g>
+	<g id="gnuplot_plot_1a"><title>newton-raphson</title>
+<g color="white" fill="none" stroke="black" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(526.7,55.7)">
+		<text><tspan font-family="{}">newton-raphson</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<path d="M304.9,49.7 L358.7,49.7 M63.5,55.4 L88.3,73.8 L113.2,73.8 L138.0,73.8 L162.8,73.8 L187.6,73.8   L212.4,73.8 L237.2,73.8 L262.0,73.8 L286.9,73.8 L311.7,73.8 L336.5,73.8 L361.3,73.8 L386.1,73.9   L410.9,75.8 L435.7,87.7 L460.6,221.4  " stroke="rgb(  0,   0, 255)"/></g>
+	</g>
+	<g id="gnuplot_plot_2a"><title>mod-secant</title>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(526.7,103.7)">
+		<text><tspan font-family="{}">mod-secant</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<path d="M304.9,97.7 L358.7,97.7 M63.5,55.4 L88.3,73.8 L113.2,73.8 L138.0,73.8 L162.8,73.8 L187.6,73.8   L212.4,73.8 L237.2,73.8 L262.0,73.8 L286.9,73.8 L311.7,73.8 L336.5,73.8 L361.3,73.8 L386.1,73.9   L410.9,75.8 L435.7,87.7 L460.6,221.0  " stroke="rgb(  0, 128,   0)"/></g>
+	</g>
+	<g id="gnuplot_plot_3a"><title>false point</title>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(526.7,151.7)">
+		<text><tspan font-family="{}">false point</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<path d="M304.9,145.7 L358.7,145.7 M63.5,94.0 L88.3,94.0 L113.2,94.0 L138.0,94.0 L162.8,94.0 L187.6,94.0   L212.4,94.0 L237.2,94.0 L262.0,94.0 L286.9,94.0 L311.7,94.0 L336.5,94.0 L361.3,94.0 L386.1,94.0   L410.9,94.0 L435.7,94.0 L460.6,94.0 L485.4,94.0 L510.2,94.0 L535.0,94.0  " stroke="rgb(255,   0,   0)"/></g>
+	</g>
+	<g id="gnuplot_plot_4a"><title>bisection</title>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<g fill="rgb(0,0,0)" font-family="{}" font-size="16.00" stroke="none" text-anchor="end" transform="translate(526.7,199.7)">
+		<text><tspan font-family="{}">bisection</tspan></text>
+	</g>
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="3.00">
+	<path d="M304.9,193.7 L358.7,193.7 M63.5,17.1 L88.3,100.3 L113.2,107.1 L138.0,117.6 L162.8,144.5 L187.6,156.2   L212.4,164.4 L237.2,191.1 L262.0,202.7 L286.9,211.0 L311.7,222.6 L336.5,249.3 L361.3,260.9 L386.1,269.1   L410.9,295.8 L435.7,307.5 L460.6,315.7 L485.4,327.3 L510.2,354.0 L535.0,365.7  " stroke="rgb(  0, 191, 191)"/></g>
+	</g>
+<g color="white" fill="none" stroke="rgb(  0, 191, 191)" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="2.00">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="2.00">
+</g>
+<g color="black" fill="none" stroke="black" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+<g color="black" fill="none" stroke="currentColor" stroke-linecap="butt" stroke-linejoin="miter" stroke-width="0.50">
+</g>
+</g>
+</svg>
\ No newline at end of file

From 6e109623ad724ad4a78871fcba90ae3fef495c3a Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Tue, 7 Feb 2017 20:47:05 -0500
Subject: [PATCH 31/37] added HW3

---
 HW3/README.html | 60 -------------------------------------------------
 1 file changed, 60 deletions(-)
 delete mode 100644 HW3/README.html

diff --git a/HW3/README.html b/HW3/README.html
deleted file mode 100644
index 950e6d3..0000000
--- a/HW3/README.html
+++ /dev/null
@@ -1,60 +0,0 @@
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<html xmlns="http://www.w3.org/1999/xhtml">
-<head>
-  <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-  <meta http-equiv="Content-Style-Type" content="text/css" />
-  <meta name="generator" content="pandoc" />
-  <title></title>
-  <style type="text/css">code{white-space: pre;}</style>
-</head>
-<body>
-<h1 id="homework-3">Homework #3</h1>
-<h2 id="due-21517-by-1159pm">due 2/15/17 by 11:59pm</h2>
-<ol style="list-style-type: decimal">
-<li><p>Create a new github repository called ‘roots_and_optimization’.</p>
-<ol style="list-style-type: lower-alpha">
-<li><p>Add rcc02007 and pez16103 as collaborators.</p></li>
-<li><p>Clone the repository to your computer.</p></li>
-<li><p>Copy your <code>projectile.m</code> function into the ‘roots_and_optimization’ folder. <em>Disable the plotting routine for the solvers</em></p></li>
-<li><p>Use the four solvers <code>falsepos.m</code>, <code>incsearch.m</code>, <code>newtraph.m</code> and <code>mod_secant.m</code> to solve for the angle needed to reach h=1.72, with an initial speed of 1.5 m/s.</p></li>
-<li><p>The <code>newtraph.m</code> function needs a derivative, calculate the derivative of your function with respect to theta, <code>dprojectile_dtheta.m</code>. This function should output d(h)/d(theta).</p></li>
-<li><p>In your <code>README.md</code> file, you will document the following under the heading <code># Homework #3</code>:</p>
-<ol style="list-style-type: lower-roman">
-<li>Compare the number of iterations that each function needed to reach an accuracy of 0.00001%. Include a table in your README.md with:</li>
-</ol>
-<pre><code>| solver | initial guess(es) | ea | number of iterations|
-| --- | --- | --- | --- |
-|falsepos   |  |  |  |
-|incsearch  |  |  |  |
-|newtraph   |  |  |  |
-|mod_secant |  |  |  |</code></pre>
-<ol start="2" style="list-style-type: lower-roman">
-<li>Compare the convergence of the 4 methods. Plot the approximate error vs the number of iterations that the solver has calculated. Save the plot as <code>convergence.png</code> and display the plot in your <code>README.md</code> with:</li>
-</ol>
-<p><code>![Plot of convergence for four numerical solvers.](convergence.png)</code></p>
-<ol start="3" style="list-style-type: lower-roman">
-<li>In the <code>README.md</code> provide a description of the files used to create the table and the convergence plot.</li>
-</ol></li>
-</ol></li>
-<li><p>The Newton-Raphson method and the modified secant method do not always converge to a solution. One simple example is the function f(x) = x*exp(-x^2). The root is at 0, but using the numerical solvers, <code>newtraph.m</code> and <code>mod_secant.m</code>, there are certain initial guesses that do not converge.</p>
-<ol style="list-style-type: lower-alpha">
-<li><p>Calculate the first 5 iterations for the Newton-Raphson method with an initial guess of x_i=2.</p></li>
-<li><p>Add the results to a table in the <code>README.md</code> with:</p></li>
-</ol>
-<pre><code>### divergence of Newton-Raphson method
-
-| iteration | x_i | approx error |
-| --- | --- | --- |
-| 0 | 2 | n/a |
-| 1 |   |     |
-| 2 |   |     |
-| 3 |   |     |
-| 4 |   |     |
-| 5 |   |     |</code></pre>
-<ol start="3" style="list-style-type: lower-alpha">
-<li>Repeat steps a-b for an initial guess of 0.2. (But change the heading from ‘divergence’ to ‘convergence’)</li>
-</ol></li>
-<li><p>Commit your changes to your repository. Sync your local repository with github. Then copy and paste the “clone URL” into the following Google Form <a href="https://goo.gl/forms/UJBGwp0fQcSxImkq2">Homework #3</a></p></li>
-</ol>
-</body>
-</html>

From 889acf40251fbf3602f3714991430b0b91864a1c Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Mon, 13 Feb 2017 16:54:49 -0500
Subject: [PATCH 32/37] update HW3

---
 HW3/README.md                                 |    6 +-
 lecture_07/.lecture_07.md.swo                 |  Bin 0 -> 16384 bytes
 lecture_07/.lecture_07.md.swp                 |  Bin 0 -> 16384 bytes
 "lecture_08/\020\267Y\001"                    |    0
 .../lecture_08-checkpoint.ipynb               |    6 +
 lecture_08/Auchain_model.gif                  |  Bin 0 -> 17748 bytes
 lecture_08/au_chain.jpg                       |  Bin 0 -> 234971 bytes
 lecture_08/goldenratio.png                    |  Bin 0 -> 94208 bytes
 lecture_08/lecture_08.ipynb                   | 1941 +++++++++++++++++
 lecture_08/lennard_jones.m                    |    4 +
 lecture_08/octave-workspace                   |  Bin 0 -> 4894 bytes
 "lecture_08/\34040\001"                       |    0
 12 files changed, 1954 insertions(+), 3 deletions(-)
 create mode 100644 lecture_07/.lecture_07.md.swo
 create mode 100644 lecture_07/.lecture_07.md.swp
 create mode 100644 "lecture_08/\020\267Y\001"
 create mode 100644 lecture_08/.ipynb_checkpoints/lecture_08-checkpoint.ipynb
 create mode 100644 lecture_08/Auchain_model.gif
 create mode 100644 lecture_08/au_chain.jpg
 create mode 100644 lecture_08/goldenratio.png
 create mode 100644 lecture_08/lecture_08.ipynb
 create mode 100644 lecture_08/lennard_jones.m
 create mode 100644 lecture_08/octave-workspace
 create mode 100644 "lecture_08/\34040\001"

diff --git a/HW3/README.md b/HW3/README.md
index 494e0d5..eb93c41 100644
--- a/HW3/README.md
+++ b/HW3/README.md
@@ -12,7 +12,7 @@
     *Disable the plotting routine for the solvers*
 
     d. Use the four solvers `falsepos.m`, `incsearch.m`, `newtraph.m` and `mod_secant.m`
-    to solve for the angle needed to reach h=1.72 m, with an initial speed of 1.5 m/s. 
+    to solve for the angle needed to reach h=1.72 m, with an initial speed of 15 m/s. 
 
     e. The `newtraph.m` function needs a derivative, calculate the derivative of your
     function with respect to theta, `dprojectile_dtheta.m`. This function should
@@ -29,7 +29,7 @@
         | solver | initial guess(es) | ea | number of iterations|
         | --- | --- | --- | --- |
         |falsepos   |  |  |  |
-        |incsearch  |  |  |  |
+        |bisect     |  |  |  |
         |newtraph   |  |  |  |
         |mod_secant |  |  |  |
         ```
@@ -49,7 +49,7 @@ using the numerical solvers, `newtraph.m` and `mod_secant.m`, there are certain
 guesses that do not converge. 
 
     a. Calculate the first 5 iterations for the Newton-Raphson method with an initial
-    guess of x_i=2. 
+    guess of x_i=2 for f(x)=x*exp(-x^2).
 
     b. Add the results to a table in the `README.md` with:
 
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+{
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+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
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diff --git a/lecture_08/lecture_08.ipynb b/lecture_08/lecture_08.ipynb
new file mode 100644
index 0000000..134ed8a
--- /dev/null
+++ b/lecture_08/lecture_08.ipynb
@@ -0,0 +1,1941 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "%plot --format svg"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Optimization\n",
+    "\n",
+    "Many problems involve finding a minimum or maximum based on given constraints. Engineers and scientists typically use energy balance equations to find the conditions of minimum energy, but this value may never go to 0 and the actual value of energy may not be of interest. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The Lennard-Jones potential is commonly used to model interatomic bonding. \n",
+    "\n",
+    "$E_{LJ}(x)=4\\epsilon \\left(\\left(\\frac{\\sigma}{x}\\right)^{12}-\\left(\\frac{\\sigma}{x}\\right)^{6}\\right)$\n",
+    "\n",
+    "Considering a 1-D gold chain, we can calculate the bond length, $x_{b}$, with no force applied to the chain and even for tension, F. This will allow us to calculate the nonlinear spring constant of a 1-D gold chain. \n",
+    "\n",
+    "![TEM image of Gold chain](au_chain.jpg)\n",
+    "\n",
+    "Computational Tools to Study and Predict the Long-Term Stability of Nanowires.\n",
+    "By Martin E. Zoloff Michoff, Patricio Vélez, Sergio A. Dassie and Ezequiel P. M. Leiva \n",
+    "\n",
+    "![Model of Gold chain, from molecular dynamics simulation](Auchain_model.gif)\n",
+    "\n",
+    "[Single atom gold chain mechanics](http://www.uam.es/personal_pdi/ciencias/agrait/)\n",
+    "\n",
+    "### First, let's find the minimum energy $\\min(E_{LJ}(x))$\n",
+    "\n",
+    "## Brute force"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
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+       "\n",
+       "<title>Gnuplot</title>\n",
+       "<desc>Produced by GNUPLOT 5.0 patchlevel 3 </desc>\n",
+       "\n",
+       "<g id=\"gnuplot_canvas\">\n",
+       "\n",
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+    }
+   ],
+   "source": [
+    "setdefaults\n",
+    "epsilon = 0.039; % kcal/mol\n",
+    "sigma = 2.934; % Angstrom\n",
+    "x=linspace(2.8,6,200); % bond length in Angstrom\n",
+    "\n",
+    "Ex = lennard_jones(x,sigma,epsilon);\n",
+    "\n",
+    "[Emin,imin]=min(Ex);\n",
+    "\n",
+    "plot(x,Ex,x(imin),Emin,'o')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ans =  3.2824\n",
+      "ans =  3.2985\n",
+      "ans =  3.3146\n"
+     ]
+    }
+   ],
+   "source": [
+    "x(imin-1)\n",
+    "x(imin)\n",
+    "x(imin+1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Golden Search Algorithm\n",
+    "\n",
+    "We can't just look for a sign change for the problem (unless we can take a derivative) so we need a new approach to determine whether we have a maximum between the two bounds.\n",
+    "\n",
+    "Rather than using the midpoint of initial bounds, here the problem is more difficult. We need to compare the values of 4 function evaluations. The golden search uses the golden ratio to determine two interior points. \n",
+    "\n",
+    "![golden ratio](goldenratio.png)\n",
+    "\n",
+    "Start with bounds of 2.5 and 6 Angstrom. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "current_min = -0.019959\r\n"
+     ]
+    },
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+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "% define Au atomic potential\n",
+    "epsilon = 0.039; % kcal/mol\n",
+    "sigma = 2.934; % Angstrom\n",
+    "Au_x= @(x) lennard_jones(x,sigma,epsilon);\n",
+    "\n",
+    "% calculate golden ratio\n",
+    "phi = 1/2+sqrt(5)/2;\n",
+    "% set initial limits\n",
+    "x_l=2.8; \n",
+    "x_u=6; \n",
+    "\n",
+    "% Iteration #1\n",
+    "d=(phi-1)*(x_u-x_l);\n",
+    "\n",
+    "x1=x_l+d; % define point 1\n",
+    "x2=x_u-d; % define point 2\n",
+    "\n",
+    "\n",
+    "% evaluate Au_x(x1) and Au_x(x2)\n",
+    "\n",
+    "f1=Au_x(x1);\n",
+    "f2=Au_x(x2);\n",
+    "plot(x,Au_x(x),x_l,Au_x(x_l),'ro',x2,f2,'rs',x1,f1,'gs',x_u,Au_x(x_u),'go')\n",
+    "hold on;\n",
+    "\n",
+    "if f2<f1\n",
+    "    plot([x_u,x1],[Au_x(x_u),f1],'k-')\n",
+    "    x_u=x1;\n",
+    "else \n",
+    "    plot([x_l,x2],[Au_x(x_l),f2],'k-')\n",
+    "    x_l=x1;\n",
+    "end\n",
+    "hold off\n",
+    "%old_min = current_min;\n",
+    "current_min=min([f1,f2,Au_x(x_l),Au_x(x_u)])\n",
+    "%error_app=abs((current_min-old_min)/current_min)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "current_min = -0.033707\n",
+      "error_app =  0.40787\n"
+     ]
+    },
+    {
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+       "\t</g>\n",
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+       "\t</g>\n",
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+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "% Iteration #2\n",
+    "d=(phi-1)*(x_u-x_l);\n",
+    "\n",
+    "x1=x_l+d; % define point 1\n",
+    "x2=x_u-d; % define point 2\n",
+    "\n",
+    "% evaluate Au_x(x1) and Au_x(x2)\n",
+    "\n",
+    "f1=Au_x(x1);\n",
+    "f2=Au_x(x2);\n",
+    "plot(x,Au_x(x),x_l,Au_x(x_l),'ro',x2,f2,'rs',x1,f1,'gs',x_u,Au_x(x_u),'go')\n",
+    "hold on;\n",
+    "\n",
+    "if f2<f1\n",
+    "    plot([x_u,x1],[Au_x(x_u),f1],'k-')\n",
+    "    x_u=x1;\n",
+    "else \n",
+    "    plot([x_l,x2],[Au_x(x_l),f2],'k-')\n",
+    "    x_l=x1;\n",
+    "end\n",
+    "hold off\n",
+    "old_min = current_min;\n",
+    "current_min=min([f1,f2,Au_x(x_l),Au_x(x_u)])\n",
+    "error_app=abs((current_min-old_min)/current_min)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "current_min = -0.038904\n",
+      "error_app = 0\n"
+     ]
+    },
+    {
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+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "% Iteration #3\n",
+    "d=(phi-1)*(x_u-x_l);\n",
+    "\n",
+    "x1=x_l+d; % define point 1\n",
+    "x2=x_u-d; % define point 2\n",
+    "\n",
+    "% evaluate Au_x(x1) and Au_x(x2)\n",
+    "\n",
+    "f1=Au_x(x1);\n",
+    "f2=Au_x(x2);\n",
+    "plot(x,Au_x(x),x_l,Au_x(x_l),'ro',x2,f2,'rs',x1,f1,'gs',x_u,Au_x(x_u),'go')\n",
+    "hold on;\n",
+    "\n",
+    "if f2<f1\n",
+    "    plot([x_u,x1],[Au_x(x_u),f1],'k-')\n",
+    "    x_u=x1;\n",
+    "else \n",
+    "    plot([x_l,x2],[Au_x(x_l),f2],'k-')\n",
+    "    x_l=x1;\n",
+    "end\n",
+    "hold off\n",
+    "old_min = current_min;\n",
+    "current_min=min([f1,f2,Au_x(x_l),Au_x(x_u)])\n",
+    "error_app=abs((current_min-old_min)/current_min)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "current_min = -0.039000\n",
+      "error_app = 0\n"
+     ]
+    },
+    {
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+   "source": [
+    "% Iteration #3\n",
+    "d=(phi-1)*(x_u-x_l);\n",
+    "\n",
+    "x1=x_l+d; % define point 1\n",
+    "x2=x_u-d; % define point 2\n",
+    "\n",
+    "% evaluate Au_x(x1) and Au_x(x2)\n",
+    "\n",
+    "f1=Au_x(x1);\n",
+    "f2=Au_x(x2);\n",
+    "plot(x,Au_x(x),x_l,Au_x(x_l),'ro',x2,f2,'rs',x1,f1,'gs',x_u,Au_x(x_u),'go')\n",
+    "hold on;\n",
+    "\n",
+    "if f2<f1\n",
+    "    plot([x_u,x1],[Au_x(x_u),f1],'k-')\n",
+    "    x_u=x1;\n",
+    "else \n",
+    "    plot([x_l,x2],[Au_x(x_l),f2],'k-')\n",
+    "    x_l=x1;\n",
+    "end\n",
+    "hold off\n",
+    "old_min = current_min;\n",
+    "current_min=min([f1,f2,Au_x(x_l),Au_x(x_u)])\n",
+    "error_app=abs((current_min-old_min)/current_min)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "## Parabolc Interpolation\n",
+    "\n",
+    "Near a minimum/maximum, the function resembles a parabola. With three data points, it is possible to fit a parabola to the function. So, given a lower and upper bound, we can choose the midpoint and fit a parabola to the 3 x,f(x) coordinates. \n",
+    "\n",
+    "$ x_{4} =x_{2} - \\frac{1}{2}  \\frac{ \\left(x_{2} -x_{1}  \\right)^{2}  \\left[f\n",
+    " \\left(x_{2}  \\right)-f \\left(x_{3} \\right) \\right]- \\left(x_{2} -x_{3}  \\right)^{2}\n",
+    " \\left[f \\left(x_{2}  \\right)-f \\left(x_{1}  \\right) \\right]}{ \\left(x_{2} -x_{1}  \\right) \\left[f \\left(x_{2}  \\right)-f \\left(x_{3}  \\right)\n",
+    " \\right]- \\left(x_{2} -x_{3}  \\right) \\left[f \\left(x_{2}  \\right)-f \\left(x_{1} \\right) \\right]}$\n",
+    "\n",
+    "Where $x_{4}$ location of the maximum or minimum of the parabola. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
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+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "% define Au atomic potential\n",
+    "epsilon = 0.039; % kcal/mol\n",
+    "sigma = 2.934; % Angstrom\n",
+    "Au_x= @(x) lennard_jones(x,sigma,epsilon);\n",
+    "\n",
+    "% set initial limits\n",
+    "x_l=2.8; \n",
+    "x_u=3.5; \n",
+    "\n",
+    "% Iteration #1\n",
+    "x1=x_l;\n",
+    "x2=mean([x_l,x_u]);\n",
+    "x3=x_u;\n",
+    "\n",
+    "% evaluate Au_x(x1), Au_x(x2) and Au_x(x3)\n",
+    " \n",
+    "f1=Au_x(x1);\n",
+    "f2=Au_x(x2);\n",
+    "f3=Au_x(x3);\n",
+    "p = polyfit([x1,x2,x3],[f1,f2,f3],2);\n",
+    "x_fit = linspace(x1,x3,20);\n",
+    "y_fit = polyval(p,x_fit);\n",
+    "\n",
+    "plot(x,Au_x(x),x_fit,y_fit,[x1,x2,x3],[f1,f2,f3],'o')\n",
+    "hold on\n",
+    "if f2<f1 && f2<f3\n",
+    "    x4=x2-0.5*((x2-x1)^2*(f2-f3)-(x2-x3)^2*(f2-f1))/((x2-x1)...\n",
+    "    *(f2-f3)-(x2-x3)*(f2-f1));\n",
+    "    f4=Au_x(x4);\n",
+    "\n",
+    "    if x4>x2\n",
+    "        plot(x4,f4,'*',[x1,x2],[f1,f2])\n",
+    "        x1=x2;\n",
+    "        f1=f2;\n",
+    "    else\n",
+    "        plot(x4,f4,'*',[x3,x2],[f3,f2])\n",
+    "        x3=x2;\n",
+    "        f3=f2;\n",
+    "    end\n",
+    "    x2=x4; f2=f4;\n",
+    "else\n",
+    "    error('no minimum in bracket')\n",
+    "end\n",
+    "hold off"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "f3 = -0.038878\r\n"
+     ]
+    },
+    {
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+       "\t</g>\n",
+       "\t<g id=\"gnuplot_plot_5a\"><title>gnuplot_plot_5a</title>\n",
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+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "p = polyfit([x1,x2,x3],[f1,f2,f3],2);\n",
+    "x_fit = linspace(x1,x3,20);\n",
+    "y_fit = polyval(p,x_fit);\n",
+    "\n",
+    "plot(x,Au_x(x),x_fit,y_fit,[x1,x2,x3],[f1,f2,f3],'o')\n",
+    "hold on\n",
+    "if f2<f1 && f2<f3\n",
+    "    x4=x2-0.5*((x2-x1)^2*(f2-f3)-(x2-x3)^2*(f2-f1))/((x2-x1)...\n",
+    "    *(f2-f3)-(x2-x3)*(f2-f1));\n",
+    "    f4=Au_x(x4);\n",
+    "\n",
+    "    if x4>x2\n",
+    "        plot(x4,f4,'*',[x1,x2],[f1,f2])\n",
+    "        x1=x2;\n",
+    "        f1=f2;\n",
+    "    else\n",
+    "        plot(x4,f4,'*',[x3,x2],[f3,f2])\n",
+    "        x3=x2;\n",
+    "        f3=f2;\n",
+    "    end\n",
+    "    x2=x4; f2=f4;\n",
+    "else\n",
+    "    error('no minimum in bracket')\n",
+    "end\n",
+    "hold off\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "f3 = -0.038878\r\n"
+     ]
+    },
+    {
+     "data": {
+      "image/svg+xml": [
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+       "\t</g>\n",
+       "\t<g id=\"gnuplot_plot_2a\"><title>gnuplot_plot_2a</title>\n",
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+       "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n",
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+       "</g>\n",
+       "\t</g>\n",
+       "\t<g id=\"gnuplot_plot_5a\"><title>gnuplot_plot_5a</title>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
+       "\t<path d=\"M173.6,380.6  \" stroke=\"rgb(191,   0, 191)\"/></g>\n",
+       "\t</g>\n",
+       "<g color=\"white\" fill=\"none\" stroke=\"rgb(191,   0, 191)\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"2.00\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"black\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"0.50\">\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "p = polyfit([x1,x2,x3],[f1,f2,f3],2);\n",
+    "x_fit = linspace(x1,x3,20);\n",
+    "y_fit = polyval(p,x_fit);\n",
+    "\n",
+    "plot(x,Au_x(x),x_fit,y_fit,[x1,x2,x3],[f1,f2,f3],'o')\n",
+    "hold on\n",
+    "if f2<f1 && f2<f3\n",
+    "    x4=x2-0.5*((x2-x1)^2*(f2-f3)-(x2-x3)^2*(f2-f1))/((x2-x1)...\n",
+    "    *(f2-f3)-(x2-x3)*(f2-f1));\n",
+    "    f4=Au_x(x4);\n",
+    "\n",
+    "    if x4>x2\n",
+    "        plot(x4,f4,'*',[x1,x2],[f1,f2])\n",
+    "        x1=x2;\n",
+    "        f1=f2;\n",
+    "    else\n",
+    "        plot(x4,f4,'*',[x3,x2],[f3,f2])\n",
+    "        x3=x2;\n",
+    "        f3=f2;\n",
+    "    end\n",
+    "    x2=x4; f2=f4;\n",
+    "else\n",
+    "    error('no minimum in bracket')\n",
+    "end\n",
+    "hold off\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Parabolic interpolation does not converge in many scenarios even though it it a bracketing method. Instead, functions like `fminbnd` in Matlab and Octave use a combination of the two (Golden Ratio and Parabolic)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Using the solutions to minimization for the nonlinear spring constant\n",
+    "\n",
+    "Now, we have two routines to find minimums of a univariate function (Golden Ratio and Parabolic). Let's use these to solve for the minimum energy given a range of applied forces to the single atom gold chain\n",
+    "\n",
+    "$E_{total}(\\Delta x) = E_{LJ}(x_{min}+\\Delta x) - F \\cdot \\Delta x$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "xmin =  3.2933\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "xmin = fminbnd(Au_x,2.8,6)\n",
+    "\n",
+    "Etotal = @(dx,F) Au_x(xmin+dx)-F.*dx;\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Octave",
+   "language": "octave",
+   "name": "octave"
+  },
+  "language_info": {
+   "file_extension": ".m",
+   "help_links": [
+    {
+     "text": "MetaKernel Magics",
+     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+    }
+   ],
+   "mimetype": "text/x-octave",
+   "name": "octave",
+   "version": "0.19.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/lecture_08/lennard_jones.m b/lecture_08/lennard_jones.m
new file mode 100644
index 0000000..d18a6ad
--- /dev/null
+++ b/lecture_08/lennard_jones.m
@@ -0,0 +1,4 @@
+function E_LJ =lennard_jones(x,sigma,epsilon)
+  E_LJ = 4*epsilon*((sigma./x).^12-(sigma./x).^6);
+end
+
diff --git a/lecture_08/octave-workspace b/lecture_08/octave-workspace
new file mode 100644
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diff --git "a/lecture_08/\34040\001" "b/lecture_08/\34040\001"
new file mode 100644
index 0000000..e69de29

From 4b1d857f609a380cb94af481215f4ad7f27da4c1 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Mon, 13 Feb 2017 16:58:14 -0500
Subject: [PATCH 33/37] update HW3

---
 HW3/README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/HW3/README.md b/HW3/README.md
index eb93c41..891eb1d 100644
--- a/HW3/README.md
+++ b/HW3/README.md
@@ -70,5 +70,4 @@ guesses that do not converge.
     'divergence' to 'convergence')
 
 3. Commit your changes to your repository. Sync your local repository with github. Then
-copy and paste the "clone URL" into the following Google Form [Homework
-#3](https://goo.gl/forms/UJBGwp0fQcSxImkq2)
+copy and paste the "clone URL" into the following Google Form [Homework 3](https://goo.gl/forms/UJBGwp0fQcSxImkq2)

From 593b1de7d5b91589adbe5d2b6706479e798fed4e Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Mon, 13 Feb 2017 17:01:25 -0500
Subject: [PATCH 34/37] updated HW3 1d

---
 HW3/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/HW3/README.md b/HW3/README.md
index 891eb1d..45214a4 100644
--- a/HW3/README.md
+++ b/HW3/README.md
@@ -11,7 +11,7 @@
     c. Copy your `projectile.m` function into the 'roots_and_optimization' folder.
     *Disable the plotting routine for the solvers*
 
-    d. Use the four solvers `falsepos.m`, `incsearch.m`, `newtraph.m` and `mod_secant.m`
+    d. Use the four solvers `falsepos.m`, `bisect.m`, `newtraph.m` and `mod_secant.m`
     to solve for the angle needed to reach h=1.72 m, with an initial speed of 15 m/s. 
 
     e. The `newtraph.m` function needs a derivative, calculate the derivative of your

From 59658f7e3b0880cbaa0d79038195e7ba8af476af Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Mon, 13 Feb 2017 17:06:10 -0500
Subject: [PATCH 35/37] =?UTF-8?q?Delete=20=10=EF=BF=BDY=01?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 "lecture_08/\020\267Y\001" | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 "lecture_08/\020\267Y\001"

diff --git "a/lecture_08/\020\267Y\001" "b/lecture_08/\020\267Y\001"
deleted file mode 100644
index e69de29..0000000

From e5f170b8bf33104074821192dd93176526ac7fd3 Mon Sep 17 00:00:00 2001
From: Ryan C Cooper <ryan.c.cooper@uconn.edu>
Date: Mon, 13 Feb 2017 17:06:15 -0500
Subject: [PATCH 36/37] =?UTF-8?q?Delete=20=EF=BF=BD40=01?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 "lecture_08/\34040\001" | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 "lecture_08/\34040\001"

diff --git "a/lecture_08/\34040\001" "b/lecture_08/\34040\001"
deleted file mode 100644
index e69de29..0000000

From 5128cfdd16e951bae9c50931c11a4a10062adbc6 Mon Sep 17 00:00:00 2001
From: "Ryan C. Cooper" <ryan.c.cooper@uconn.edu>
Date: Tue, 14 Feb 2017 09:29:11 -0500
Subject: [PATCH 37/37] update lecture 08

---
 lecture_07/.lecture_07.md.swo                 |  Bin 16384 -> 0 bytes
 lecture_08/goldmin.m                          |   36 +
 lecture_08/lecture_08.ipynb                   | 1032 ++++++++++++++++-
 lecture_08/lecture_08.md                      |  626 ++++++++++
 .../lecture_08_files/lecture_08_11_0.svg      |  168 +++
 .../lecture_08_files/lecture_08_12_0.svg      |  163 +++
 .../lecture_08_files/lecture_08_13_0.svg      |  163 +++
 .../lecture_08_files/lecture_08_16_1.svg      |  142 +++
 .../lecture_08_files/lecture_08_17_1.svg      |  136 +++
 .../lecture_08_files/lecture_08_19_1.svg      |  135 +++
 .../lecture_08_files/lecture_08_23_0.svg      |  196 ++++
 .../lecture_08_files/lecture_08_3_0.svg       |  147 +++
 .../lecture_08_files/lecture_08_6_1.svg       |  169 +++
 .../lecture_08_files/lecture_08_7_1.svg       |  169 +++
 .../lecture_08_files/lecture_08_8_1.svg       |  169 +++
 .../lecture_08_files/lecture_08_9_1.svg       |  169 +++
 lecture_08/octave-workspace                   |  Bin 4894 -> 16015 bytes
 17 files changed, 3557 insertions(+), 63 deletions(-)
 delete mode 100644 lecture_07/.lecture_07.md.swo
 create mode 100644 lecture_08/goldmin.m
 create mode 100644 lecture_08/lecture_08.md
 create mode 100644 lecture_08/lecture_08_files/lecture_08_11_0.svg
 create mode 100644 lecture_08/lecture_08_files/lecture_08_12_0.svg
 create mode 100644 lecture_08/lecture_08_files/lecture_08_13_0.svg
 create mode 100644 lecture_08/lecture_08_files/lecture_08_16_1.svg
 create mode 100644 lecture_08/lecture_08_files/lecture_08_17_1.svg
 create mode 100644 lecture_08/lecture_08_files/lecture_08_19_1.svg
 create mode 100644 lecture_08/lecture_08_files/lecture_08_23_0.svg
 create mode 100644 lecture_08/lecture_08_files/lecture_08_3_0.svg
 create mode 100644 lecture_08/lecture_08_files/lecture_08_6_1.svg
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 create mode 100644 lecture_08/lecture_08_files/lecture_08_8_1.svg
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diff --git a/lecture_08/goldmin.m b/lecture_08/goldmin.m
new file mode 100644
index 0000000..e5b0ecf
--- /dev/null
+++ b/lecture_08/goldmin.m
@@ -0,0 +1,36 @@
+function [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,varargin)
+% goldmin: minimization golden section search
+%   [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,p1,p2,...):
+%     uses golden section search to find the minimum of f
+% input:
+%   f = name of function
+%   xl, xu = lower and upper guesses
+%   es = desired relative error (default = 0.0001%)
+%   maxit = maximum allowable iterations (default = 50)
+%   p1,p2,... = additional parameters used by f
+% output:
+%   x = location of minimum
+%   fx = minimum function value
+%   ea = approximate relative error (%)
+%   iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+phi=(1+sqrt(5))/2;
+iter=0;
+while(1)
+  d = (phi-1)*(xu - xl);
+  x1 = xl + d;
+  x2 = xu - d;
+  if f(x1,varargin{:}) < f(x2,varargin{:})
+    xopt = x1;
+    xl = x2;
+  else
+    xopt = x2;
+    xu = x1;
+  end
+  iter=iter+1;
+  if xopt~=0, ea = (2 - phi) * abs((xu - xl) / xopt) * 100;end
+  if ea <= es | iter >= maxit,break,end
+end
+x=xopt;fx=f(xopt,varargin{:});
\ No newline at end of file
diff --git a/lecture_08/lecture_08.ipynb b/lecture_08/lecture_08.ipynb
index 134ed8a..d99107a 100644
--- a/lecture_08/lecture_08.ipynb
+++ b/lecture_08/lecture_08.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 1,
    "metadata": {
     "collapsed": false
    },
@@ -20,24 +20,6 @@
     "Many problems involve finding a minimum or maximum based on given constraints. Engineers and scientists typically use energy balance equations to find the conditions of minimum energy, but this value may never go to 0 and the actual value of energy may not be of interest. "
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -64,7 +46,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
@@ -243,7 +225,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
@@ -281,7 +263,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
@@ -515,7 +497,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -738,7 +720,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
@@ -748,7 +730,7 @@
      "output_type": "stream",
      "text": [
       "current_min = -0.038904\n",
-      "error_app = 0\n"
+      "error_app =  0.13359\n"
      ]
     },
     {
@@ -888,30 +870,30 @@
        "\t<g id=\"gnuplot_plot_2a\"><title>gnuplot_plot_2a</title>\n",
        "<g color=\"black\" fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke-width=\"3.00\">\n",
        "\t<g onmousemove=\"gnuplot_svg.showHypertext(evt,'')\" onmouseout=\"gnuplot_svg.hideHypertext()\"><title> </title>\n",
-       "\t<use color=\"rgb(255,   0,   0)\" transform=\"translate(165.8,380.6) scale(9.00)\" xlink:href=\"#gpPt5\"/></g>\n",
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+   "execution_count": 7,
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@@ -970,7 +952,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "current_min = -0.039000\n",
+      "current_min = -0.038904\n",
       "error_app = 0\n"
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@@ -1111,30 +1093,30 @@
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-    "## Parabolc Interpolation\n",
+    "## Parabolic Interpolation\n",
     "\n",
     "Near a minimum/maximum, the function resembles a parabola. With three data points, it is possible to fit a parabola to the function. So, given a lower and upper bound, we can choose the midpoint and fit a parabola to the 3 x,f(x) coordinates. \n",
     "\n",
@@ -1202,7 +1184,7 @@
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+   "execution_count": 8,
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@@ -1436,18 +1418,11 @@
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-   "execution_count": 32,
+   "execution_count": 9,
    "metadata": {
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-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "f3 = -0.038878\r\n"
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-    },
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-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "f3 = -0.038878\r\n"
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-    },
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@@ -1888,7 +1856,7 @@
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@@ -1897,24 +1865,962 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "xmin =  3.2933\r\n"
+      "xmin =  0.32933\n",
+      "Emin =   -2.7096e-04\n"
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    ],
    "source": [
-    "xmin = fminbnd(Au_x,2.8,6)\n",
+    "epsilon = 0.039; % kcal/mol\n",
+    "epsilon = epsilon*6.9477e-21; % J/atom\n",
+    "epsilon = epsilon*1e18; % aJ/J\n",
+    "% final units for epsilon are aJ\n",
+    "\n",
+    "sigma = 2.934; % Angstrom\n",
+    "sigma = sigma*0.10; % nm/Angstrom\n",
+    "x=linspace(2.8,6,200)*0.10; % bond length in um\n",
+    "\n",
+    "Ex = lennard_jones(x,sigma,epsilon);\n",
     "\n",
-    "Etotal = @(dx,F) Au_x(xmin+dx)-F.*dx;\n"
+    "%[Emin,imin]=min(Ex);\n",
+    "\n",
+    "[xmin,Emin] = fminbnd(@(x) lennard_jones(x,sigma,epsilon),0.28,0.6)\n",
+    "\n",
+    "plot(x,Ex,xmin,Emin,'o')\n",
+    "ylabel('Lennard Jones Potential (aJ/atom)')\n",
+    "xlabel('bond length (nm)')\n",
+    "\n",
+    "Etotal = @(dx,F) lennard_jones(xmin+dx,sigma,epsilon)-F.*dx;\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 114,
    "metadata": {
-    "collapsed": true
+    "collapsed": false
    },
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: called from\n",
+      "    goldmin at line 17 column 1\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
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+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
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+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
+      "warning: Matlab-style short-circuit operation performed for operator |\n",
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+      "warning: Matlab-style short-circuit operation performed for operator |\n",
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+      "warning: Matlab-style short-circuit operation performed for operator |\n",
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+   "source": [
+    "N=50;\n",
+    "dx = zeros(1,N); % [in nm]\n",
+    "F_applied=linspace(0,0.0022,N); % [in nN]\n",
+    "for i=1:N\n",
+    "    optmin=goldmin(@(dx) Etotal(dx,F_applied(i)),-0.001,0.035);\n",
+    "    dx(i)=optmin;\n",
+    "end\n",
+    "\n",
+    "plot(dx,F_applied)\n",
+    "xlabel('dx (nm)')\n",
+    "ylabel('Force (nN)')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For this function, it is possible to take a derivative and compare the analytical result:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 105,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "F =\n",
+      "\n",
+      "@(dx) 4 * epsilon * 6 * (sigma ^ 6 ./ (xmin + dx) .^ 7 - 2 * sigma ^ 12 ./ (xmin + dx) .^ 13)\n",
+      "\n"
+     ]
+    },
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+   "source": [
+    "dx_full=linspace(0,0.06,50);\n",
+    "F= @(dx) 4*epsilon*6*(sigma^6./(xmin+dx).^7-2*sigma^12./(xmin+dx).^13)\n",
+    "plot(dx_full,F(dx_full),dx,F_applied)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "## Curve-fitting\n",
+    "Another example is minimizing error in your approximation of a function. If you have data (now we have Force-displacement data) we can fit this to a function, such as:\n",
+    "\n",
+    "$F(x) = K_{1}\\Delta x + \\frac{1}{2} K_{2}(\\Delta x)^{2}$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "function SSE = sse_of_parabola(K,xdata,ydata)\n",
+    "    % calculate the sum of squares error for a parabola given a function, func, and xdata and ydata\n",
+    "    % output is SSE=sum of squares error\n",
+    "    K1=K(1);\n",
+    "    K2=K(2);\n",
+    "    y_function = K1*xdata+1/2*K2*xdata.^2;\n",
+    "    SSE = sum((ydata-y_function).^2);\n",
+    "end\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 113,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "The nonlinear spring constants are K1=0.16 nN/nm and K2=-5.98 nN/nm^2\n",
+      "The mininum sum of squares error = 7.35e-08\n"
+     ]
+    }
+   ],
+   "source": [
+    "[K,SSE_min]=fminsearch(@(K) sse_of_parabola(K,dx,F_applied),[1,1]);\n",
+    "fprintf('\\nThe nonlinear spring constants are K1=%1.2f nN/nm and K2=%1.2f nN/nm^2\\n',K)\n",
+    "fprintf('The mininum sum of squares error = %1.2e',SSE_min)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "metadata": {
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+       "\t<use color=\"rgb(  0,   0, 255)\" transform=\"translate(439.7,60.8) scale(9.00)\" xlink:href=\"#gpPt5\"/>\n",
+       "</g>\n",
+       "\t</g>\n",
+       "\t<g id=\"gnuplot_plot_2a\"><title>gnuplot_plot_2a</title>\n",
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+       "</svg>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.SVG object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot(dx,F_applied,'o',dx,K(1)*dx+1/2*K(2)*dx.^2)"
+   ]
   }
  ],
  "metadata": {
diff --git a/lecture_08/lecture_08.md b/lecture_08/lecture_08.md
new file mode 100644
index 0000000..8a81a2a
--- /dev/null
+++ b/lecture_08/lecture_08.md
@@ -0,0 +1,626 @@
+
+
+```octave
+%plot --format svg
+```
+
+# Optimization
+
+Many problems involve finding a minimum or maximum based on given constraints. Engineers and scientists typically use energy balance equations to find the conditions of minimum energy, but this value may never go to 0 and the actual value of energy may not be of interest. 
+
+The Lennard-Jones potential is commonly used to model interatomic bonding. 
+
+$E_{LJ}(x)=4\epsilon \left(\left(\frac{\sigma}{x}\right)^{12}-\left(\frac{\sigma}{x}\right)^{6}\right)$
+
+Considering a 1-D gold chain, we can calculate the bond length, $x_{b}$, with no force applied to the chain and even for tension, F. This will allow us to calculate the nonlinear spring constant of a 1-D gold chain. 
+
+![TEM image of Gold chain](au_chain.jpg)
+
+Computational Tools to Study and Predict the Long-Term Stability of Nanowires.
+By Martin E. Zoloff Michoff, Patricio Vélez, Sergio A. Dassie and Ezequiel P. M. Leiva 
+
+![Model of Gold chain, from molecular dynamics simulation](Auchain_model.gif)
+
+[Single atom gold chain mechanics](http://www.uam.es/personal_pdi/ciencias/agrait/)
+
+### First, let's find the minimum energy $\min(E_{LJ}(x))$
+
+## Brute force
+
+
+```octave
+setdefaults
+epsilon = 0.039; % kcal/mol
+sigma = 2.934; % Angstrom
+x=linspace(2.8,6,200); % bond length in Angstrom
+
+Ex = lennard_jones(x,sigma,epsilon);
+
+[Emin,imin]=min(Ex);
+
+plot(x,Ex,x(imin),Emin,'o')
+```
+
+
+![svg](lecture_08_files/lecture_08_3_0.svg)
+
+
+
+```octave
+x(imin-1)
+x(imin)
+x(imin+1)
+```
+
+    ans =  3.2824
+    ans =  3.2985
+    ans =  3.3146
+
+
+## Golden Search Algorithm
+
+We can't just look for a sign change for the problem (unless we can take a derivative) so we need a new approach to determine whether we have a maximum between the two bounds.
+
+Rather than using the midpoint of initial bounds, here the problem is more difficult. We need to compare the values of 4 function evaluations. The golden search uses the golden ratio to determine two interior points. 
+
+![golden ratio](goldenratio.png)
+
+Start with bounds of 2.5 and 6 Angstrom. 
+
+
+```octave
+% define Au atomic potential
+epsilon = 0.039; % kcal/mol
+sigma = 2.934; % Angstrom
+Au_x= @(x) lennard_jones(x,sigma,epsilon);
+
+% calculate golden ratio
+phi = 1/2+sqrt(5)/2;
+% set initial limits
+x_l=2.8; 
+x_u=6; 
+
+% Iteration #1
+d=(phi-1)*(x_u-x_l);
+
+x1=x_l+d; % define point 1
+x2=x_u-d; % define point 2
+
+
+% evaluate Au_x(x1) and Au_x(x2)
+
+f1=Au_x(x1);
+f2=Au_x(x2);
+plot(x,Au_x(x),x_l,Au_x(x_l),'ro',x2,f2,'rs',x1,f1,'gs',x_u,Au_x(x_u),'go')
+hold on;
+
+if f2<f1
+    plot([x_u,x1],[Au_x(x_u),f1],'k-')
+    x_u=x1;
+else 
+    plot([x_l,x2],[Au_x(x_l),f2],'k-')
+    x_l=x1;
+end
+hold off
+%old_min = current_min;
+current_min=min([f1,f2,Au_x(x_l),Au_x(x_u)])
+%error_app=abs((current_min-old_min)/current_min)
+```
+
+    current_min = -0.019959
+
+
+
+![svg](lecture_08_files/lecture_08_6_1.svg)
+
+
+
+```octave
+% Iteration #2
+d=(phi-1)*(x_u-x_l);
+
+x1=x_l+d; % define point 1
+x2=x_u-d; % define point 2
+
+% evaluate Au_x(x1) and Au_x(x2)
+
+f1=Au_x(x1);
+f2=Au_x(x2);
+plot(x,Au_x(x),x_l,Au_x(x_l),'ro',x2,f2,'rs',x1,f1,'gs',x_u,Au_x(x_u),'go')
+hold on;
+
+if f2<f1
+    plot([x_u,x1],[Au_x(x_u),f1],'k-')
+    x_u=x1;
+else 
+    plot([x_l,x2],[Au_x(x_l),f2],'k-')
+    x_l=x1;
+end
+hold off
+old_min = current_min;
+current_min=min([f1,f2,Au_x(x_l),Au_x(x_u)])
+error_app=abs((current_min-old_min)/current_min)
+```
+
+    current_min = -0.033707
+    error_app =  0.40787
+
+
+
+![svg](lecture_08_files/lecture_08_7_1.svg)
+
+
+
+```octave
+% Iteration #3
+d=(phi-1)*(x_u-x_l);
+
+x1=x_l+d; % define point 1
+x2=x_u-d; % define point 2
+
+% evaluate Au_x(x1) and Au_x(x2)
+
+f1=Au_x(x1);
+f2=Au_x(x2);
+plot(x,Au_x(x),x_l,Au_x(x_l),'ro',x2,f2,'rs',x1,f1,'gs',x_u,Au_x(x_u),'go')
+hold on;
+
+if f2<f1
+    plot([x_u,x1],[Au_x(x_u),f1],'k-')
+    x_u=x1;
+else 
+    plot([x_l,x2],[Au_x(x_l),f2],'k-')
+    x_l=x1;
+end
+hold off
+old_min = current_min;
+current_min=min([f1,f2,Au_x(x_l),Au_x(x_u)])
+error_app=abs((current_min-old_min)/current_min)
+```
+
+    current_min = -0.038904
+    error_app =  0.13359
+
+
+
+![svg](lecture_08_files/lecture_08_8_1.svg)
+
+
+
+```octave
+% Iteration #3
+d=(phi-1)*(x_u-x_l);
+
+x1=x_l+d; % define point 1
+x2=x_u-d; % define point 2
+
+% evaluate Au_x(x1) and Au_x(x2)
+
+f1=Au_x(x1);
+f2=Au_x(x2);
+plot(x,Au_x(x),x_l,Au_x(x_l),'ro',x2,f2,'rs',x1,f1,'gs',x_u,Au_x(x_u),'go')
+hold on;
+
+if f2<f1
+    plot([x_u,x1],[Au_x(x_u),f1],'k-')
+    x_u=x1;
+else 
+    plot([x_l,x2],[Au_x(x_l),f2],'k-')
+    x_l=x1;
+end
+hold off
+old_min = current_min;
+current_min=min([f1,f2,Au_x(x_l),Au_x(x_u)])
+error_app=abs((current_min-old_min)/current_min)
+```
+
+    current_min = -0.038904
+    error_app = 0
+
+
+
+![svg](lecture_08_files/lecture_08_9_1.svg)
+
+
+## Parabolic Interpolation
+
+Near a minimum/maximum, the function resembles a parabola. With three data points, it is possible to fit a parabola to the function. So, given a lower and upper bound, we can choose the midpoint and fit a parabola to the 3 x,f(x) coordinates. 
+
+$ x_{4} =x_{2} - \frac{1}{2}  \frac{ \left(x_{2} -x_{1}  \right)^{2}  \left[f
+ \left(x_{2}  \right)-f \left(x_{3} \right) \right]- \left(x_{2} -x_{3}  \right)^{2}
+ \left[f \left(x_{2}  \right)-f \left(x_{1}  \right) \right]}{ \left(x_{2} -x_{1}  \right) \left[f \left(x_{2}  \right)-f \left(x_{3}  \right)
+ \right]- \left(x_{2} -x_{3}  \right) \left[f \left(x_{2}  \right)-f \left(x_{1} \right) \right]}$
+
+Where $x_{4}$ location of the maximum or minimum of the parabola. 
+
+
+```octave
+% define Au atomic potential
+epsilon = 0.039; % kcal/mol
+sigma = 2.934; % Angstrom
+Au_x= @(x) lennard_jones(x,sigma,epsilon);
+
+% set initial limits
+x_l=2.8; 
+x_u=3.5; 
+
+% Iteration #1
+x1=x_l;
+x2=mean([x_l,x_u]);
+x3=x_u;
+
+% evaluate Au_x(x1), Au_x(x2) and Au_x(x3)
+ 
+f1=Au_x(x1);
+f2=Au_x(x2);
+f3=Au_x(x3);
+p = polyfit([x1,x2,x3],[f1,f2,f3],2);
+x_fit = linspace(x1,x3,20);
+y_fit = polyval(p,x_fit);
+
+plot(x,Au_x(x),x_fit,y_fit,[x1,x2,x3],[f1,f2,f3],'o')
+hold on
+if f2<f1 && f2<f3
+    x4=x2-0.5*((x2-x1)^2*(f2-f3)-(x2-x3)^2*(f2-f1))/((x2-x1)...
+    *(f2-f3)-(x2-x3)*(f2-f1));
+    f4=Au_x(x4);
+
+    if x4>x2
+        plot(x4,f4,'*',[x1,x2],[f1,f2])
+        x1=x2;
+        f1=f2;
+    else
+        plot(x4,f4,'*',[x3,x2],[f3,f2])
+        x3=x2;
+        f3=f2;
+    end
+    x2=x4; f2=f4;
+else
+    error('no minimum in bracket')
+end
+hold off
+```
+
+
+![svg](lecture_08_files/lecture_08_11_0.svg)
+
+
+
+```octave
+p = polyfit([x1,x2,x3],[f1,f2,f3],2);
+x_fit = linspace(x1,x3,20);
+y_fit = polyval(p,x_fit);
+
+plot(x,Au_x(x),x_fit,y_fit,[x1,x2,x3],[f1,f2,f3],'o')
+hold on
+if f2<f1 && f2<f3
+    x4=x2-0.5*((x2-x1)^2*(f2-f3)-(x2-x3)^2*(f2-f1))/((x2-x1)...
+    *(f2-f3)-(x2-x3)*(f2-f1));
+    f4=Au_x(x4);
+
+    if x4>x2
+        plot(x4,f4,'*',[x1,x2],[f1,f2])
+        x1=x2;
+        f1=f2;
+    else
+        plot(x4,f4,'*',[x3,x2],[f3,f2])
+        x3=x2;
+        f3=f2;
+    end
+    x2=x4; f2=f4;
+else
+    error('no minimum in bracket')
+end
+hold off
+
+```
+
+
+![svg](lecture_08_files/lecture_08_12_0.svg)
+
+
+
+```octave
+p = polyfit([x1,x2,x3],[f1,f2,f3],2);
+x_fit = linspace(x1,x3,20);
+y_fit = polyval(p,x_fit);
+
+plot(x,Au_x(x),x_fit,y_fit,[x1,x2,x3],[f1,f2,f3],'o')
+hold on
+if f2<f1 && f2<f3
+    x4=x2-0.5*((x2-x1)^2*(f2-f3)-(x2-x3)^2*(f2-f1))/((x2-x1)...
+    *(f2-f3)-(x2-x3)*(f2-f1));
+    f4=Au_x(x4);
+
+    if x4>x2
+        plot(x4,f4,'*',[x1,x2],[f1,f2])
+        x1=x2;
+        f1=f2;
+    else
+        plot(x4,f4,'*',[x3,x2],[f3,f2])
+        x3=x2;
+        f3=f2;
+    end
+    x2=x4; f2=f4;
+else
+    error('no minimum in bracket')
+end
+hold off
+
+```
+
+
+![svg](lecture_08_files/lecture_08_13_0.svg)
+
+
+Parabolic interpolation does not converge in many scenarios even though it it a bracketing method. Instead, functions like `fminbnd` in Matlab and Octave use a combination of the two (Golden Ratio and Parabolic)
+
+## Using the solutions to minimization for the nonlinear spring constant
+
+Now, we have two routines to find minimums of a univariate function (Golden Ratio and Parabolic). Let's use these to solve for the minimum energy given a range of applied forces to the single atom gold chain
+
+$E_{total}(\Delta x) = E_{LJ}(x_{min}+\Delta x) - F \cdot \Delta x$
+
+
+```octave
+epsilon = 0.039; % kcal/mol
+epsilon = epsilon*6.9477e-21; % J/atom
+epsilon = epsilon*1e18; % aJ/J
+% final units for epsilon are aJ
+
+sigma = 2.934; % Angstrom
+sigma = sigma*0.10; % nm/Angstrom
+x=linspace(2.8,6,200)*0.10; % bond length in um
+
+Ex = lennard_jones(x,sigma,epsilon);
+
+%[Emin,imin]=min(Ex);
+
+[xmin,Emin] = fminbnd(@(x) lennard_jones(x,sigma,epsilon),0.28,0.6)
+
+plot(x,Ex,xmin,Emin,'o')
+ylabel('Lennard Jones Potential (aJ/atom)')
+xlabel('bond length (nm)')
+
+Etotal = @(dx,F) lennard_jones(xmin+dx,sigma,epsilon)-F.*dx;
+
+```
+
+    xmin =  0.32933
+    Emin =   -2.7096e-04
+
+
+
+![svg](lecture_08_files/lecture_08_16_1.svg)
+
+
+
+```octave
+N=50;
+dx = zeros(1,N); % [in nm]
+F_applied=linspace(0,0.0022,N); % [in nN]
+for i=1:N
+    optmin=goldmin(@(dx) Etotal(dx,F_applied(i)),-0.001,0.035);
+    dx(i)=optmin;
+end
+
+plot(dx,F_applied)
+xlabel('dx (nm)')
+ylabel('Force (nN)')
+```
+
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: called from
+        goldmin at line 17 column 1
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+    warning: Matlab-style short-circuit operation performed for operator |
+
+
+
+![svg](lecture_08_files/lecture_08_17_1.svg)
+
+
+For this function, it is possible to take a derivative and compare the analytical result:
+
+
+```octave
+dx_full=linspace(0,0.06,50);
+F= @(dx) 4*epsilon*6*(sigma^6./(xmin+dx).^7-2*sigma^12./(xmin+dx).^13)
+plot(dx_full,F(dx_full),dx,F_applied)
+```
+
+    F =
+    
+    @(dx) 4 * epsilon * 6 * (sigma ^ 6 ./ (xmin + dx) .^ 7 - 2 * sigma ^ 12 ./ (xmin + dx) .^ 13)
+    
+
+
+
+![svg](lecture_08_files/lecture_08_19_1.svg)
+
+
+## Curve-fitting
+Another example is minimizing error in your approximation of a function. If you have data (now we have Force-displacement data) we can fit this to a function, such as:
+
+$F(x) = K_{1}\Delta x + \frac{1}{2} K_{2}(\Delta x)^{2}$
+
+
+
+```octave
+function SSE = sse_of_parabola(K,xdata,ydata)
+    % calculate the sum of squares error for a parabola given a function, func, and xdata and ydata
+    % output is SSE=sum of squares error
+    K1=K(1);
+    K2=K(2);
+    y_function = K1*xdata+1/2*K2*xdata.^2;
+    SSE = sum((ydata-y_function).^2);
+end
+    
+```
+
+
+```octave
+[K,SSE_min]=fminsearch(@(K) sse_of_parabola(K,dx,F_applied),[1,1]);
+fprintf('\nThe nonlinear spring constants are K1=%1.2f nN/nm and K2=%1.2f nN/nm^2\n',K)
+fprintf('The mininum sum of squares error = %1.2e',SSE_min)
+```
+
+    
+    The nonlinear spring constants are K1=0.16 nN/nm and K2=-5.98 nN/nm^2
+    The mininum sum of squares error = 7.35e-08
+
+
+
+```octave
+plot(dx,F_applied,'o',dx,K(1)*dx+1/2*K(2)*dx.^2)
+```
+
+
+![svg](lecture_08_files/lecture_08_23_0.svg)
+
diff --git a/lecture_08/lecture_08_files/lecture_08_11_0.svg b/lecture_08/lecture_08_files/lecture_08_11_0.svg
new file mode 100644
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@@ -0,0 +1,168 @@
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+		<text><tspan font-family="{}">4</tspan></text>
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+		<text><tspan font-family="{}">4.5</tspan></text>
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+		<text><tspan font-family="{}">0.7</tspan></text>
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diff --git a/lecture_08/octave-workspace b/lecture_08/octave-workspace
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