{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import sin, cos, factorial\n",
    "\n",
    "\n",
    "def f_sin(x, p):\n",
    "    if p == 0:\n",
    "        return sin(x)\n",
    "\n",
    "        return x\n",
    "    if p % 4 == 1:\n",
    "        return cos(x)\n",
    "\n",
    "    if p % 4 == 2:\n",
    "        return -sin(x)\n",
    "\n",
    "    if p % 4 == 3:\n",
    "        return -cos(x)\n",
    "\n",
    "    return sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def taylor(df, x, a, n):\n",
    "\n",
    "    f = 0.0\n",
    "\n",
    "    for i in range(n+1):\n",
    "        term = df(a, i) * (x - a)**i / factorial(i)\n",
    "        f += term\n",
    "\n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ac3550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "from IPython.html.widgets import interact, interactive, fixed\n",
    "from  IPython.html.widgets import FloatSliderWidget as fWidget\n",
    "from  IPython.html.widgets import IntSliderWidget as iWidget\n",
    "\n",
    "x = 0.1\n",
    "a = 0.8\n",
    "n = 1\n",
    "\n",
    "def plot_data(a, n):\n",
    "    xs = np.linspace(-2, 2, 50)\n",
    "    ts = [taylor(f_sin, i, a, n) for i in xs]\n",
    "\n",
    "    plt.plot(xs, np.sin(xs))\n",
    "    plt.plot(xs, ts)\n",
    "    plt.xlim(-2,2)\n",
    "    plt.ylim(-2,2)\n",
    "    plt.axvline(a)\n",
    "    plt.show()\n",
    "    \n",
    "interact(plot_data, \n",
    "         a = fWidget(value=0.8, min=-1.9, max=1.9),\n",
    "         n = iWidget(value=2, min=1, max=8))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}