diff --git a/01_Introduction/lecture_01-Copy1.ipynb b/01_Introduction/.ipynb_checkpoints/01-Introduction-checkpoint.ipynb
similarity index 98%
rename from 01_Introduction/lecture_01-Copy1.ipynb
rename to 01_Introduction/.ipynb_checkpoints/01-Introduction-checkpoint.ipynb
index fa4f5eb..b543fee 100644
--- a/01_Introduction/lecture_01-Copy1.ipynb
+++ b/01_Introduction/.ipynb_checkpoints/01-Introduction-checkpoint.ipynb
@@ -33,7 +33,7 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 1,
"metadata": {
"collapsed": true,
"slideshow": {
@@ -64,7 +64,7 @@
"metadata": {
"collapsed": false,
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
}
},
"outputs": [],
@@ -97,7 +97,7 @@
"metadata": {
"collapsed": false,
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
}
},
"outputs": [
@@ -199,7 +199,7 @@
"metadata": {
"collapsed": false,
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
}
},
"outputs": [
@@ -226,20 +226,29 @@
"fprintf('%7.1f | %18.2f | %15.2f\\n',M(:,1:3)');"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Set default values for plotting"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true,
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
}
},
"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)"
]
@@ -412,15 +421,6 @@
"source": [
"plot(t,v_analytical,'-',t,v_numerical,'o-')"
]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": []
}
],
"metadata": {
diff --git a/01_Introduction/.ipynb_checkpoints/lecture_01-Copy1-checkpoint.ipynb b/01_Introduction/01-Introduction.ipynb
similarity index 90%
rename from 01_Introduction/.ipynb_checkpoints/lecture_01-Copy1-checkpoint.ipynb
rename to 01_Introduction/01-Introduction.ipynb
index 495f361..b543fee 100644
--- a/01_Introduction/.ipynb_checkpoints/lecture_01-Copy1-checkpoint.ipynb
+++ b/01_Introduction/01-Introduction.ipynb
@@ -13,35 +13,36 @@
]
},
{
- "cell_type": "code",
- "execution_count": 13,
+ "cell_type": "markdown",
"metadata": {
- "collapsed": true,
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "subslide"
}
},
- "outputs": [],
"source": [
- "%plot --format svg"
+ "An object falling is subject to the force of \n",
+ "\n",
+ "- gravity ($F_g$=mg) and \n",
+ "- drag ($F_d=cv^2$)\n",
+ "\n",
+ "Acceleration of the object:\n",
+ "\n",
+ "$\\sum F=ma=F_g-F_d=mg - cv^2 = m\\frac{dv}{dt}$\n",
+ "\n"
]
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 1,
"metadata": {
"collapsed": true,
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
}
},
"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)"
+ "%plot --format svg"
]
},
{
@@ -59,45 +60,18 @@
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": 18,
"metadata": {
"collapsed": false,
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
}
},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "t =\n",
- "\n",
- " 0\n",
- " 2\n",
- " 4\n",
- " 6\n",
- " 8\n",
- " 10\n",
- " 12\n",
- "\n",
- "t =\n",
- "\n",
- " 0\n",
- " 2\n",
- " 4\n",
- " 6\n",
- " 8\n",
- " 10\n",
- " 12\n",
- "\n"
- ]
- }
- ],
+ "outputs": [],
"source": [
- "t=[0,2,4,6,8,10,12]'\n",
- "% or\n",
- "t=[0:2:12]'"
+ "t=[0,2,4,6,8,10,12]';\n",
+ "% or \n",
+ "t=[0:2:12]';"
]
},
{
@@ -108,16 +82,22 @@
}
},
"source": [
- "Define constants and analytical solution (meters-kilogram-sec)"
+ "### Define constants and analytical solution (meters-kilogram-sec)\n",
+ "\n",
+ "g=9.81 m/s$^2$, c=0.25 kg/m, m=60 kg\n",
+ "\n",
+ "$v_{terminal}=\\sqrt{\\frac{mg}{c}}$\n",
+ "\n",
+ "$v=v_{terminal}\\tanh{\\left(\\frac{gt}{v_{terminal}}\\right)}$"
]
},
{
"cell_type": "code",
- "execution_count": 4,
+ "execution_count": 19,
"metadata": {
"collapsed": false,
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
}
},
"outputs": [
@@ -125,6 +105,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
+ "v_terminal = 48.522\n",
"v_analytical =\n",
"\n",
" 0.00000\n",
@@ -139,14 +120,36 @@
}
],
"source": [
- "c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c);\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)"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Define numerical method\n",
+ "#### Finite difference approximation\n",
+ "\n",
+ "$\\frac{v(t_{i+1})-v(t_{i})}{t_{i+1}-t_{i}}=g-\\frac{c}{m}v(t_{i})^2$\n",
+ "\n",
+ "solve for $v(t_{i+1})$\n",
+ "\n",
+ "$v(t_{i+1})=v(t_{i})+\\left(g-\\frac{c}{m}v(t_{i})^2\\right)(t_{i+1}-t_{i})$\n",
+ "\n",
+ "or\n",
+ "\n",
+ "$v(t_{i+1})=v(t_{i})+\\frac{dv_{i}}{dt}(t_{i+1}-t_{i})$\n"
+ ]
+ },
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 6,
"metadata": {
"collapsed": false,
"slideshow": {
@@ -192,11 +195,11 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 10,
"metadata": {
"collapsed": false,
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
}
},
"outputs": [
@@ -223,9 +226,36 @@
"fprintf('%7.1f | %18.2f | %15.2f\\n',M(:,1:3)');"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Set default values for plotting"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": true,
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "set (0, \"defaultaxesfontsize\", 18)\n",
+ "set (0, \"defaulttextfontsize\", 18) \n",
+ "set (0, \"defaultlinelinewidth\", 4)"
+ ]
+ },
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 15,
"metadata": {
"collapsed": false,
"slideshow": {
diff --git a/01_Introduction/lecture_01.ipynb b/01_Introduction/lecture_01.ipynb
deleted file mode 100644
index 307bc0c..0000000
--- a/01_Introduction/lecture_01.ipynb
+++ /dev/null
@@ -1,366 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Freefall Model\n",
- "## Octave solution (will run same on Matlab)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "%plot --format svg"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "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"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "t =\n",
- "\n",
- " 0\n",
- " 2\n",
- " 4\n",
- " 6\n",
- " 8\n",
- " 10\n",
- " 12\n",
- "\n"
- ]
- }
- ],
- "source": [
- "t=[0,2,4,6,8,10,12]'"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Define constants and analytical solution (meters-kilogram-sec)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "v_analytical =\n",
- "\n",
- " 0.00000\n",
- " 18.61630\n",
- " 32.45521\n",
- " 40.64183\n",
- " 44.84646\n",
- " 46.84974\n",
- " 47.77002\n",
- "\n"
- ]
- }
- ],
- "source": [
- "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)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "v_numerical =\n",
- "\n",
- " 0.00000\n",
- " 19.62000\n",
- " 36.03213\n",
- " 44.83284\n",
- " 47.70298\n",
- " 48.35986\n",
- " 48.49089\n",
- "\n"
- ]
- }
- ],
- "source": [
- "v_numerical=zeros(length(t),1);\n",
- "for i=1:length(t)-1\n",
- " v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*2;\n",
- "end\n",
- "v_numerical"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Display time, velocity (analytical) and velocity (numerical)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "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 | 18.62 | 19.62\n",
- " 4.0 | 32.46 | 36.03\n",
- " 6.0 | 40.64 | 44.83\n",
- " 8.0 | 44.85 | 47.70\n",
- " 10.0 | 46.85 | 48.36\n",
- " 12.0 | 47.77 | 48.49\n"
- ]
- }
- ],
- "source": [
- "fprintf('time (s)|vel analytical (m/s)|vel numerical (m/s)\\n')\n",
- "fprintf('-----------------------------------------------')\n",
- "M=[t,v_analytical,v_numerical];\n",
- "fprintf('%7.1f | %18.2f | %15.2f\\n',M(:,1:3)');"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/svg+xml": [
- ""
- ],
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "plot(t,v_analytical,'-',t,v_numerical,'o-')"
- ]
- }
- ],
- "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/01_Introduction/lecture_01.md b/01_Introduction/lecture_01.md
deleted file mode 100644
index 807e888..0000000
--- a/01_Introduction/lecture_01.md
+++ /dev/null
@@ -1,111 +0,0 @@
-
-# Freefall Model
-## Octave solution (will run same on Matlab)
-
-
-```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
-
-
-```octave
-t=[0,2,4,6,8,10,12]'
-```
-
- t =
-
- 0
- 2
- 4
- 6
- 8
- 10
- 12
-
-
-
-Define constants and analytical solution (meters-kilogram-sec)
-
-
-```octave
-c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c);
-
-v_analytical = v_terminal*tanh(g*t/v_terminal)
-```
-
- v_analytical =
-
- 0.00000
- 18.61630
- 32.45521
- 40.64183
- 44.84646
- 46.84974
- 47.77002
-
-
-
-
-```octave
-v_numerical=zeros(length(t),1);
-for i=1:length(t)-1
- v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*2;
-end
-v_numerical
-```
-
- v_numerical =
-
- 0.00000
- 19.62000
- 36.03213
- 44.83284
- 47.70298
- 48.35986
- 48.49089
-
-
-
-Display time, velocity (analytical) and velocity (numerical)
-
-
-```octave
-fprintf('time (s)|vel analytical (m/s)|vel numerical (m/s)\n')
-fprintf('-----------------------------------------------')
-M=[t,v_analytical,v_numerical];
-fprintf('%7.1f | %18.2f | %15.2f\n',M(:,1:3)');
-```
-
- time (s)|vel analytical (m/s)|vel numerical (m/s)
- -----------------------------------------------
- 0.0 | 0.00 | 0.00
- 2.0 | 18.62 | 19.62
- 4.0 | 32.46 | 36.03
- 6.0 | 40.64 | 44.83
- 8.0 | 44.85 | 47.70
- 10.0 | 46.85 | 48.36
- 12.0 | 47.77 | 48.49
-
-
-
-```octave
-plot(t,v_analytical,'-',t,v_numerical,'o-')
-```
-
-
-
-![]()
-
diff --git a/01_Introduction/lecture_01.pdf b/01_Introduction/lecture_01.pdf
deleted file mode 100644
index c54f29e..0000000
Binary files a/01_Introduction/lecture_01.pdf and /dev/null differ
diff --git a/01_Introduction/lecture_01_notes.pdf b/01_Introduction/lecture_01_notes.pdf
deleted file mode 100644
index d84a44d..0000000
Binary files a/01_Introduction/lecture_01_notes.pdf and /dev/null differ
diff --git a/01_Introduction/output_10_0.svg b/01_Introduction/output_10_0.svg
deleted file mode 100644
index 5c7cdea..0000000
--- a/01_Introduction/output_10_0.svg
+++ /dev/null
@@ -1,143 +0,0 @@
-
\ No newline at end of file