diff --git a/HW_1_plotting.ipynb b/HW_1_plotting.ipynb
index 160a6cb..bbd151b 100644
--- a/HW_1_plotting.ipynb
+++ b/HW_1_plotting.ipynb
@@ -182133,14 +182133,22 @@
   "language_info": {
    "file_extension": ".m",
    "help_links": [
+    {
+     "text": "GNU Octave",
+     "url": "https://www.gnu.org/software/octave/support.html"
+    },
+    {
+     "text": "Octave Kernel",
+     "url": "https://github.com/Calysto/octave_kernel"
+    },
     {
      "text": "MetaKernel Magics",
-     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+     "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
     }
    ],
    "mimetype": "text/x-octave",
    "name": "octave",
-   "version": "0.19.14"
+   "version": "5.1.0"
   }
  },
  "nbformat": 4,
diff --git a/Matlab refresher.ipynb b/Matlab refresher.ipynb
new file mode 100644
index 0000000..8cefa3e
--- /dev/null
+++ b/Matlab refresher.ipynb	
@@ -0,0 +1,34 @@
+{
+ "cells": [
+  {
+   "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/double_pendulum.ipynb b/double_pendulum.ipynb
index c77b169..9cc0981 100644
--- a/double_pendulum.ipynb
+++ b/double_pendulum.ipynb
@@ -2,13 +2,35 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
    "source": [
-    "%plot --format svg"
+    "import numpy as np\n",
+    "from numpy import sin,cos,pi\n",
+    "from scipy.linalg import *\n",
+    "from scipy.optimize import fsolve,root\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pretty_plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pretty_plots.setdefaults()"
    ]
   },
   {
@@ -19,7 +41,9 @@
    },
    "outputs": [],
    "source": [
-    "setdefaults"
+    "from __future__ import print_function\n",
+    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
+    "import ipywidgets as widgets"
    ]
   },
   {
@@ -31,256 +55,180 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "t=np.linspace(0,2*pi/50,100); # create time varying from 0-0.126 s (or one period)\n",
+    "x=20*sin(50*t);     # define x in terms of time \n",
+    "dx=20*50*cos(50*t); # define dx/dt in terms of time (note dx=dx/dt)\n",
+    "t1=0.2*pi*cos(50*t); # define theta1 (t1) \n",
+    "dt1=-10*pi*sin(50*t); # define dtheta1/dt (dt1)\n",
+    "t2=0.2*pi*sin(50*t-pi/3); # define theta2 (t2) ;\n",
+    "dt2=10*pi*sin(50*t-pi/3); # define dtheta2/dt (dt2);\n",
+    "L1=1;L2=1.5; # set lengths for L1 and L2 (none were given in problem so 1 and 1.5 mm were\n",
+    "             # chosen arbitrarily"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 1.26847839, -1.26847839])"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "xnx=np.array([x,-x])\n",
+    "xnx[:,1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
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+       "Text(0.5, 1.0, 'End velocity')"
       ]
      },
+     "execution_count": 49,
      "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
      "output_type": "display_data"
     }
    ],
    "source": [
-    "clear all; close all\n",
-    "t=linspace(0,2*pi/50,100); % create time varying from 0-0.126 s (or one period)\n",
-    "x=20*sin(50*t);dx=20*50*cos(50*t); % define x and dx/dt in terms of time (note dx=dx/dt)\n",
-    "t1=0.2*pi*cos(50*t); dt1=-10*pi*sin(50*t); % define theta1 (t1) and dtheta1/dt\n",
-    "t2=0.2*pi*sin(50*t-pi/3); dt2=10*pi*sin(50*t-pi/3); % define theta2 (t2) and dtheta2/dt;\n",
-    "L1=1;L2=1.5; % set lengths for L1 and L2 (none were given in problem so 1 and 1.5 mm were\n",
-    "             % chosen arbitrarily\n",
-    "rcc=[x+L1*sin(t1);-L1*cos(t1)]; % position of connection between links\n",
-    "rco=[x+L1*sin(t1)+L2*sin(t2);-(L1*cos(t1)+L2*cos(t2))]; % create a row vectors of\n",
-    "                                                        % x-component and y-component of\n",
-    "                                                        % pendulum position C (r_C/O) \n",
-    "vco=[dx+L1*cos(t1).*dt1+L2*cos(t2).*dt2;(L1*sin(t1).*dt1+L2*sin(t2).*dt2)]; % create row\n",
-    "                                                                            % vectors of\n",
-    "                                                                            % the x- and\n",
-    "                                                                            % y-component\n",
-    "                                                                            % velocity of\n",
-    "                                                                            % point C\n",
-    "\n",
+    "rcc=np.array([x+L1*sin(t1),-L1*cos(t1)]) # position of connection between links\n",
+    "rco=np.array([x+L1*sin(t1)+L2*sin(t2),-(L1*cos(t1)+L2*cos(t2))])    # create a row vectors of\n",
+    "                                                                    # x-component and y-component of\n",
+    "                                                                    # pendulum position C (r_C/O) \n",
+    "vco=np.array([dx+L1*cos(t1)*dt1+L2*cos(t2)*dt2,\n",
+    "     (L1*sin(t1)*dt1+L2*sin(t2)*dt2)]) # create row\n",
+    "                                                                            # vectors of\n",
+    "                                                                            # the x- and\n",
+    "                                                                            # y-component\n",
+    "                                                                            # velocity of\n",
+    "                                                                            # point C\n",
     "\n",
-    "figure(1)\n",
-    "plot(t,vco(1,:),t,vco(2,:))\n",
-    "xlabel('time (s)')\n",
-    "ylabel('velocity (mm/s)')\n",
-    "legend('x-component','y-component')\n",
-    "title('Velocity of end point')"
+    "plt.plot(t,vco[0,:],label=r'$v_x$')\n",
+    "plt.plot(t,vco[1,:],label=r'$v_y$')\n",
+    "plt.xlabel('time (s)')\n",
+    "plt.ylabel('v (mm/s)')\n",
+    "plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n",
+    "plt.title('End velocity')"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Link positions over time (animation)\n",
+    "# Create interactive animation for 2-bar linkage\n",
     "\n",
-    "![links](./pendulum.gif)\n"
+    "1. Create function that plots the links at timesteps\n",
+    "\n",
+    "2. use `interact` to generate the interactive figure"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_links(i,rcc,rco,t):\n",
+    "    plt.plot([x[i],rcc[0,i],rco[0,i]],[0,rcc[1,i],rco[1,i]]) # plot lines for 2 links\n",
+    "    plt.plot(rco[0,:],rco[1,:],'--'); # this plots all of the positions in the x-y-plane\n",
+    "                                                #over time\n",
+    "    plt.plot(rco[0,i],rco[1,i],'o');# this plots the position as a circle at\n",
+    "                                            # timestep i\n",
+    "    plt.axis([-30, 30, -3, 0]) # this sets the axis bounds "
+   ]
+  },
+  {
+   "cell_type": "code",
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diff --git a/figures/animation_rotating_pendulum/.ipynb_checkpoints/frame001-checkpoint.png b/figures/animation_rotating_pendulum/.ipynb_checkpoints/frame001-checkpoint.png
new file mode 100644
index 0000000..9a4d28c
Binary files /dev/null and b/figures/animation_rotating_pendulum/.ipynb_checkpoints/frame001-checkpoint.png differ
diff --git a/hw2_work/hw2_work.ipynb b/hw2_work/hw2_work.ipynb
index a802c7d..bdf8110 100644
--- a/hw2_work/hw2_work.ipynb
+++ b/hw2_work/hw2_work.ipynb
@@ -1480,14 +1480,22 @@
   "language_info": {
    "file_extension": ".m",
    "help_links": [
+    {
+     "text": "GNU Octave",
+     "url": "https://www.gnu.org/software/octave/support.html"
+    },
+    {
+     "text": "Octave Kernel",
+     "url": "https://github.com/Calysto/octave_kernel"
+    },
     {
      "text": "MetaKernel Magics",
-     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+     "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
     }
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diff --git a/intro_to_numerical_integration.ipynb b/intro_to_numerical_integration.ipynb
index 88c53f5..e7cdfee 100644
--- a/intro_to_numerical_integration.ipynb
+++ b/intro_to_numerical_integration.ipynb
@@ -2,44 +2,58 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 1,
    "metadata": {
-    "collapsed": true,
-    "slideshow": {
-     "slide_type": "skip"
-    }
+    "collapsed": true
    },
    "outputs": [],
    "source": [
-    "setdefaults"
+    "import numpy as np\n",
+    "from numpy import sin,cos,pi\n",
+    "from scipy.linalg import *\n",
+    "from scipy.optimize import fsolve,root\n",
+    "import matplotlib.pyplot as plt"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true,
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
+   "execution_count": 2,
+   "metadata": {},
    "outputs": [],
    "source": [
-    "%plot --format svg"
+    "import pretty_plots"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": true,
-    "slideshow": {
-     "slide_type": "skip"
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/ryan/bin/pretty_plots.py:6: MatplotlibDeprecationWarning: \n",
+      "The text.latex.unicode rcparam was deprecated in Matplotlib 3.0 and will be removed in 3.2.\n",
+      "  plt.rcParams['text.latex.unicode'] = True\n"
+     ]
     }
+   ],
+   "source": [
+    "pretty_plots.setdefaults()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
    },
    "outputs": [],
    "source": [
-    "pkg load odepkg"
+    "from __future__ import print_function\n",
+    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
+    "import ipywidgets as widgets"
    ]
   },
   {
@@ -67,7 +81,6 @@
   {
    "cell_type": "markdown",
    "metadata": {
-    "collapsed": true,
     "slideshow": {
      "slide_type": "fragment"
     }
@@ -82,36 +95,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 75,
    "metadata": {
-    "collapsed": false,
     "slideshow": {
      "slide_type": "fragment"
     }
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "f =\n",
-      "\n",
-      "@(x, y) (x .* y .^ 3 - x .^ 3 .* y)\n",
-      "\n",
-      "ans = 0\n"
-     ]
+     "data": {
+      "text/plain": [
+       "0.0"
+      ]
+     },
+     "execution_count": 75,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "f= @(x,y) (x.*y.^3-x.^3.*y)\n",
-    "f(1,1)"
+    "f= lambda x,y: (x*y**3-x**3*y)\n",
+    "f(0.1,0.1)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 84,
    "metadata": {
-    "collapsed": false,
     "slideshow": {
      "slide_type": "subslide"
     }
@@ -119,50169 +129,41 @@
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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
      "output_type": "display_data"
     }
    ],
    "source": [
-    "x=linspace(-1,1,101); % 10 data points from -1 to 1\n",
-    "y=linspace(-1,1,101); % 10 data points from -1 to 1\n",
-    "[X,Y]=meshgrid(x,y); % 100 data points from -1 to 1 on the x- and y-axes\n",
-    "Z=f(X,Y);            % Z=f(X,Y) evaluated at the 100 data points\n",
+    "x=np.linspace(-1,1,101); # 10 data points from -1 to 1\n",
+    "y=np.linspace(-1,1,101); # 10 data points from -1 to 1\n",
+    "X,Y=np.meshgrid(x,y); # 100 data points from -1 to 1 on the x- and y-axes\n",
+    "Z=f(X,Y);# Z=f(X,Y) evaluated at the 100 data points\n",
     "\n",
-    "pcolor(X,Y,Z) % also mesh(), surf(), ..."
+    "plt.contourf(X,Y,Z) # also pcolor, countour, ..."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**For more plotting examples and options check out the [Matplotlib gallery](https://matplotlib.org/gallery/index.html)**"
    ]
   },
   {
@@ -50299,7 +181,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 55,
    "metadata": {
     "collapsed": true,
     "slideshow": {
@@ -50308,44 +190,49 @@
    },
    "outputs": [],
    "source": [
-    "function dr = my_ode(t,r)\n",
-    "    % Help documentation for \"my_ode.m\"\n",
-    "    % input is time, t (s) and r=[position (m); velocity (m/s)] and time\n",
-    "    % output is dr=[velocity (m/s); acceleration (m/s/s)] at time, t\n",
-    "    % the ODE is defined by:\n",
-    "    %\n",
-    "    % a = -2*v-9*x+cos(t/2)\n",
+    "def my_ode(t,r):\n",
+    "    \"\"\" Help documentation for \"my_ode\"\n",
+    "     input is time, t (s) and r=[position (m); velocity (m/s)] and time\n",
+    "     output is dr=[velocity (m/s); acceleration (m/s/s)] at time, t\n",
+    "     the ODE is defined by:\n",
     "    \n",
-    "    dr=zeros(size(r));\n",
-    "    dr(1)=r(2);\n",
-    "    dr(2)=-2*r(2)-9*r(1)+cos(2*t);\n",
-    "\n",
-    "end"
+    "     a = -2*v-9*x+cos(t/2)\"\"\"\n",
+    "    \n",
+    "    dr=np.zeros(np.size(r))\n",
+    "    dr[0]=r[1]\n",
+    "    dr[1]=-2*r[1]-9*r[0]+cos(2*t);\n",
+    "    return dr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Given any `[position, velocity]` and `time`, the defined `my_ode` returns the velocity and acceleration:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 56,
    "metadata": {
-    "collapsed": false,
     "slideshow": {
      "slide_type": "subslide"
     }
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "ans =\n",
-      "\n",
-      "    2  -12\n",
-      "\n"
-     ]
+     "data": {
+      "text/plain": [
+       "array([  2., -12.])"
+      ]
+     },
+     "execution_count": 56,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "my_ode(0,[1 2])"
+    "my_ode(0,[1, 2])"
    ]
   },
   {
@@ -50358,38 +245,39 @@
    "source": [
     "## Euler approximation\n",
     "\n",
-    "$r_{i+1}=r_{i}+\\frac{dr_{i}}{dt}\\Delta t$"
+    "The simplest integration routine is the Euler approximation. A first-order Taylor series expansion about the current timestep:\n",
+    "\n",
+    "$r_{i+1}=r_{i}+\\frac{dr_{i}}{dt}\\Delta t$\n",
+    "\n",
+    "We can integrate the equation as such"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 67,
    "metadata": {
-    "collapsed": false,
     "slideshow": {
      "slide_type": "fragment"
     }
    },
    "outputs": [],
    "source": [
-    "dt=0.01;\n",
-    "t=[0:dt:6*pi/2]; % [start: by some incr: to end]\n",
-    "x0=0.1;\n",
-    "v0=0;\n",
-    "r=zeros(length(t),2);\n",
-    "r(1,:)=[x0;v0];\n",
-    "for i=2:length(t)\n",
-    "    dr=my_ode(t(i-1),r(i-1,:));\n",
-    "    r(i,:)=r(i-1,:)+dr*dt;\n",
-    "end\n",
+    "dt=0.01\n",
+    "t=np.arange(0,6*pi/2,dt) # (start, stop, by some incr)\n",
+    "x0=0.1\n",
+    "v0=0\n",
+    "r=np.zeros((len(t),2))\n",
+    "r[0,:]=np.array([x0,v0])\n",
+    "for i in range(1,len(t)):\n",
+    "    dr=my_ode(t[i-1],r[i-1,:])\n",
+    "    r[i,:]=r[i-1,:]+dr*dt\n",
     "    "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 68,
    "metadata": {
-    "collapsed": false,
     "slideshow": {
      "slide_type": "subslide"
     }
@@ -50397,177 +285,36 @@
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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
      "output_type": "display_data"
     }
    ],
    "source": [
-    "plot(t,r(:,1))\n",
-    "xlabel('time (s)')\n",
-    "ylabel('position (m)')"
+    "plt.plot(t,r[:,0])\n",
+    "plt.xlabel('time (s)')\n",
+    "plt.ylabel('position (m)')"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
-    "collapsed": false,
     "slideshow": {
      "slide_type": "subslide"
     }
@@ -50576,16 +323,24 @@
     "## Runge-Kutta\n",
     "\n",
     "\n",
-    "Using `ode23` and `ode45` have the same syntax\n",
+    "Using `solve_ivp` in Python you can use more advanced integration routines, such as [Runge-Kutta 5(4)](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html#r179348322575-1), [Runge-Kutta 3(2)](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html#r179348322575-3), [Adams/BDF method](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html#r179348322575-7), etc. \n",
     "\n",
     "Numerical integration algorithms for differential equations:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from scipy.integrate import solve_ivp # import the ordinary differential equation integrator in Python"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
    "metadata": {
-    "collapsed": false,
     "slideshow": {
      "slide_type": "subslide"
     }
@@ -50593,306 +348,74 @@
    "outputs": [
     {
      "data": {
-      "image/svg+xml": [
-       "<svg height=\"420px\" viewBox=\"0 0 560 420\" width=\"560px\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
-       "\n",
-       "<title>Gnuplot</title>\n",
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-       "\t</g>\n",
-       "\t<g id=\"gnuplot_plot_2a\"><title>ode45</title>\n",
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-       "\t\t<text><tspan font-family=\"{}\">ode45</tspan></text>\n",
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-       "\t<g id=\"gnuplot_plot_3a\"><title>Euler</title>\n",
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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
      "output_type": "display_data"
     }
    ],
    "source": [
-    "[t23,r23]=ode23(@(r,t) my_ode(r,t),[t(1),t(end)],[x0 v0]);\n",
-    "[t45,r45]=ode45(@(r,t) my_ode(r,t),[t(1),t(end)],[x0 v0]);\n",
-    "plot(t23,r23(:,1),'-',t45,r45(:,1),'.',t,r(:,1))\n",
-    "legend('ode23','ode45','Euler')\n",
-    "axis([0 10 -0.2 0.3])\n",
-    "xlabel('time (s)')\n",
-    "ylabel('position (m)')"
+    "\n",
+    "r23=solve_ivp(my_ode,[t[0],t[-1]],[x0, v0],method='RK23');\n",
+    "r45=solve_ivp(my_ode,[t[0],t[-1]],[x0, v0],method='RK45'); # default = 'RK45'\n",
+    "plt.plot(r23.t,r23.y[0],'o',label='RK45')\n",
+    "plt.plot(r45.t,r45.y[0],'s',label='RK23')\n",
+    "plt.plot(t,r[:,0],label='Euler')\n",
+    "plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n",
+    "#axis([0 10 -0.2 0.3])\n",
+    "plt.xlabel('time (s)')\n",
+    "\n",
+    "plt.ylabel('position (m)')"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
   "celltoolbar": "Slideshow",
   "kernelspec": {
-   "display_name": "Octave",
-   "language": "octave",
-   "name": "octave"
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
   },
   "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"
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.3"
   }
  },
  "nbformat": 4,
diff --git a/octave-workspace b/octave-workspace
index 41ef164..88f4685 100644
Binary files a/octave-workspace and b/octave-workspace differ
diff --git a/rotating_ball_bearing.ipynb b/rotating_ball_bearing.ipynb
index 7962499..7604a83 100644
--- a/rotating_ball_bearing.ipynb
+++ b/rotating_ball_bearing.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 1,
    "metadata": {
     "collapsed": true
    },
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 2,
    "metadata": {
     "collapsed": true
    },
@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
@@ -50,7 +50,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -59,10 +59,6 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "wn =\n",
-      "\n",
-      "@(omega) sqrt (-(5 / 7 * omega .^ 2 - 9.81 / 45e-3))\n",
-      "\n",
       "T =\n",
       "\n",
       "   0.42555   0.51899\n",
@@ -71,13 +67,13 @@
     }
    ],
    "source": [
-    "wn=@(omega)sqrt(-(5/7*omega.^2-9.81/45e-3))\n",
+    "wn=@(omega)sqrt(-(5/7*omega.^2-9.81/45e-3));\n",
     "T=2*pi./wn([0,10])"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
@@ -89,7 +85,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
@@ -301,14 +297,22 @@
   "language_info": {
    "file_extension": ".m",
    "help_links": [
+    {
+     "text": "GNU Octave",
+     "url": "https://www.gnu.org/software/octave/support.html"
+    },
+    {
+     "text": "Octave Kernel",
+     "url": "https://github.com/Calysto/octave_kernel"
+    },
     {
      "text": "MetaKernel Magics",
-     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+     "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
     }
    ],
    "mimetype": "text/x-octave",
    "name": "octave",
-   "version": "0.19.14"
+   "version": "5.1.0"
   }
  },
  "nbformat": 4,
diff --git a/rotating_plate.ipynb b/rotating_plate.ipynb
index e2df2f8..6462ef2 100644
--- a/rotating_plate.ipynb
+++ b/rotating_plate.ipynb
@@ -29,12 +29,12 @@
    "source": [
     "![square plate](./plate.png)\n",
     "\n",
-    "Square plate 50 mm-by-50 mm is pinned at center of top and rotates with a torque, $\\tau(t)$=2 N-m. The plate has mass, m=0.8 kg. What is the rotation rate of the system and the resulting $\\theta(t)$? The plate starts at rest at 10$^{o}$ off the vertical position"
+    "Square plate 50 mm-by-50 mm is pinned at center of top and rotates with a torque, $\\tau(t)$=0.05 N-m. The plate has mass, m=0.8 kg. What is the rotation rate of the system and the resulting $\\theta(t)$? The plate starts at rest at 10$^{o}$ off the vertical position"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 3,
    "metadata": {
     "collapsed": true
    },
@@ -51,7 +51,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
@@ -62,7 +62,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -218,7 +218,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
diff --git a/tmp b/tmp
new file mode 100644
index 0000000..320c557
--- /dev/null
+++ b/tmp
@@ -0,0 +1,25 @@
+
+t=linspace(0,2*pi/50,100); # create time varying from 0-0.126 s (or one period)
+x=20*sin(50*t);dx=20*50*cos(50*t); # define x and dx/dt in terms of time (note dx=dx/dt)
+t1=0.2*pi*cos(50*t); dt1=-10*pi*sin(50*t); # define theta1 (t1) and dtheta1/dt
+t2=0.2*pi*sin(50*t-pi/3); dt2=10*pi*sin(50*t-pi/3); # define theta2 (t2) and dtheta2/dt;
+L1=1;L2=1.5; # set lengths for L1 and L2 (none were given in problem so 1 and 1.5 mm were
+             # chosen arbitrarily
+rcc=[x+L1*sin(t1);-L1*cos(t1)]; # position of connection between links
+rco=[x+L1*sin(t1)+L2*sin(t2);-(L1*cos(t1)+L2*cos(t2))]; # create a row vectors of
+                                                        # x-component and y-component of
+                                                        # pendulum position C (r_C/O) 
+vco=[dx+L1*cos(t1).*dt1+L2*cos(t2).*dt2;(L1*sin(t1).*dt1+L2*sin(t2).*dt2)]; # create row
+                                                                            # vectors of
+                                                                            # the x- and
+                                                                            # y-component
+                                                                            # velocity of
+                                                                            # point C
+
+
+figure(1)
+plot(t,vco(1,:),t,vco(2,:))
+xlabel('time (s)')
+ylabel('velocity (mm/s)')
+legend('x-component','y-component')
+title('Velocity of end point')