{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Demo Notebook: To demonstrate jupyther capabilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Jupyter Demos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "### Setup\n",
    "# imports\n",
    "import numpy as np\n",
    "# Setup plotting\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x106e828d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2Ue1OFJxg7qa5fLbzMwJrB3JPu3sY1HKQ846BrgGO5x/n1U2v8tXur/Dz8mN0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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106cf5410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# derivative of functions\n",
    "def D(f):\n",
    "    # define derivative function\n",
    "    def deriv(x, h=1e-8):\n",
    "        return (f(x+h)-f(x))/h\n",
    "    # returns the function that makes the derivative\n",
    "    return deriv\n",
    "\n",
    "# define a function g(x) = x^3\n",
    "def g(x):\n",
    "    return x**3\n",
    "\n",
    "dg=D(g) # get derivative of g\n",
    "x = np.linspace(-1.5,1.5,100)\n",
    "plot(x,x)\n",
    "plot(x,g(x))\n",
    "plot(x,dg(x))\n",
    "legend(['x','g(x)','dg(x)'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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