04 - Differentiation and Integration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 - Differentiation\n",
    "\n",
    "### 4.1.1 - Numeric solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x, a, b, c, d):\n",
    "    return a * np.sin(b*x + c) + d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b, c, d = 1.0, 4.0, 3.0, 1.0\n",
    "arr = (a, b, c, d)\n",
    "dstep = 0.01\n",
    "x = np.arange(-5, 5, dstep)\n",
    "y = f(x, *arr)\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1jxfg42WZZ5AoL+dX1fbv0CG8YUiAhV1+95AjEvZUKCvjH1olRtq2LdfOmtC5nQij9HBM6Nzl5eoeoyn8t23jBLoT/nV1wW/x58Tjlceb0PfDzl8DImFPhdJS9Y6RlcUlYiZ0Diceu5zMEbQw1tRwnDSswi7vr8pftn/Q/Ud6vE74V1cHvyxCJOyRsKeEE2EEzBjOETkLBRxzDC+/GnTnrqjgV7uzBiVMEUb5+6vyl0IUNH8nhQOAOYa1rIwrdKzWwU9EQYEZoTANiIQ9FcrKnAm7CR77jh1c3eLUMAXN36nH1bYtJ8HCyt80YbezDn48TOEvR9sqYVSAz6mtNaMqzCUiYU8Gp1UBgBnC6KTUUcIE/k493uxsFqOw8jdlxFFaykYyL0/tPFOEXebHVGEKfw2IhD0ZnFYFAA2hmLo6vZxU4GTWqUT79mYMpQHnD6cJ/PPy1EMBzZrxX9DC4nS0aoowhp2/BkTCngxOk0cAC2NtLa8zExSclnsBZnnsqqEAwBz+TkIBgBmGyUnhAMCzhLOygm9/p/wjYc9wuBVGINjO4Zb/zp3Avn16OamgrIz30bS7AFU8TMhxlJWph2EkTDBMTj3e7GwW9yD5uw2jAsG3vwZEwp4MTqsCADM6R2kpLyrVrJn6uSaUPJaXuxPGoENhTmrwJYIWdiLnMWogeP6yosrJs9usGT83kbADQoguQoj3hRDFQohVQoif6yAWKEpLeRjtJBRgQgKsqsoZd8CMkjW3wnLwIG8zFxTceOxBjzhkRVVYhd1NfgYwI8ekATo89kMAbiOiPgBOBXCTEKKvhusGh9JS3rnczibQiTBBGCsr1VZFjIcJIw63Hru8RhCoreX2dyOM27ezuAYBN6NVIHhhd5Mfk+dFHjtARKVEtKT+39UAigEoLKtmINx4XC1a8OSIuM5RXc37dviGyko2TE6QZMSxfTuHLn2DW49dXgMcWdi2zcc5J9u2cRhIk2GS/H2LLOkSxvqln2UdgW8rQWs2THISdNigNcYuhOgG4CQAn+u8rsTevcDKlV5cOQFuQhlCfNc5iouBESNY61u0AK64oiEE6Cmqqpx77PJ7l5fjo4+AQYN4qe2WLYFbb/VhtvjevWwJ3YQyAKCsDDNmAD16sI1r2xb4/e99EHgpCi6FncrK8Y9/sD7l5/PCic8844NA6ghlHDyIA+Xb8ZvfcLu3bQscfzzwxhv6aKaE08lVEvXP7u7dwA03cA6/dWvg1FOBhQv10fQa2oRdCNEMwAwAtxLRriSfXy+EKBJCFFVWVjq6xw03AGee6YO4uwllAED79ti1pgxDhwIrVgC//S1w883AjBnA97/vw+KDbjz2vDygbVus/7QM55wD7NoFPPggcNllwKOPAuee6/GquE7XWZGoP+/DaWW48EJ+KP/yF2D4cOCee4DLL/dY3DXx/9d9ZfjZz4B+/YCHHgJ69gSuvRa4+25NPFNBPpsuczS3XlqG3/0OGDUK+NOfuFuddx7w739r4pkKFRX8o6tOrpIoKAC+/RZnn74fTz0FXHUVOwRbtgBnnQW8/bZeup6BiFz/AcgF8BaAX9g5fvDgweQE69cTdehA1LUr0Y4dji5hD61bE910k+PTa0ZPoFU5J1K3bkSbNze8P38+UdOmRKefTnTggAaeybBnDxFA9MADji+xr1c/KsyaRMOGHd7O06YRCUF0+eVEdXUauCbDZ58x/9dfd3Z+XR0dym1ED+DXdMEFh7fzgw/ype+9VwvT5HjuOb7JV185O3/zZiKArsOTdNttDe1cW0t0/fV86eef10f3CNxzD1FWFtGhQ87Of+89IoDOxjx67LGGt/ftIxo9mi/9ySd6qCbFpZcS9e7t+PS6fz1JBFD37G8O64IVFUQDBxK1bEn09dcaeDoEgCKyobE6qmIEgH8DKCaiv7q9Xjp07w7MmsXW8xe/8OgmsqLChcf+4ZoCxA6VYvbsw/eKOP104OmngU8/BR55RAPXZJAel0P+dXXAF+Xt0TGrDIWFh0+evOgi4P77galT+XfwBC5DAdW7BbbWFaBPq1I8//zh+e9f/Qq4+mrg//0/YMkSDVyTwaXHvmEPe8pn9C7Hn/7UMMcpKwt47DEe8f30pw2hcO2oquLYW3a2o9OLNjH/q86twI03NrzfuDHwyitAt27sBdfUaOCaDC5H2++t4HN//7+VGDu24f1YDCgs5N/jxz82Y/fIdNARivkegKsAjBBCLKv/G2t1klMMG8ai/uyzwLJlHtxAzhh1GMr45BNgwfp2yBfbcGLfI8f8l14KjBvHAunJwynX8nbI/z//AdZVt8MJbSuSatMddwADBgA//7lHc5icrrNSjwceAMpqYzjzhMojNo8Sgg1qfj6Hxjx5OOXKgs2bOzr99t/kYQdaYvIZlUfsCpidzf2+pobDe57AhTDW1QG3/4WF/Ypzjwy3tmgBPPUUsGED8Le/uWKZGlVVjvv+7t3AX19k/pecfST/bt04LPnBB2ykTIaOqphPiEgQ0QAiGlT/52ma5K67OIx2++0eXNyFx0sE/PrXwMGWMQhZzpAEDz/M1Wy/+50boinggv/+/RzDzS6Iodm+5HmQnBwWx5ISHn1oh4vk19atHE/P6xhDq4PJ+bduzR77Z58Bb73lhmgKyFJNB8sJfP45MH06UNsmdfv36gXcdBMnUletcks2CVwI40svAR+saAMSAnk7k/MfMQIYP57j1p4soujCMD3yCLBmO5+btS05/+uuA/r3B+67z+zVfUM587RVK+DOOzmRUVSk+eIuPN4PPmDBGH5RfcdKkSTu1Qu45hp+OLWXW8t7OuD/4os8ihj8gxjErl0pa6mHDwfOOIO9Y+1D6vJyLqNwMIfg73/nSFqPYbGUbQ8AP/wh0LUr8H//54HX7mLW6UMPcd9u1SuWtnzqnnt46fyHHnJKMg0cCiMRJ0n79Mvm3y8N/z/8gQufHn/cDdEUJBwapt27gT//GThlTPpnNysLuPdeYPVq4OWX3ZD1FqEUdgC4/noe2v1Vd1Tfhccrh/lnTE7fOQCO9+7f78GQVBomRf51ddyxBw2qF8b4ayVACOA3v2EPWXvnrqhw5K1XVwNPPAFMngw075Fe2PPyOKT0+eec79CK8nJH/NetA2bOBG68kUdM6fi3bcsVMlOnerC9rkNhnDcP+OILDpOKWHr+/fsDY8awIdbqGFRX84QLB8/u88/zEkk3392SnYo0hmnyZKBvXw/zZBoQWmFv0YKTGNOmAZs3a7ywQ4997Vrgtdf4wczrZC3sxx0HTJjAMUetkwwrKzleorhk7JtvAsXFwC9/CYh21vxHjgROOMEDr8uhx/jMMzyR5Je/BJ+/b1/aovurr+Y+5Al/B8L+yCP8s918M5i/RUnwrbdyKOCf/3TIMxnq6jg+4qD9//IXjkBdcQVs8f/Vr1g7X3rJIddkcPjsEnEp75AhwGmnCz4/Df+sLA6HFRWZW9seWmEHuHFraznhpw3yB23bVum0xx7jB/PGG9HwYFh07p/8hPviq6864JkK0uNSjPE+9RQ/mBdfDFv8heB5BQsXaq4wcTC5ioj5DxvGf3b4N23K4j59uuXPpEbEgce7bx/w3HPc9h07gvlXVaWNE3XvDowdC0yZwvtma8GOHfxAKfLfuJEdgxtvrF+Q04awDx/Ok5a01rU7DEPOm8ehlVtuqX9sbPC/8kpeM+yxxxxy9RihFvbu3TkZ8+yzGqdcV1Wxt6swweHgQeCFF4Dzz6+fySw7lkXnGDWKY71PPeWCbyIceLyVlcCcOVyGlpsL24bpmms41qvV63XAf/FiTiT+6Ef1b9jkf8MNPHJ/9lkHPJNh1y7uDIr8Cwv51MP4HzzIsYE0uPZazom8+aZDvolwKIzPP8+vP/xh/Rs2hFEI5j9/Po8UtcBhGPKZZ7jC8+KL0XC+Bf8WLfh5efnlYLdeSIVQCzvAD8P69cBHH2m6oAOP6+23uR9cfXX9G7m5nAWz6BzZ2dy5332XS8C0wAH/qVPZ67vmmvo3bApjq1b8MEybpilWKkMBivynTOEKw8MeTMCSf79+PLdACpNrOMzPTJnCBn74cBx+vgX/887jqI82r9eBMBLxiPnss4Fjj61/s107VjuLspGrr+ZR7jPPOOSbCAehmOpqNqyXXBK3/H+7draGcddey2HUGTMccPUYoRf2SZPYemrrHA48xuee4740enTcmzasPtDg5WiLNTrgP2UKxxf7969/o00bDiTa4H/FFextvv66OtUjsH07i7sC//37ue0mTWJDA8C2MALMf+VKTvy5hgOPd8sWNuzXXIOGunUZo7fgn5vL4jhnTso8txocCOP8+Zz4/c5bB7j905T7SrRvz3M6nn9eU+mgA8M6YwaHwq66Ku5Nm8/uySdzOOnFFxV5+oDQC3uTJsCFF7LV1eI1Knq8O3ZwjPyyyxKiNzY7R9euwPe+p7G6RJH/8uU80euwBzMri3MMNviffTY/oFOnqlM9Ag4ezNdfZ+fwu9FG/Pk2+F98MXuNWvg78HhfeIFtmVP+V1zBo62ZMxV4poKD9p8yhfMVkyfHvanIv7wc+PBD+zRToqqKH0KFDWZeeIHX4Tn11Lg3YzH2ViyqGoTgtYc++khzAYcGhF7YAR5GVVdrijUqerwzZ/Lvf5jFB2wLO8CzUVes0DDhRK6RqsB/2jQOCV1yScIHNvnn5PC5r7+uYXlTBx7vK6+wgztyZNybzZvzA26Df34+L2z20ksa8jQOhPGVV1hUevaMe1NBGAcO5AorLTMhFT32gwe5/0+alKClCvzHjmXDoIW/XPzOZuHAli3Ae+9xIvSwUxT4X345D05Mq2nPCGE/+2x2MKdNc3khB1UNM2ZwEnfIkIQPFIT9wgvZSXbdubdt4+9gkz8R8z/rrCSn2IwzAty59+/X4DUqerz79rFBmTQpYWkTIZTa//LLgU2bOKzgCorCuH49sHQp//6HQUFYhOBRxwcfaJjsVlnJQ+AmTWwd/v77HD1Lyd/GGtVNmvBM1Bkz2FC4gmJF1YwZ/AxcfnnCBwrt36sXV2KZFo7JCGHPzQUuuACYPdvl+iW7d7NC2ewcu3ZxfHTSpCROgixZs+EGFhSwcXrpJZczIRWF8csvga++4rY7AgrCOHQoG7fp023yTAVFj/ftt7lU3S3/CRM4+aqFf+PG7ILagDSEh4UxAL5Gs2a2F++/5BLuZq6TeA6cmqZNecRzGBSEEWD+27ax9+wKistVz5zJeaXjjkv4wAH/5cs512AKMkLYAfZa9uwB5s51cRFFj2vuXC6XmzQpyYexGIdGbMYnLrmEJzm5SuIpCuOMGWyQUvK32bHlNebNY2PnGIqhmBkzeO2X76pJ4qHAv1kzFqfCQpeGVYbxbIYCZszgBFz37kk+VODfvz/PhHQ94lMIQ9bWcnuddx6OWGztuzkgNvmPHs3RM9f8FTz2igrg44+TGFXAdvJaQj4/nq146gAZI+xnncW/qSuvS1EYZ83iPnDaaUk+VOwc55/PelBYaOvw5FA0TDNmcLlf0l3EYjGO19uc/TJpEg+lXe2SU1nJT/h3dWepceAAj9AmTEixrEws/XoriZg0iRNgixcr8E2EgsdbUgIsWJBitAEoCTvASyp/8onLHboU+Mt7JeWfm8sW1yb/xo05HDN7tsvJVgr8Z8/mUU5SYVf02Lt1A046KRJ2T5CTA0ycyKVfjqtjFISxpobjuxMmpFi6WrFztG/PIutK2BUMkxwdpBUWwPYSfKedxrbMVedW8Ljee4/n7+gSxvHj+Xd0xV/B45X30cV/4kQWqjlzbJ9yJBSEccYMFuSxqRboVsjRAMx/2zYXa/co7qMwcyaPlAYMSPJhq1bcGRT4T5rE3D1bJ18RGSPsAD8ku3cD77zj8AIKwjhvHt8raRgj/hqKnXvZMp6i7QjSMNlYDkHGY5N6LIAy/+xsNnJvvOHCsCrESGfMYOd+1KgUB8Ri/APZJNO2LW+76Jewz5jBE6SOPz7FAYrCPnAgTxBy7RjY4F9Xx8L4gx+kqSxU5D96NBcyOeavsI/Czp38/E6enCJqlpVluV5MIuRzpHV5EBfIKGE/+2w2to6TSAoe+6xZPDFqxIgUBzgUdsBF56istL2liOPnAAAgAElEQVQcwowZXMnz3WzBRDjgP2kSa+m8ebZPORw2heXQIRaAcePSRG0c8i8u5oSyI9j0eGV8N6W3DjR4vDaD/kJw/3n7bYd70tbU8Ik2+C9cyKWCafkrCnvz5lyy6jjPoZCfeeMNDuWldGoA5VBe375A796a5hNogBZhF0I8I4SoEEJ4vc10WuTlcax69myHpVOVlRwfbNEi7WG1tXyP887TKyy9enEizLHXYtPj3bwZWLTIxoMpr2kTI0bwA+qYv81QzCef8KGWwgg4MqyOvPb9+3kyhQ3+r76aJr4rEYvxNRVUeuJEPsXRhssKFVUzZ3Loc/z4NAcpCjvAI74NGxxuVq/Iv6AgYVJSIhT5ywICWQIaNHR57FMAjLY6yA9ccAE37PvvOzjZ5sqI8+fzb54yDAOw4jdvrty5J07kmWyOdpexKYyzZ/NrWv4KtcgSjRqxsXv1VQdTxIlsG6bCQo7vjk7X4xwYpi5deBTjyDAphPEKC9PEdyUc8P/+93k1CEf8bY5WidjwjRgRt4RDMiiU+0q4KiCw6bHv28fVbBMn4oitBw+DA8M0eTKPJl3lOTRBi7AT0UcAjFjj7NxzubbWUTjGprDMmsUiNmaMxYEOOoerJJiCMJ5wQpr4LqBcsiYxaRKfopwE27OHwwEWwkjE/EeNsigXdyCMAPP//HMHG1jYFMbqap77MHGihf/ggH9ODoen5sxxMGK1aZiKiznxLkc3KRGLcUdWWPpQetGuDJMF/3ff5a6W1qkBlJO/AHDKKbzssgnVMb7F2IUQ1wshioQQRZXaFsA+Eo0bs9dYWOjAa7Th8RLxUG7UKBtLUjgQ9pNPBjp3dtG5Lfhv386zFC0fzJwcdv8U+Y8Zw0ZPuXPbFMbly4FvvuFhe1q4EHbAQZ7DpjC++SbHd20JY/x1bWLiRP6NP/5Y6TTb7S/75fnnW1zPBf8lS3gmsBLkfSwKBwoLOQ2VdO5DPGIxnoOiYCGzspj/m28Ce/faPs0T+CbsRPQkEQ0hoiExxdUHVXHBBRxBUJ4ibiP5tXQpdzpLiw84EnaZBHvrLcXOIUMZFm37xhs8XLQUFsARf5kEmzVLMQlmUxgLC7mN0sZ3AY4T5OQo8+/Th0cyykkwBf75+VzamhYOQmEAj1gbN3bgGNgU9ldf5ZnGnTpZXM+FsMv7KKGqin/zNHvlxufGLOsLJH/FZTMnT+Zwj6M8h0ZkVFWMxNix3LmVwzE2hHHWLLbMlsICOBJGgI3Gvn0s7raxZw9nzmx4XB068LDREi74b9zIpZu2oSCM3/uejd3nhPUWZ6kwaRKPapQ2ULAhjAcP8tyH8ePZ5qSFQ2GUU/yVq0sqK7nN2rRJeciWLVwRY8spcJC8Bnh6f58+Dg2TRd//9FM+zLZTAygb1jPP5LlZQYdjMlLYmzXjGtuZMxVyN4cO8RjWonPMmsU/nq1BhxRGxfqtM8/k50vJMNkQxpoaThxNmGCROJJwKOznn8/XV+rcNoRxwwYOxdh6MAFXhqm2VjHPUVnJXzqNMH74IddQ2+LftCnP1XfAf+JErnxaulThpKoq5p50th1DJt2VhNEh/w8/VKwusZFfmjWLPfW0SXcJh/xzcxtm0bpe1MwFdJU7vgTgMwDHCyFKhBDX6riuG1xwAU/bXrTI5gmyDCWNMK5Zw0vr2grDyGsdOMAZMwXk5LD4vvYan24LNqoC5s1jx95rYYzFuEJDSdhtGCY5PLeMr8cTccB/yBAONSjzb9s2rcUsLOTVDFNOqkqEQ/7jxjENpXCGjdFqYSF71CecYON6NreHTIaJE9mwvvaawkkW+SWZdB85ksOFlnAYigFYH3bs0LTGvEPoqoq5jIg6EFEuEXUmIp1b1DrC+PFsPW17vTY8RvmgKwk74KhzX3ABL6hle8U7G1UBhYVcon/22TavGYuxwXOwUPmkSVyPvHatzRNszCEoLOQ6/169bF4zP9/RgymTYEp5DotQgBSWH/wgyaJZqSBLBhUhDatSnsCC/44d3Bctq3kk8vL4t3TAf8gQLiBQHrGm4b9iBY/4bDs18loO+J97Lv/GQYZjMjIUA3Ae5ZxzGtZctoQNj3HmTO50XbrYJOGic5xzDnsWtju3hccuE0djxyrs0y1L1hzsoKG84p3FHIKqKq70sP1gAo49XqAhCWY7z2Hh8S5ezDFqJf4ODRPA/FeuBFavtnmCBf+5cxWS7hIO2z8rix2bt96yOdiV+yhYODW2ku4SbdrwCQ74N2nC1WGzZmnYvMUhMlbYAe4c69dzXNYSFh57SQknjtLOFkyEC49duWzTwmNfsIDzQMrCAjjif+yxXLpp22u0EJY5c/ghUea/fbujJQNlnsO2YbLgX1jI4evzzlMg4cIwyc0vbK92auGxFxbyQnXDhimQcGGYLryQawFs7aUr91Gw4H/aaVwrbws5OZwFdch/0iReEGzhQkenu0ZGC7tMEtryei08dpmltx2GAVx57AAbpqoqnkJvicpKdsVTBBCnT7c5qSoeLvlPmsQGZetWGwdbCOP06TxSOvlkBQKKK1TGQ06Zf+01m0mwNMJIBPz3v2wsbKzP1gAXwtipE1cP2RL2urq0Hu/evQ0rmdpKuks4DCUBXA5aUMDtZgkLp0buVKX07MrrOTSs553HfSiocExGC3ssxg+TLWG3WBlx5kwuw7KVOIonEH9tRYwerVC2mSaUUVvL2waOGWO5DM7hcDHiABQn+6QRxm+/5brgSy6xvYcFQ4NhspUEq6tj45FCWJYv54XFjthX1gqxGMciLDZVToWLLuLYsuWiZjt3cidJ0f5vvMFJd2X+DstNATYgkyc33DstLMKQcgOPiy5SJOHCsLZuzbmsmTNdbt7iEBkt7AB7vcXF/JcWaVZG3LqV65qVO0azZrY3VU51+ujRNss203i8n3zCw0JHDybguHP37ctVFLa8xjT8Z83iaIrf/OXyFJb8v/2Wf6AU/F95hcMwaRctSwYNIz7ABn+LMOTLL3MY5qyzFAlIj92hsl14Iec5LDept8H/tNPSrGSaCi48doAN09q1Gjapd4CMF3bpNVp6vWk8xpdfTrHprRXkJBmHDybAnWPLFuCzzywOTMP/lVcaNg1WgkthEYLb7IMPOEeREgcPsmucRhh79gQGD1Yk4HLEccwx3H+mT7dwmtMIi9zBfuRIpe04GS75d+7MIQ1LYU8Thty1i8MwF12UtsQ9OfLzefKEpcudHGecYXNXtDShmC+/5A1lLr3UAQGXz65caOyllxxfwjEyXtg7dWJrbZnES+Mxvvgii0raRbNSwaXVnziRRfm55ywOTMH/0CGOU44bZ3uP5QbIHetd8L/iCha3tJ1bxsCTKF9FBdffK4dh4q/n4uG88krOv6bdSzdNKGDRIp6F61hYAFf8L76YhS1tOCaNYZo9m7U5CP45Oey1z57N0aKUSNP+r7zC/UZ5tA24HnEUFPCo74UX/K+OyXhhB3hIunQpJ1FSIoXHu3o1L0p0xRUOb+7S6jdvzvxfeYWHpSmRoo73nXf4I+UwhoRL/r168Yp9zz+f5qA0wjJtGj8UQQnjOedwGMIW/ySG9cUXORqnVM0j4dJjB1jQsrIsHIM0HvvUqez5J93X1woa+P/wh9zvp01Lc1BVVdI5ENKhOOusFPv6WiE/nz2jtFYlPa6+mteW+ugjx5dwhKNC2GWJYtoMewphf/FFfjAcCQvgqjJA4ppruG/JKd1HIE0o49//5q81bpzDm7sccQDAVVdxEu+LL1IckELYiYCnnuLR0oknOrixnCTjgn9ODnDZZVxumXKKewr+NTXsrU2aZLF2eSpoMEwdO3LSfMqUNGWzKfhv3sy15Ndco1gNI6GB/ymncNHCs8+mOUg6NQlDuo8/Br7+mvk7ggbDNGECO2eWI27NOCqEvXt3jjU+/XSKIVGKlREPHgSeeYaHU44sPuCqMkBi+HD2mv7znxQHpFgOoaKCK1KuvlphUlIiXHrsAIcDcnPTPJwphGXxYjYG113n4uYa+F95JS/tMHVqigNSVFTNmsV5Vcf8W7dmRXXZf370Iy4ASLniYGUlJxQSYnXPPsvPy7VOFwjRIIxCAP/zP5xjSjnZKkWp5lNPsV13FIYBtBimJk34/tOnO041OMJRIewA8NOfsvVOuh9nipURX32VH4if/tTFjfPzldd1TkR2NovzW2+l2Og6hTA+9xyPJB0/mICWEUd+PsdKn302xU5vKfg/9RTrzWWXubi5hhHHySfzjON//jNFuLWqqiEfEYenn2anIuW+uFbIzuZZUi7bf9w4btqnn05xQJLRam0tj/ZGjuTv4AgahBFgw5qdncYxSBKG3L6dR+hXXOEgtyShwTABbFh37+bRm184aoT9wgv5t3/ssSQfpogxPvYYl0iNHevixi4mycTjxhvZeXv00SQfJuFfWws8/jiPVPr2dXFjDSMOAPjZzziclDRWncTj3b6dw2AXX8xVqI6hwWMXgvkXF6dwDLZtO0JYiot5bZVrr3UYxpDQYJjy8tjrLSxM4xgk8H/jDY4N//jHLm7csqWjNfET0aEDrxj61FMpvN4k/KdM4VCYK/6aDNPpp3M48ZFH/EuiHjXC3qgRD4lnz06yMFUSj/GLL3jf1BtucFDmFQ9NnaNzZxa5p59OkstJwn/mTE4W33abq9vyNXfv5qfEBU49lTv33/+epHNXVXEgMm5n8Mcf54f4f//X1W21jDgATj7HYikMaxJheeghHm385Ccub6zBMAHALbewgXnkkSQfJglDPvgg0LWrg9ma8dBQ7itx221s7KdMSfJhQijmwAHgr3/lpOlJJ7m4qSaPXQjg1ls5lOTXBhxHjbAD3Lnz8oDf/z7hgyQe7333scPh+sHU1DkAFrnqauCJJxI+SOBPxA9m794KS9ymgsvZsxJCMP/i4iSlpwnCuHcv8Le/8eSsgQNd3bZhxOFy+l+jRsBNN/ESA0uWJHyYwL+khIfd113noHY9ERo8doAdg0svZcfgiL0jEvjPn89/t92WdkMie9DE//TTeZ2aP/85YU7BoUOcyIjjP3Uq/wa33+7ypk2a8NRvDYbp4ot55PGnP7m+lC0cVcLeoQN74M8/z2urf4cEj3fpUhafW2/l/JUraPLYAY7zjhkDPPBAQmRHPjj1mzy8/DInHu+6y+VoA9DK/9JLOSx0zz0J63IlCMtf/sLic/fdrm/ZMElGwyaUsj/cc0/CBwn877qLDZnr0RKgzeMFmHdNDXD//QkfxHnsRMCvfsUbILnKzUho4i8EO1sbNyY4NnKbq3r+e/cCv/0te+q2NtSwuqkm/nl5wK9/zVGA9993fTlL6NpoY7QQ4ishxFohxB06rukVbr+dkyk33BDnxMV5vHV1nCxt25YfZNfQKIwAW/xdu4B77417s6qKFSc3F3v28Hc86SROuLqGJo8dYCPzu9/xZJm//S3ugzhhLClhw3XhhbymuGtoHDG1bAnccQdPVjps67Y4/gsWsOPwi184mMKeDDKUpCE4e/zxwPXXA//6Fy/pC4Dd3+rq7/hPncoVKH/8o4ukYzw0eewAV6eNHMmG6btRR8LkpD/9ics0H3nEwYS2ZNDI/4Yb2Nj37q3lculBRK7+AGQDWAegB4A8AMsB9E13zuDBgylI/OtfRADR3/9e/8YddxDl5hLV1dEf/sCfTZmi6WYHDvAF77tP0wWJfvYzvuTcufVvXHIJ0XHHUV0d0Y9+RCQE0UcfabrZl1/yzaZO1XK5ujqiCROIGjUiWrGi/s1jjyW66io6eJBo+HCiJk2I1q/XcjuiV19l/osWabnc/v1EgwYRtWtHVFZGDb/v/ffTrl1EvXoRdepEtGuXltsRPfwwX//bb7VcrrycKBbj77B3LxGVlPD1n3iCvvmGqHVrolNOIaqt1XI7op/+lKhNG00XI1q5kigvj2j8+HqOH3zA/OfNo88/58f4kku03Y5o1CiiYcM0XtAdABSRDV3W4bEPBbCWiNYT0QEALwNwG9n1FNddx5Uut95aX5tcWQnKz8eTTwncfTeX12nxdgEOUrZsqc1jBzh+3r8/18e+/z6AqipQ23zcfTfX3d91F6+zoQWaRxxCAE8+yRN2Ro+uXyCpqgqHWuXjmmt4XZl//tNFiV0iNPPPy+My0upq5l+6kmNie47Jx7hxnLCeOtXm9mt2oHHEAXCI5ZlneMXJyZOB6g3cLhV1+Tj3XA6RTZ3qspInHrEYh0scrImfDP36cWL6tdc4/3VwK7dLcWU+xo/nCVmPP67lVgyNHruvsKP+6f4AXAjg6bj/XwXgH+nOCdpjJ2KP6owz2Ni/33ICfdX4RAKIxowh2rNH88169SK69FKtlywpITruOPbOv246gN5pNoEAouuu0+htEREdOsQ3+c1vNF6UaPly9hyb5+4jAuiBFr8ngOiPf9R6G6I1a/hHfu45rZedO5dHFqccs4IIoB82m0bZ2UQvvaT1NkRvvsn858/XetknnyTKziaa3OIdIoBG5n1IzZsTffyx1tvwsBjgoYIm1NUR3XknX/bO1o8TAdQ5awt16kS0erW22zBuuYWoRQvNF3UO+OixJ4tkHVGCIIS4XghRJIQoqjTAAjZvzjXJDz8MtKmrxK5GMTz2GJdDJswzcQ+NCTCJTp04QXrPPUCLA1U40CIfr7zC3rA2bwvQNkkmEQMGcJz3f69mj7fpsfl47z2OYWuFZo9dYvRoYNky4MLhfN3uQ/KxZImLpSdSQbPHLvHjHwOffgqc2Y/5nzY+HytWaMprxENjjkZCCOAPf+Ba+37tuF0uvyUfy5c7XKgvHWIxTmo5XBM/KORouEYJgPhdQDsDOGLPHCJ6EsCTADBkyJAAlp4/Erm59QnSx6uAQYMw5EaPbpSfb7FurTM0awbcfx8BD1Ri7NUx4GLtt2BoqgVPRLt2wH0/qwL+Ddz8f/mA3U22VdCqFRsnD5yJ3r2BX/+oCpgL/PbRfMDJejZW8MgwAcDQocDQy6uAz4D7H8sH2mm/havtFa0wZgyAN6uA0hZ48GGna2ZYQPLfto3jPCGBDt9uEYDeQojuQog8AJcCSLVclZmw2AjXNbyM01VX83IFrgum00DT7NOksNgkwTU0lqwlhdf8PRTG764rxHelstrhgcd+GPx4doHQxdldCzsRHQJwM4C3ABQDmEZEAewZ4hBJJjhohxQWL/bIstirVQvCLIzy2l7zV9rMVAFyDRov+bduzVP/vYAfhsnrvgN41/4eQcuvSURvAHhDx7V8h5zg4GXniMU4Rrd7t8ZyiXpY7PeoBbGYjS2cHMIPYfdyxFRVxUsIOl4+0wa85G+xibhreC2MVVWccPIKR6vHHnr45fEC3nRuix3atcDLEYfk71UoAPDeY/fSKAHh5q9hTfy0iDz2pIiE3a9QQPy9dMIPwxSL8XKRLnaSSQmvQwGAZ8lfAP4Ie5g9dsC79ifyvv3btOEcROSxhwx+CWP8vXTCT8PkFX8/PN5t29JsIeQCkcduDa+S73v28OI3Xj67OTnseEQee8iQCR5748aaFvZIAa9DSX4IC1Gave1cIMweux8eL+Cdx+7HswuEcvZpJOx+JR/j76UT8sHUsuJRCvjB30uEnb+mNfGPwM6dXBXmdSjGK4/dj9E24O2IySNEwu5HVUOLFjwbyiuP3Y+ODYTbY5f30ol9+zgc4Jdh0s3fT4/Xi+R75LGnRCTsfgijnCTjldcSVmHxKxTglbDLRfHDyt9Pj7emRv9uzn5UhAGRxx5K+CEsgHedw+uZd0DDTjK6DdPevfzAhzUU46fHCISfv1eGya/ktRflvh4hEnY/PHbAO2H3c8QR1lCAVx5v2Pn76bHH308Xqqq4asXVbuc2EItxLsKLcl+PEAm7Xx67F3G6Awd45bmw8vdLGBs35hXTwso/7B67l4bJ68IBIJSTlI5uYScKt8fuV4wRCLfHLu/hFX+v1omRaN2a12L2gr/XpbKAt4bJL6cGCFUC9egW9j17eA0XvzqHxp1kAPgrjF7UImeKsHu5HALAot62rX5hCbvH66dTBkQee2jgt7AADYuO6YBfMVLAm6oevw2TF/y9Xg5BwivD5Efbt2zJbRRW/pHHHjL4LYyA3s7tt2HatYvj+rpQVcXeaKtW+q6ZCmEWRsAbw+SXx+tVua8fFWFA5LGHDn57jIDezu2nYfKiZK2qisMYWvfySwGvPHa/hN0Lw+THHAgJ3aG82lrv91GQaNrUm3JfD3F0C3vYPXavd7+Jh1cjDj+Fce9e/tOFyGO3D90e+7ZtXPzg54jjaPHYhRAXCSFWCSHqhBBDdJHyDWH32KXHm52t75qpkAnCDjTMFtUBv/lv2wbU1em53v79vK2iX8Ku22P30ymT9zmKPPaVACYD+EgDF/9RWclruHg9wQFoKInT3bn97Njynrrgt8cL6OPv13IIEnJN/B079FzPb2HU7bEHwf9o8diJqJiIvtJFxndUVPhT7gUAjRrxtnhh93gj/gw/S2UB/fyD8Hi3b9dX7ht57GkRxdj96hiA/s7hJ3854gizxwvoE0Y/w3iA/hGHn5PbgIY18XWV+0Yee1pYCrsQ4l0hxMokfxNUbiSEuF4IUSSEKKo0xfJVVgLt2vl3P92dw09h1L2TzK5d7L357fHqFsbIY7cH3YZV8vd61q9ELMZ9dv9+f+7nEpYzK4hopI4bEdGTAJ4EgCFDhpixTFplJdC9u3/3i8WArVv1XKuuzr86XgmdhslvYdQ9LT/sHnsQHm/8fd2ispJ/09xcPdezQnzyvWNHf+7pAlEoJqzCuGMHe7x+jjh0hpL8Fkbd0/L95q87+V5ZydVUrVvruZ4VvPDY/Q6jyvuGAG7LHScJIUoAnAbgdSHEW3popcD06cCdd+q51v79PLQKq7D77XEB4fbY5b3Cyr9JE/7T6fG2bevP5DDAG4/d774PhCbO7rYqZhYRdSaiRkTUnoh+oItYUixcCDz8sJ7d5v1OHsl7ye3U3CIIYQ+zxy7vpVPY/VoOQUJnLXjYhdHPWbOAd2vKe4RwhWL69GFPe/1699cKyuMF9HTuigp+DSL5q2MnmSCEXbdh8tPjBfTWgvst7Hl5vPdvWPl7tQuURwiXsPfsya+bNrm/VhDCqDNOF5RhOniQZyy6RUVFw8PuF3R67BUV/vYdINweO6CPfxCFA3LZjshj9wDyQZKi7AaZ4rH77fECejq3FEY/JodJxGL6puX7XSoLhNtjB/Tx37GDw7F+8s/JYXGPPHYPkCnCrstjb9WKvV6/oNswBSGMuqblV1SE1+M9dIgnCoWVfxD5McCbpYc9QriEvXVrLtHSJezZ2f4nvwA9nTuoobS8t1sE5fEC4TZMu3cDNTXuriMXQgtCGHX1fSC8hskHhEvYs7K4cXUJe36+v8mvli3ZmOgSliAeTCC8/HUZpgMH2OsPIsYOuG//IIWxstJ98j0o/iFaViBcwg7oq2wIwuPNytI3nAuzx0sUnMcL6BPGoPi77T/yfD/zM/J+NTXu18QP2jCFAOET9nbt9Hnsfj+YgN7hqN8du3lzjum77dx79nA9f1Aery5hDGrEEWaPPf7+ThG0x66j3NdjHL3CHkQoANDjsdfVBSPsunaSCdrjdcs/iFJZQL/HHtZQXmUl0KwZb1fnJ2IxTjzv3OnvfR3g6BX2IIQR0JOAkeVeQYw4dAxHgxLGJk2AY44Jr7Dr9tj9WhlRQqfHHpRTBoQizh5OYa+udlcZcPAgi2NQnSOsQ2lAD38pjEEZ1rAaJrlCpQ5h9HNlRAmdHntQfUfe33CEU9gBd40bVB2svOe2be7WuwlSGHUKe1hzHBUV/m2pGA+5QuXRLoyRx26J8Aq7m3BM0B4vEW8T5hRBxagBPR5v0O2vSxj9nDUroSNHE5QwtmjBMziPdsPkA45uYQ9KGOM5OEHQwrhjB4eznKKigpNfTZro42UXukIxQfQdQE+OJihhlMl3N+1PFHnsNhA+YZc/aJg9dsBd5whinRgJ2WZy9qITBCmMukIxQfIPq8cOuDdMu3fzCq9B8G/alCtxIo/dA+jw2IOOUQPuOncQ68RI6DJMQQpLdbW7vSvD7LHX1rJRDqr93RqmIJ0yXeW+PsDtDkoPCSFWCyG+EELMEkJ4v/CKrF9167FnZTUsxekndIVignwwAfeGKUiPF3DPP8j2d7NCpUzcFxTo5WUXbg1TeTm/Bsn/KPDY3wHQn4gGAFgDQNO+dWkgBIuCW2H0e5MEiUzweAF37R90KANw3v579vBfkB67mxUqgxZGtx57WRm/tm+vh48qjgaPnYjeJqJD9f9dAKCze0o24HaSUnl5cB27cWMedYRdGJ3yD2qdGAl5Xylwqggy8Q64b/+ghTEW44qwQ4esj02GsBsmn6DTZf0RgLkar5caboW9rCy4jgEwf6fCAjD/Dh308VGBLPNzyn/HDn6ogxpxyN/dKf8ga/AB97NPTRBGIl4P3gnKyrj/hTX56xMshV0I8a4QYmWSvwlxx9wN4BCAF9Nc53ohRJEQoqjSrcULu7B36NDgOaniwAHuWEHxz8nhzu2Uf9Aer2w3p/yDTLwDmeGxA87FsayM2yAnRx8nFeTnA7t2uUu++wDL1iGikek+F0JcA2AcgHOIUi97RkRPAngSAIYMGeJueTQp7ETqk0SIghf2ggLgyy+dnSuFJWj+paXOzg1aGGX9fFgNk9uqsPJyDgf6uddsPOJDYX37qp8fZBgVaDCIFRVAly7B8bCA26qY0QBuB3A+EblcZFkB7dqxxdy1S/3cXbt4nZmghdGpsMjzwjrikAYhqFCSEHraPyiPVwqjG/7t2wczaxZwP2KS/IOC7LdOHRuf4DbG/g8AzQG8I4RYJoR4QgMna7jpHCYIY0EBJ5CcDOdM4R9WYQfc82/RIphZswDPXWjb1jn/oD1et8IYNH+3hsknuApUEVEvXUSUEGoUIzwAABLKSURBVN85jj9e7VxThFFyOfZYtXNN4V9W5iwUVlrasON7UCgoAIqLnZ1bWhqsUQL4/k6FsawM6NFDLx8VtGwJNGrkjL8Mo0YeuyXCN/MUcNe4Jgij5O9mxBFk5y4o4LVinCxkVlrK5wcxh0DCbSgpzMJeXh5s3xHCeftXV/POWybE2A332CNhDwJuQ0mtW7PXExTc8g9aGN2EwkwQdqfJ60OHOPkbZN8HnBumoEs1AV6uOT/fGf+DB30zCOEU9pYtObPvVNhzc1kcg4JbYQz6wXTD3xRhBNRr2YnM4C89XtW9N+V+nUF67IBzYTdhtAo4H3F88QWfW1ion1MCwinscjjntHMUFARXFQC4q2yIhN09nPKXoYCg+XfowPMZVENhJoxW5f3DWvgg7+9Ee5Yu5dcTT9TLJwnCKeyAe2EPEnI4F+ZQhuSigoMHzQgFOOVvQkVP/P1V+78coZjg8X77rXoozCT+TrSnuJj33O3eXT+nBETCHhTCzF+GwlSFUT6YQQtj2IVd8lftP6Z4vE6LB8rKgOxs/zfhToTTUNjWrUDHjr4UDkTCHhScDEd37+aVBYPmLyf5OBWWoIXRaShMft+g2z/sHrtTw1Rezr9ddrZ+TiqQVWGq6934GIYMt7Dv2MExT7uoreWpwEF3bMCZsJvicUkOYfV48/KchcJM4e/U4926FWjenJdVCBJu+JvQ953yj4TdBpw0blUVb1BgQueIn+RjF5Gw64PTEUejRrx7VZBo3py3aVPlX1ICdOrkDScVOB1xbNliBn8nIw4i5t/Zn5XNwy/sKo27devh5waJggJOHqlsmCD5myLsqg+mPD6oBbTi4ZR/hw7BVlRJOOFvijDKpZ/Dyt+J9uzcyWFUn/iHV9idWM2SEn41YVU2+QNLsbYDyd8nq58WnTrxNms1NfbPKS3lEEgQe7UmonNnFgoVmFCqKeEkx2SKMObksHFXGfHV1PCI24S+7yRaIPtaJOwWcGI1TRJGyUFysoOSEl58KuhQANDAX0UcTRLGzp2Zj8pOPibxV50kU1fH/E0QdkDdMEkHyAT+culnFf6RsNtELMbZcVVhl95C0JDCuHmz/XNKSvg8E0IBctSjYphMEsbOnTmZrjL71CT+HTuyWNjN0VRUsBEzwakBmL9K3/FZGNNCCG5HVacMiGLslsjK4odMtXE7dgy+XApgHkKo8zflwXQy4ti82YwwGKDOf88enulpSvt36cLlrzt32jveJGEEmL+KU5Mp/Dt29IZPAsIr7ADQtaszj9cE5OZyniCswi4fMLv89+/n0EFYhV32s65dveGjCtmOdvu//J4mCeO2bcBem/vzmMhfVdjz831bvC/cwq7auCYJI6A2nKut5TijKfybNeNYv13+0mMJq7Bv2sSvpvBXFXYTPV5Arf80acKznk1Aly5qORqfS03dbo33/4QQX9TvnvS2EMKfcYaE9NjtxBmJzBR2uw9meTmLe1j5m+bxtmnDyyKoeuxhFvbsbDPyS0BDP1Dhb0p+CeD2r6uzX9XmYw074N5jf4iIBhDRIABzAPxWAyf76NqVh/h2dmzfsYOHfaZ4LICax25SRY+ECn/ThFE1AbZ5M59jSv/p0IGFWkUYTckvAc4MkyltDxjP35WwE1H8btJNASiuiuMSsnHlMDkdTBTGLl14c207m3Kbyj+swg6oCfumTSymubnecrKL7GwWajt9HzBn1qmEalWYafxVhF06n2ERdgAQQvxeCLEZwBVI47ELIa4XQhQJIYoq7XjYdqAynJMxRpOEUaUW3ERh79yZQ0QHDlgfu2kThz+C2gQ6GVQ9dpOMEqCWY9q4EejWzUs2amjUiMNCdvgfPMi/k0n8VYRdGl/V/Y1dwFLYhRDvCiFWJvmbAABEdDcRdQHwIoCbU12HiJ4koiFENCQWi+lhr+Kxf/PN4eeYABWvZfNmfhjy873lpAIVw2SiMMrZp7W11sdu3mxOfkDCrrDX1vIz4sM64Eqwy7+khOPZJgl7ixb8Z4f/hg386mP7Wwo7EY0kov5J/l5NOHQqgAu8oZkCbdvywvV2Gzcvz7c6UluQFlwanXRYv547hinJI6DhQdu40fpYE4Wxe3f2Bq0SYEQsjKYZJhkKsyoe2LqVv6dJwgjYF/YAhNEW7PKXz4eP7e+2KqZ33H/PB7DaHR1lAiwWdjz29etZSE1JHgEcc8vNBdatsz52wwbzOnaPHvy6fr31sSZ67Hb5f/stLw9tGv8uXewVD0hhNE3Y5bNrZZgCEEZb6NrVnlO2YQM/5yGKsT9QH5b5AsC5AH6ugZMaVIRdPsimIDubO6uVsBCx+JvGv3NnXqLBiv+uXTxr08cYoy3YFXYpLCaOOIAG4U4Fyd80x6B7d95Hdtu29Mdt2MAzzU0zrD16cN+xMkwbNnDf8dGpdFsVc0F9WGYAEY0nIsXl8jSgRw/7Hq9pwggAPXtaC8v27SyOpvHPyWGxtuIvf5+ePb3npIIuXfhhCyv/Xr34de3a9Mdt3NgwujUJKvy7dDGnIkmiZ09e0sFqJ6UAEtfhnnkKcOeoqkq/rrlsfNM8FqDB6qeD/Nw0YQfs8TdVGHNzWezs8jet/WXOxUoYN2zg3JJP09ltQ/YHK8dswwbzwjCAfcMUQBg1/MLeuz7Mn65x5VDVtAcTYE7bt/NfKpiaPALCLewAt6kd/u3a8c5FJqFxY/Zk7Xi8JgqjXcO0caOZfd+OYdqzh1fWjIRdEdJqfv116mPkg2ti57AT5zWZf8+ePGJKN8lq3TpeZtk0YQTsGybZz0xDr17hFfbGjTlPk47//v1c1WMi/x49rA2TTK5Gwq6Inj2tG9f0UAZgLez5+Vw3axok/3QJvHXrzPTWAeZfUcFL4KaCyfx79kzf92tquLjAVP69eqX3eGVy0kT+jRtzpUs6/vKzSNgVIa1+Oo993TqgdWszdh5KhPzBrTqHid460CDsVvxNNKqAtWHdv59rxU0UFsA6x7R2LU/u6dPHX152YWWYVtdXUJ9wgj98VGE1YgqIf/iFHbBu3OJiczt2ixZA+/bAmjWpjzGZvwxRrE4xhWHPHh6OmvpgHn88v6biv2YNe4zHHecfJxXI9k9lWMMgjJWVqUN5kr/8nUxDz57pnZriYt53wWenMjOEvXfv9B77qlVA377+8VFFv37MMRl27OAYY79+/nKyi+bNubIkFf/iYn41lf/xx3ONdCr+8n1T+VvlmKQwmm6YUjk2xcU8IjcxPwOw9pSXpx4xFRcHYlQzQ9iPP56Ho1VVR35WWcnvh0HY6+qO/OzLL/k1DPyTwXT+xxzD4RjJMxGrVnGtu6ke4/HHM7+VK5N/XlzMcw1MWnwtHv3782sq/qtXmzvaAIATT+TXZPyJmH8Ao+3MEPYBA/h1+fIjPzNdWAAWxj17ks+gDQv/1auTL6a1ahWv0WNqVQmQ3jCtWsXcTasBl2jUiIXviy+Sf756tblGCeC2bdw4OX8pjGEQ9hUrjvxMevKRx+4QAwfy67JlR34WBmGUXksycVm1ir1KE8u9JPr14yRjsljjl1+ysOTk+M/LLvr141BGsuWHV60yNwwjMWBAcmE8cIA9Sen4mIjsbO7/yYRxwwZeckA+Hyaic2feri8Zf/mbBMA/M4Q9FuNNEJJ57IsXc0WMSeuYJ0IKR7KHc+lS7hhZBv9UsuMma/9ly8x+MAH2ug4dOjIcs2cPJ+VN5z9gACeod+48/P1Vq1jchwwJhpddnHhi8r6/eDG/msxfiNT8i4r49eST/eWETBF2ABg0KLmwLFwIDBtm1nK3iWjVipNbn39++Pu1tdw5hg0LhpddDBjAIYFE/lu2cKngqacGw8suZPsm8i8q4rxHGNofOLL/S2EcPNhfPqoYMIDnEpSWHv5+URGH8Uw3rAMHsrAnhiKLiji5GkCZdeYI++DB7KHEl03t3s3vmf5gAix+n312+Epxq1ax12g6/7w8bv8FCw5/Xwql6cLerRsvGZDIX/7f9PYfOpRf588//P3FizlMYGoNvsRpp/HrJ58c/n5RUYPTYDJOO41DRolee1FRYKONzBH24cPZYsZ37rB4XAB3joqKw2dwhkUYAea4ePHhceoFC1j0ZQ7EVAjBfSSZsPfuzRu6mIz8fM4hffTR4e8vWMAG1+TRKsChiiZNgI8/bnjv0KFAhVEJZ5zBr/GGqbSU9yCIhN0lTjuNV+v74IOG9z78sOGhNR1SvOM7x0cf8UNruscFMP+amobhP8D8Bw823+MCuP+sXs2VDAA7BPPnN3iTpuPMM5mvDAdUVnJ+Y8SIYHnZQW4ut3O8YVq8mEffZ58dHC+76NqV/+IN07vv8uvw4YFQ0iLsQohfCiFICBHchpxNmrCAywYFgNdf5/fatAmMlm0MGMAz1F5/nf9fWwvMnQuMGWO+xwUAI0dyhcOcOfz/igrOb4wZEywvu5A8587l14ULWRxHjw6OkwrOOovDAXKU9847/DpyZHCcVHDWWRzKkHH2t97ifh8GwwSwgM+bx1sQAsDbb7NTNmhQIHRcC7sQoguAUQBsbGPkMSZMAJYs4Vls69YBixYB48cHzcoesrKY6xtv8AP6/vu8s8y4cUEzs4fWrXlIOn06e7szZnC+ICz8Bw7kyqlp0/j/06ezoQqLsI8dyyOjl1/m/7/0En+fU04JlpddXHAB95f//pdfp04Fvv99szZvT4cLLuA9H959l/NihYXA+ecHV81GRK7+APwXwEAAGwHk2zln8ODB5Am2bCHKzib6yU+IbrqJ/11S4s29vMCCBUQA0UMPEZ17LlEsRrRvX9Cs7OP555n/yy8TnXAC0cknE9XVBc3KPu69l/m//z5Ry5ZEF18cNCM1XHIJUfPmRB98wH3/jjuCZqSGwYOJevYkmjmTf4ennw6akX3s28fP64gRRA8/zPw//FD7bQAUkR1dtnNQypN5A+u/1f87eGEnIrrlFv5aAIt72DB2bAP/hx8Omo0a9u8n6tevgf/s2UEzUkNFBVG7dsw9L49o2bKgGanhyy+JcnOZf6tWRJWVQTNSw9y5DX3nuOO4P4UJjz7awP/ccz1xauwKu+V0QCHEuwAKknx0N4C7wJtYW0IIcT2A6wGgq5d7Lz74INC0KTfvb3/r3X28wgsvAPfey+s833JL0GzUkJfHMfY//AE4/fTwhMEkYjEOhf3jH8DFF5tfzZOIPn04tvvcc8BPfhKeMIbE6NHAK6/wd7j9du5PYcLNN/PrmjWsPQHmxgRZ7bCd6kQhTgQwD8De+rc6A9gKYCgRlaU7d8iQIVQkZ2VFiBAhQgRbEEIsJiLLGkrHC3gQ0QoA7eJuuBHAECJKssRihAgRIkTwC5lTxx4hQoQIEQC48NgTQUTddF0rQoQIESI4R+SxR4gQIUKGIRL2CBEiRMgwRMIeIUKECBmGSNgjRIgQIcMQCXuECBEiZBgcT1BydVMhKgF84/uN3SMfwNFWpx9958zH0fZ9gfB+52OJKGZ1UCDCHlYIIYrszPrKJETfOfNxtH1fIPO/cxSKiRAhQoQMQyTsESJEiJBhiIRdDU8GTSAARN8583G0fV8gw79zFGOPECFChAxD5LFHiBAhQoYhEnYHMGLzbp8ghHhICLFaCPGFEGKWEKJV0Jy8ghBitBDiKyHEWiHEHUHz8RpCiC5CiPeFEMVCiFVCiJ8HzckvCCGyhRBLhRBzgubiBSJhV4RRm3f7g3cA9CeiAQDWALgzYD6eQAiRDeCfAMYA6AvgMiFE32BZeY5DAG4joj4ATgVw01HwnSV+DqA4aBJeIRJ2dTwM4NcAjorkBBG9TUSH6v+7ALxTViZiKIC1RLSeiA4AeBnAhIA5eQoiKiWiJfX/rgYLXadgWXkPIURnAOcBeDpoLl4hEnYFCCHOB7CFiJYHzSUg/AjA3KBJeIROADbH/b8ER4HISQghugE4CcDnwTLxBY+AnbO6oIl4BW0bbWQKdG3eHSak+85E9Gr9MXeDh+4v+snNRyTbefioGJUJIZoBmAHgViLaFTQfLyGEGAeggogWCyGGB83HK0TCngAiGpns/frNu7sDWC549/HOAJYIISw37zYdqb6zhBDiGgDjAJxDmVsfWwKgS9z/5ebsGQ0hRC5Y1F8koplB8/EB3wNwvhBiLIDGAFoIIV4goisD5qUVUR27Qxwtm3cLIUYD+CuAs4ioMmg+XkEIkQNODp8DYAuARQAuJ6JVgRLzEII9lP8A+JaIbg2aj9+o99h/SUTjguaiG1GMPYIV/gGgOYB3hBDLhBBPBE3IC9QniG8G8BY4iTgtk0W9Ht8DcBWAEfW/7bJ6TzZCyBF57BEiRIiQYYg89ggRIkTIMETCHiFChAgZhkjYI0SIECHDEAl7hAgRImQYImGPECFChAxDJOwRIkSIkGGIhD1ChAgRMgyRsEeIECFChuH/A6o41CYOMjV9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, color='b')\n",
    "plt.plot(x, np.gradient(y, dstep), color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1.2 - Analytic (Symbolic) solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Symbolic calculus is also a world of its own. We'll leave it to you to figure it out, check here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import webbrowser\n",
    "webbrowser.open('http://docs.sympy.org/latest/modules/solvers/solvers.html')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "from scipy.misc import derivative\n",
    "from sympy.parsing.sympy_parser import parse_expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = sp.Symbol('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 6 x + 2$"
      ],
      "text/plain": [
       "6*x + 2"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq = '3*x**2 + 2*x - 5'\n",
    "sp.diff(eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sympy_exp = parse_expr(eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 9.0 \\cdot 10^{-125}$"
      ],
      "text/plain": [
       "0.e-124"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy_exp.evalf(subs={x:1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2.0$"
      ],
      "text/plain": [
       "2.00000000000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "##Directly get the derivative\n",
    "deriv_eq = parse_expr(str(sp.diff(eq)))\n",
    "deriv_eq.evalf(subs={x:0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Alternatively, define a simple function\n",
    "#Numerical derivative value\n",
    "def f(x):\n",
    "    return 3*x**2 + 2*x - 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#If you have a function defined as f:\n",
    "derivative(f, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4 x \\sin{\\left(x \\right)} \\cos{\\left(x \\right)} + 2 \\sin^{2}{\\left(x \\right)}$"
      ],
      "text/plain": [
       "4*x*sin(x)*cos(x) + 2*sin(x)**2"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Example with trig functions\n",
    "eq2 = '2*x*sin(x)**2'\n",
    "sp.diff(eq2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Practical example: Error analysis for the Experimental Physics courses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy as sp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ f(a,b,c) = k \\frac{a b^{2}}{c^{2}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eq = 'k*a*b**2/c**2'\n",
    "a = sp.Symbol('a')\n",
    "b = sp.Symbol('b')\n",
    "c = sp.Symbol('c')\n",
    "k = sp.Symbol('k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next example needs the individual error multiplied in each paramter, but we're going to assume they're all unity just for the sake of the readability of the example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2*a*b**2*k/c**3 + 2*a*b*k/c**2 + b**2*k/c**2\n",
      "b*k*(-2*a*b + c*(2*a + b))/c**3\n"
     ]
    }
   ],
   "source": [
    "errlin = sp.diff(eq, a) + sp.diff(eq, b) + sp.diff(eq, c)\n",
    "print(errlin)\n",
    "print(sp.simplify(errlin))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sqrt(4*a**2*b**4*k**2/c**6 + 4*a**2*b**2*k**2/c**4 + b**4*k**2/c**4)\n",
      "sqrt(b**2*k**2*(4*a**2*b**2 + c**2*(4*a**2 + b**2))/c**6)\n"
     ]
    }
   ],
   "source": [
    "errsq = sp.sqrt( sp.diff(eq, a)**2 + sp.diff(eq, b)**2 + sp.diff(eq, c)**2 )\n",
    "print(errsq)\n",
    "print(sp.simplify(errsq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\sqrt{\\frac{4 a^{2} b^{4} k^{2}}{c^{6}} + \\frac{4 a^{2} b^{2} k^{2}}{c^{4}} + \\frac{b^{4} k^{2}}{c^{4}}}\n"
     ]
    }
   ],
   "source": [
    "print(sp.latex(errsq))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\sqrt{\\frac{4 a^{2}}{c^{6}} b^{4} k^{2} + \\frac{4 a^{2}}{c^{4}} b^{2} k^{2} + \\frac{b^{4} k^{2}}{c^{4}}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.592592592592593$"
      ],
      "text/plain": [
       "0.592592592592593"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errlin.evalf(subs={a:1, b:2, c:3, k:1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.69487640886273$"
      ],
      "text/plain": [
       "0.694876408862730"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errsq.evalf(subs={a:1, b:2, c:3, k:1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import webbrowser\n",
    "url = 'http://www.scipy-lectures.org/advanced/sympy.html'\n",
    "webbrowser.open(url)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1.3 - ODEs\n",
    "\n",
    "$$ \\tau \\frac{\\mathrm{d} y}{\\mathrm{d} t} = -y + ku $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def firstorder(y,t):\n",
    "    tau = 5.0\n",
    "    K= 2.0\n",
    "    u = 1.0\n",
    "    dydt = (-y + K*u)/tau    \n",
    "    return dydt    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nsteps = 50\n",
    "t = np.linspace(0,nsteps-1, nsteps)\n",
    "y = odeint(firstorder, 0.0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, y, marker='o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f57400b9e48>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = 2.0\n",
    "u = np.zeros(nsteps)\n",
    "u[4:] = 1.0\n",
    "u[20:] = -1.0\n",
    "u[30:] = 0.0\n",
    "plt.plot(t,u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f_order(y,t,K,u):\n",
    "    tau = 5.0\n",
    "    dydt = (-y + K*u)/tau\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ys = np.zeros(nsteps)\n",
    "y0 = 0.0\n",
    "ys[0] = y0\n",
    "for i in range(nsteps-1):\n",
    "    ts = [t[i], t[i+1]]\n",
    "    y = odeint(f_order, y0, ts, args=(K, u[i]))\n",
    "    y0 = y[1]\n",
    "    ys[i] = y0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5742ed46a0>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,ys)\n",
    "plt.plot(t,u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 - Integration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2.1 - Symbolic integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.integrate import quad, nquad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x**2 - 5.0*x - 8.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_min = -5.0\n",
    "x_max = 10.0\n",
    "x = np.arange(x_min, x_max, .1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make the next plot step by syep to remember spectators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.gca()\n",
    "ax.spines['bottom'].set_position(('data',0))\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "ax.spines['top'].set_color(None)\n",
    "ax.spines['right'].set_color(None)\n",
    "plt.plot(x, f(x), label='f(x)')\n",
    "plt.legend(loc='upper center')\n",
    "plt.fill_between(x, f(x), 0, where=f(x) >= 0, facecolor='blue')\n",
    "plt.fill_between(x, f(x), 0, where=f(x) <= 0, facecolor='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral = 67.50000000000001\n",
      "Error = 2.3550323351523795e-12\n"
     ]
    }
   ],
   "source": [
    "I, err = quad(f, x_min, x_max)\n",
    "print(\"Integral = \"+str(I))\n",
    "print(\"Error = \"+str(err))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def g(x, a, b, c, d):\n",
    "    return a*np.exp(-b*x+c)+d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1.0\n",
    "b = 1.0\n",
    "c = -3.0\n",
    "d = 0.0\n",
    "ax = plt.gca()\n",
    "ax.spines['bottom'].set_position(('data',0))\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "ax.spines['top'].set_color(None)\n",
    "ax.spines['right'].set_color(None)\n",
    "plt.plot(x, g(x, a, b, c, d), label='g(x)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1.0\n",
    "b = 1.0\n",
    "c = -3.0\n",
    "d = 0.0\n",
    "#Tupple with the function arguments\n",
    "arr = (a, b, c, d)\n",
    "#Start plotting\n",
    "ax = plt.gca()\n",
    "ax.spines['bottom'].set_position(('data',0))\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "ax.spines['top'].set_color(None)\n",
    "ax.spines['right'].set_color(None)\n",
    "plt.plot(x, g(x, *arr), label='g(x)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral = 7.389053838601245\n",
      "Error = 2.7510477454461937e-09\n"
     ]
    }
   ],
   "source": [
    "I, err = quad(g, x_min, x_max, args=arr)\n",
    "print(\"Integral = \"+str(I))\n",
    "print(\"Error = \"+str(err))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing the same function, but with different arguments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "arr1 = (1.0, 1.0, -3.0, -0.5)\n",
    "arr2 = (1.0, 1.0, -3.0, 0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.gca()\n",
    "ax.spines['bottom'].set_position(('data',0))\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "ax.spines['top'].set_color(None)\n",
    "ax.spines['right'].set_color(None)\n",
    "plt.plot(x, g(x, *arr1))\n",
    "plt.plot(x, g(x, *arr2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral = -0.11094616139875546\n",
      "Error = 2.7510475299941865e-09\n"
     ]
    }
   ],
   "source": [
    "I, err = quad(g, x_min, x_max, args=arr1)\n",
    "print(\"Integral = \"+str(I))\n",
    "print(\"Error = \"+str(err))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral = 7.389053838601245\n",
      "Error = 2.7510477454461937e-09\n"
     ]
    }
   ],
   "source": [
    "I, err = quad(g, x_min, x_max, args=arr2)\n",
    "print(\"Integral = \"+str(I))\n",
    "print(\"Error = \"+str(err))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2.2 - Numerical integration from samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 1, 10, endpoint=True)\n",
    "y = x\n",
    "yn = x + 0.1*np.random.randn(len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WvwEtBsCwT0nOgPlbwlmx+wxuzo68078lj9/pRyUn2TKgvJNwF6Ki2P9fWPc6tBiAaehyvj10gQ83RHIlJYNHAn14tXdzvCq72LpKYSES7kJUBPv/C6GvQvP+HAiczeRP9hN2/hqd/WqwcmAQrb2r2bpCYWES7kLYuwNLIfRVUhv35i39Ij8tPUS9aq7MG9mBgW3ryZYBdkrCXQh7dnA5rH2FU57dGHxiNBn6Mv/s7s+EexvjXkn++tsz+ekKYaf04a9Qa15il0Mnnjj/FD3bePNWvxY0qOFu69JEKZBwF8IOnTx2gAY//YtDpgBmVX+HVaPacUfjmrYuS5QiCXch7MjlG+nM23CUx46M4YaDK+d7LODHbh1ly4AKSMJdCDuQacrmsz0xfLw5irdNn9DM8Rw3h69mWKtOti5N2IiEuxDl3C9RCUxdE050/A1eq/87j1zZCl1fwqNVL1uXJmxIwl2IcupM4k3eW3uczccv0bCmO58/WIu7t8yHBkFw/9u2Lk/YmIS7EOXMjfQs5v98guU7T1PJ0YE3+7bgiS71cFnZBxycYNitjcBExSXhLkQ5kZ2t+f7XON7fEEnC9XSGdWrA672bU7uqK6x7Ey4cgUe+gOq+ti5VlAES7kKUA7+eTWJKcBhH4pJp71Od/z4eSHuf6saDEaGw7xMIegZaDrBtoaLMkHAXogy7dC2NWesi+OG3c9Su4sKch9sxpL03Dn8sbUyOg//9A+q2hV7TbFusKFPMCnelVB9gLuAILNVaz8xnzMPAZEADR7TWj1qwTiEqlLRME8t2nmbh1miyTJp/3NeE5+5viodLrr+ypiz4bhyYMmH4CnCSHR3FLYWGu1LKEVgI9ATigANKqWCtdXiuMf7AW8DdWuskpZTs8i9EMWit2Rh+ielrj3P2Sgq9AurwTv8AfGvms2XAthkQuxce+i/UbFL6xYoyzZwr9yAgWmt9CkAp9TUwGAjPNeZpYKHWOglAax1v6UKFsHeRF68zdU0Yu6Iv06xOZT4f14Wu/l75Dz65FXbMhvajoO3DpVuoKBfMCXdvIDbX/TigS54xzQCUUrswpm4ma63X5z2QUmo8MB7A11fe0RcC4GpKBh9tiuLzfWep7OLElEGteKyLL06OBXRDuhEPP4wHr2bQ7/3SLVaUG+aEe36bUuh8juMP3Ac0AHYopVprra/+5UlaLwGWAAQGBuY9hhAVSpYpm6/2n2X2piiupWbyWJeGvNSzGZ4elQp+Una2Eezp1+Dxn6CSR+kVLMoVc8I9DvDJdb8BcD6fMXu11pnAaaVUJEbYH7BIlULYmd0nE5kaEk7Exevc0diTSQNb0bJe1cKfuOsjOLUVBnwEdVpZv1BRbpkT7gcAf6VUI+AcMALIuxLmJ2AksEIp5YUxTXPKkoUKYQ9ir6Qwfe1x1oddpEENNxaN6kjvVnXN64Z0di/8PB0ChkCnJ6xfrCjXCg13rXWWUup5YAPGfPpyrXWYUmoqcFBrHZzzWC+lVDhgAl7TWl+2ZuFClCcpGVl8su0ki385haNSvNqrGU91a4yrs6OZB7hiLHus1gAGzQNpjScKYdY6d611KBCa53sTc93WwMs5X0KIHFprgo+cZ0ZoBBevpTG4fX3e7NuCetXcinIQCH4BblyCcRvAVZpZi8LJJ1SFsJKjcVeZEhLOoZgk2nhXY8GjHQj08yz6gfYvgYg10Gs6eMv+7MI8Eu5CWFjC9XQ+2BDB6kNx1PSoxPtD2zKsU4NbWwYUxfnDsPEd8O8Ndz5n+WKF3ZJwF8JCMrKyWbH7NPO2RJOeZeLpbo15/oGmVHUt5va76dfhuyfA3QuGfCLz7KJIJNyFKCGtNVsj45m25jinE2/yQIvavNO/JY1rVS7JQWHNy5B0BsasAQ9pbi2KRsJdiBKIjr/BtDXhbI9KoHEtDz59ojP3N7fA1kqHv4Dfv4X7/g/87i758USFI+EuRDEkp2Yyb8sJVu4+g5uzI+/0b8mYu/xwLmjLgKJIiITQ18CvG9zzasmPJyokCXchisCUrfn2YCwfbojkSkoGIzr78Eqv5nhVttB2u5mpsHosOLsbuz06mLkOXog8JNyFMNP+01eYEhJG2PlrdParwcqBQbT2tvCa8/VvQXw4PPY9VK1n2WOLCkXCXYhCnLuaysx1EYQcOU/9aq7MH9mBAW3rmbdlQFEc+wEOfQp3/RP8e1j22KLCkXAX9uPwV7BpIrQcCPe+DlXqluhwqRkmFv9ykkXbT6I1/Ku7PxPubYJbJStMlVw5DSH/Au9A6D6x8PFCFELCXZR/mamw7nX4dRXUagG/roTDX8Idz8Ld/wK36kU6nNaatb9fYEZoBOeuptK/bT3e6tuCBjXy6YZkCVkZxnp2FAxbDo7FXBcvRC4S7qJ8u3wSVo+Bi79Dt1eMpYPJZ43dE3fOgYPLoetL0OUZcC58P5ew88lMCQln/+krtKxXlTkPt6NLYyuvMd8yBc7/Bg+vghoNrftaosJQxp5fpS8wMFAfPHjQJq8t7ER4MPzvOWNFyYNLoFmvvz5+4ShsmQrRm6BKPbjvTaMtnePfr2ku30hn9qYovt5/lurulXi1V3Me6eyDY3G2DCiKqA3w5cPQ+SnoP9u6ryXsglLqkNY6sNBxEu6i3MnKgM2TYO9/jI20hq+A6rdp23hmJ2yeAnH7oWZTeOAdaDkYHBzINGWzak8MH2+OIjXDxON3+vGv7v5Ucy+FqZHkc7CoK1T1hqc2g7Or9V9TlHvmhrtMy4jyJTkOVj9hBHXQM9DrPXC6TVs6AL+uMG4jRK4zruRXj4V67Tna4kVeOliDkwk36ebvxaSBATStXaVUTgNTFvzwNGSlw/BPJdiFxUm4i/LjxGYjEE0ZMOxTaP2Q+c9VClr0g2a9Sdj9GWrbv2l7YSzvO7Qhe8BEAu8OsvzSxtv55X2I2QVDFoGXf+m9rqgwLPBZaSGsLNtkvEH6xTBj7nz89qIFe47raZnM2BDFXetq0zNzDruavkpH1wt03jwc9e1oSIiyQvH5OP0LbH8f2o2E9iNL5zVFhSNX7qJsu5EA34+D09uNN0P7fQCVirYkMTtb892vcby/PpLEG+kM79SA1/o0p3aVAZD+IuxZCLvnQ8RaaP+Y8cZrtQZWPJ+njbn/fh9a5zWEQMJdlGUxu4359bSrMGgBdBxd5EMcikliSkgYR+OS6eBbnWVjAmnnk2vdu0sVI8w7PwU7ZsOBpXD0Wwh62lha6V6MzkkFyc6GnyZAahKM+g5cSrAlsBCFkHAXZY/WsGuu8eZnDT8jCOu2KdIhLianMWt9BD/+do46VV346JF2DGnvXfC8uocX9JlhfPBp20xjJc6vq4ytAO541jJBvGc+RG82rtiLeD5CFJUshRRlS2oS/PQPiAyFgMHGFbtrVbOfnpZpYtnO0yzcGk1WtmZ8t8Y8e18TPFyKeB0Tfxy2TIPIteBR29jOoOOYwlfmFCT2AHzaB5r3Mz6sJF2VRDHJOndR/pz/Db59HK5dMJY4dnnG7BDUWrMh7BLTQ8OJvZJKn1Z1+b9+LfGtWcItA2L3w+bJxsqW6g2NNfKth4FDEdYipCbBonuM2xN2FHk7BCFyk3XuovzQGg4uM7a79agNT6wDn85mPz3y4nWmhISx++RlmtepwpdPdeGupl6Wqc0nCMauhegtsGWysRRz11xjcy//XoX/46M1BL8A18/DE+sl2EWpkXAXtpV+w9gN8dh30LQnPLTE7Dcxr6ZkMGdTFJ/vjaGKqzNTB7fi0SBfnCzRDSk3pYwteJs8AGE/wM/TjC0DfO+CHpPA946Cn3tgKRwPgZ5Ti/QPlhAlJeEubCc+wpiGuXzCmO7o+opZ0x1Zpmy+3H+WOZuiuJ6Wxeg7GvJij2bU8CjmfLi5HBygzTBoOQh+W2WsVV/eG5r1he7vQp1Wfx1/4ShseNv4R+vOF6xbmxB5yJy7sI0j38CaF6FSZRi2DBrdY9bTdkcnMiUknMhL17mrSU0mDWxF87qltGVAXhk3Yd8i2DkX0q9B20fg/reMFT7pN2DJvcavz+4yVuMIYQEWnXNXSvUB5gKOwFKt9cwCxg0DVgOdtdaS3OLvMtNg/RtwaAU0vNvYv9yMphqxV1J4b204G8Iu4ePpxqJRnejdqk7pbhmQVyUPYy18pydg18ewbzEc+x4Cn4SURGM74jHBEuzCJgoNd6WUI7AQ6AnEAQeUUsFa6/A846oA/wT2WaNQYQeunIJvx8DFo8Ye6/e/k+/2u7ndTM/iP9ui+e+O0zg5KF7r3ZxxXRvh6lyGGke7expz6l0mwPZZxjy7NsG9b5j9PxIhLM2cK/cgIFprfQpAKfU1MBgIzzNuGvA+8KpFKxT24XgI/PSc8ebkyG+geZ/bDtda89Phc8xcF8Gla+k82MGbN/q0oG61Mrx7YtX6MHCuMb9+Zgd0KPonaoWwFHPC3RuIzXU/DuiSe4BSqgPgo7Veo5SScBe3mDKNdeJ7FkD9DjB8ZaHdho7EXmVKSBi/nr1KuwbV+M9jnejUsEbp1GsJXk2NLyFsyJxwz29S8893YZVSDsBHwNhCD6TUeGA8gK/vbZorCPuQfA6+exJi90Lnp6H3dHByKXB4/PU03l8fyXeH4vCq7MIHw9oytGMDHKzdDUkIO2ROuMcBPrnuNwDO57pfBWgNbMt5c6suEKyUGpT3TVWt9RJgCRirZUpQtyjrTv4M3z9lNKMYthxaDy1waHqWiRW7zjD/52jSs0w8c29jnr+/KVVcpVG0EMVlTrgfAPyVUo2Ac8AI4NE/HtRaJwN/LgdQSm0DXpXVMhVUtslY/719FtRuaeyjUkAzCq01W47H897acM5cTqFHy9q83T+ARl4epVy0EPan0HDXWmcppZ4HNmAshVyutQ5TSk0FDmqtg61dpCgnbiTAD0/BqW3Q7lGj4XMBe69Hx19n6prj/BKVQJNaHqx8Moh7m9Uq3XqFsGNmrXPXWocCoXm+N7GAsfeVvCxR7pzda/QmTU2CQfONlSL5rEFPTs1k7uYTrNpzBrdKjkwcEMDoOxvibOktA4So4GT7AVFyEWuN9evVGsC4TVCv7d+GmLI13xyI5cONkSSlZDAyyJdXejajZuWC32AVQhSfhLsombAfjTdO67U3mmq4/X3J4r5Tl5kSEk74hWsE+XkyaVAArepXs0GxQlQcEu6i+I58Y7SN8+kCj602WtblEpeUwox1Eaw9eoH61VxZ8GgH+repZ9stA4SoICTcRfH8+pmxT3mjbjDya2OflRypGSYWbT/Jou0nUQpe7OHPM/c0wa1SGdoyQAg7J+Euiu7AMlj7MjTpDiO+AGc3wFjauOboBWaEHud8choD2tbjrX4t8a7uZuOChah4JNxF0ez9BNa/aexhPnwFOBt7vRw7l8zUkHD2n7lCQL2qfDyiA0GNzGu6IYSwPAl3Yb6dH8PmSUaziqHLwKkSl2+k8+HGSL4+EEsN90rMeKgNDwf64ChbBghhUxLuwjzb34et041tBB5cQiYOrNxxirlbTpCaYeLJuxvxz+7+VHOTLQOEKAsk3MXtaQ0/vwc7PjQ+dTp4AdtOXGbamnBOJtzknma1mDigJU1r26gbkhAiXxLuomBaw6Z3Yfd86DiG03dOZ9qqX/k5Ih6/mu4sGxPIAy1qy9JGIcogCXeRP61h3RuwfzEZHccx23Ecyz/egYuTI//XrwVj72pEJSfZMkCIskrCXfxddjasfQkOrSCy0RgeO9KHxJtnGN6pAa/1aU7tKmW4G5IQApBwF3llm4wPJx3+gm/dHub1473o6OvBsrGtaOdT3dbVCSHMJOEubjFlkbr6adwifmBO5jC+cX6Yjx8JYHD7+jKvLkQ5I+EuAEhLSyNu6aM0TdzCh6aRcM9L/HxfEzxc5I+IEOWR/M2t4LTWbDxyFvfgcXTLPsDqms/yyGMT8fHMv8mGEKJ8kHCvwI5fuMaM4N94Mu5dujke4VTnKQzv/6KtyxJCWICEewWUdDODOZui+GFfJMtcPqKL4zFMA+bROHCMrUsTQliIhHsFkmXK5ot9Z5mzKQqdfp21nnNpmBKGGrIIx3YjbF2eEMKCJNwriF3RiUwJCSPq0g16NHZlvmkhbvHHYOhSY7+ESQM9AAAPHElEQVQYIYRdkXC3c2cvp/De2nA2hl/Cx9ON5Y804f4DE1AJx+DhldByoK1LFEJYgYS7nbqZnsXCrdEs3XEaJ0fFa72bM65DFVy/GgqJkfDI59C8j63LFEJYiYS7ncnO1vx0+Bwz10UQfz2dhzp483qfFtR1SIZVgyHptNEWr2l3W5cqhLAiCXc7cjj2KlNCwvjt7FXaNajGJ6M60alhDbh2HlYMNH59bDU0usfWpQohrEzC3Q7EX0tj1vpIvv81Dq/KLnwwrC1DOzbAwUHB1VhYORBuJsKoH6DhnbYuVwhRCiTcy7H0LBPLd55hwc8nyDRpJtzbhOfub0IV15xuSFdOw8pBkJYMj/8EDQJtW7AQotSYFe5KqT7AXMARWKq1npnn8ZeBp4AsIAF4UmsdY+FaRQ6tNZuPx/Pe2nBiLqfQo2Vt3ukfgJ+Xx61BidHGFXtWKowJhvrtbVewEKLUFRruSilHYCHQE4gDDiilgrXW4bmG/QYEaq1TlFLPAu8Dj1ij4IruxKXrTF0Tzo4TiTStXZmVTwZxb7Nafx0UHwGrBhnb945ZA3Vb26ZYIYTNmHPlHgREa61PASilvgYGA3+Gu9Z6a67xe4FRlixSQHJKJh9tjuKzvTG4V3Jk4oAARt/ZEGfHPN2QLh4zVsU4OMLYtVC7hW0KFkLYlDnh7g3E5rofB3S5zfhxwLqSFCVuMWVrvtp/ltkbI7mamsnIIF9e6dmMmpVd/j74/GH4bAg4ucGYEPBqWvoFCyHKBHPCPb8uDTrfgUqNAgKBewt4fDwwHsDX19fMEiuuvacuMzk4jIiL1wlq5MmkgQG0ql8t/8FxB+Gzh8C1mjHH7tmodIsVQpQp5oR7HOCT634D4HzeQUqpHsDbwL1a6/T8DqS1XgIsAQgMDMz3HwgBcUkpzAiNYO3vF/Cu7sbCRzvSr03dgrshxeyBL4aBRy3jir26T/7jhBAVhjnhfgDwV0o1As4BI4BHcw9QSnUAFgN9tNbxFq+ygkjJyGLR9lMs3n4SpeClHs0Yf09j3Co5FvykU9vhqxFQ1du4Yq9av/QKFkKUWYWGu9Y6Syn1PLABYynkcq11mFJqKnBQax0MfABUBlbnXF2e1VoPsmLddkVrTcjRC8wIPc6F5DQGtqvPW31bUL+62+2feHA5hL4ONZvC4/+DKnVKp2AhRJln1jp3rXUoEJrnexNz3e5h4boqjGPnkpkcHMbBmCRa1a/K3BEdCGrkefsnZaXDutfh0Apo2hOG/hfcapRKvUKI8kE+oWojiTfS+XBDJN8cjMXTvRIzH2rD8EAfHB0KmFf/w/WL8M1oiNsPXV+GB94xlj0KIUQuEu6lLCMrm1V7zjB38wlSM02Mu7sRL3T3p5qbc+FPjj0A34yC9GswfAW0etDa5QohyikJ91K0NTKeaWvCOZVwk/ua1+LdAQE0qVXZvCf/ugrWvgJV6sGoTfKpUyHEbUm4l4JTCTeYtiacrZEJNPby4NOxnbm/RW3znpyVARveggNLofH9MGw5uBcyJy+EqPAk3K3oWlom87ecYMXuM7g4OfJ2v5aMucuPSk4OhT8Z4EY8fDsGzu6Gu/4J3SeBo/zIhBCFk6SwguxszepDsXywIZLLNzN4uJMPr/ZuTq0q+WwZUJBzh4w3TlOuwNBl0GaY9QoWQtgdCXcLO3jmClNCwvn9XDKdGtbg07FBtGlQwJYBBTn8JYS8CJXrwLiNUK+tdYoVQtgtCXcLuZCcyozQCIKPnKduVVfmjmjPoHb1C94yID+mTNj4DuxbBH7dYPhK8KhpvaKFEHZLwr2E0jJNLPnlFJ9sO4lJa/75QFMm3NcE90pF/K29mQirx8KZHXDHP6DnNJlfF0IUm6RHMWmtWXfsItPXHufc1VT6tanLW31b4uPpXvSDnT9srF+/EQ8PLoZ2IyxfsBCiQpFwL4bjF64xJSSMvaeu0KJuFb58ugt3NfEq3sGOfgvBL4B7TXhyPXh3tGyxQogKScK9CK7czGDOpki+3HeWqm7OTBvSmpGdfXDK2w3JHKYs2DwJ9iyAhncb8+uVaxX+PCGEMIOEuxkyTdl8sTeGOZuiuJlh4vE7/Xixhz/V3SsV74ApV4z59dPbIWg89P43OJqx/YAQQphJwr0QO08kMiUkjBPxN+ja1IuJAwNoVqdK8Q948Xf4+lFjA7DBC6GDtJsVQliehHsBYi7f5L21x9kUfglfT3eWjO5Ez4A6RVvamNexH+B/zxmt8J5YBw0CLVewEELkIuGex430LBZujWbZjtM4OSpe79OccV0b4eJUgm11s02wZSrs+hh8usDDn0ljDSGEVUm458jO1vz42zlmrY8g/no6D3X05o0+LahT1bVkB05Ngu/Gwckt0OkJ6Ps+OBVzrl4IIcwk4Q78djaJKSHhHI69Sjuf6iwe3YkOvhbobHQp3JhfT46DAR9D4BMlP6YQQpihQod7/LU0Zq2P5Ptf46hVxYXZw9vxYAdvHArrhmSO8GD4cQK4VIaxa8G3S8mPKYQQZqqQ4Z6eZWLZztMs/DmaTJPm2fua8Nz9TansYoHfjuxs2DoddnwI3oHwyOdQtV7JjyuEEEVQocJda82m8EtMDz1OzOUUegbU4Z3+LWlY08MyL5B6FX4YDyc2GEsc+88BpyJs8yuEEBZSYcL9xKXrTF0Tzo4TifjXrsxn44Lo5m/BT4QmRBrz60lnoN+H0PkpKMmySSGEKAG7D/fklEw+2hzFZ3tj8KjkyKSBAYy6oyHOxdkyoCARocYVu7MrPB4Mfndb7thCCFEMdhvupmzNV/vPMntjJMmpmTzaxZeXezbH08OCyxCzs2H7LNg+E+p3MObXqzWw3PGFEKKY7DLc95y8zJSQMCIuXqdLI08mDWxFQP2qln2R65dgzUsQuRbajYQBH4Gzm2VfQwghismuwj32Sgoz1h0n9PeLeFd34z+PdaRv67rF3zIg2wRXYyDxBCRGGfPqf9xOvQLKEfrMhC4TZH5dCFGm2EW4p2RksWjbSRb/cgql4OWezRh/T2Ncnc3cMiAjBS5HG6H9x1dClPE9U/qtce5e4NUMAgYZv/p1k/6mQogyyaxwV0r1AeYCjsBSrfXMPI+7AKuATsBl4BGt9RnLlvp3WmuCj5xn5roILiSnMbh9fd7o04L61fOZHtHaaGWXGAWJua7AE6Ig+Wyuk3GA6g2N8G76gPHrH1/untY+JSGEsIhCw10p5QgsBHoCccABpVSw1jo817BxQJLWuqlSagQwC3jEGgX/4fe4ZKaEhHEwJonW3lWZP7IDgX6exlTK5ZO3wjt3kKcm3TqAkxt4+YNPEHQcbdz2agaeTYxVL0IIUY6Zc+UeBERrrU8BKKW+BgYDucN9MDA55/Z3wAKllNJaawvWCkDijXQ+WB9JyKETdHBP5Ks7sulS5TIO+5dC6B9TKRm3nuBRO2cqZQjUan4rxKs2AAcLLocUQogyxJxw9wZic92PA/JulPLnGK11llIqGagJJOYepJQaD4wH8PX1LVbBv/00j3+eWMQsl0QwAYcxplJqNMqZSumRE+LNoGZTmUoRQlRI5oR7fstA8l6RmzMGrfUSYAlAYGBgsa7qu3UIINPhHvAOgFo5c+GejeVj/kIIkYs54R4H+OS63wA4X8CYOKWUE1ANuGKRCvNwbdUf11b9rXFoIYSwG+ZMOh8A/JVSjZRSlYARQHCeMcHAmJzbw4CfrTHfLoQQwjyFXrnnzKE/D2zAWAq5XGsdppSaChzUWgcDy4DPlFLRGFfsI6xZtBBCiNsza5271joUCM3zvYm5bqcBwy1bmhBCiOKStYBCCGGHJNyFEMIOSbgLIYQdknAXQgg7JOEuhBB2SNlqObpSKgGIKebTvciztUEFIOdcMcg5VwwlOeeGWutCG0DbLNxLQil1UGsdaOs6SpOcc8Ug51wxlMY5y7SMEELYIQl3IYSwQ+U13JfYugAbkHOuGOScKwarn3O5nHMXQghxe+X1yl0IIcRtlOlwV0r1UUpFKqWilVJv5vO4i1Lqm5zH9yml/Eq/Sssy45xfVkqFK6WOKqW2KKUa2qJOSyrsnHONG6aU0kqpcr+ywpxzVko9nPOzDlNKfVnaNVqaGX+2fZVSW5VSv+X8+e5nizotRSm1XCkVr5Q6VsDjSik1L+f346hSqqNFC9Bal8kvjO2FTwKNgUrAESAgz5h/AItybo8AvrF13aVwzvcD7jm3n60I55wzrgrwC7AXCLR13aXwc/YHfgNq5Nyvbeu6S+GclwDP5twOAM7Yuu4SnvM9QEfgWAGP9wPWYXSyuwPYZ8nXL8tX7n825tZaZwB/NObObTCwMuf2d0B3pVR+Lf/Ki0LPWWu9VWudknN3L0ZnrPLMnJ8zwDTgfSCtNIuzEnPO+WlgodY6CUBrHV/KNVqaOeesgao5t6vx945v5YrW+hdu35FuMLBKG/YC1ZVS9Sz1+mU53PNrzO1d0BitdRbwR2Pu8sqcc85tHMa//OVZoeeslOoA+Git15RmYVZkzs+5GdBMKbVLKbVXKdWn1KqzDnPOeTIwSikVh9E/4oXSKc1mivr3vUjMatZhIxZrzF2OmH0+SqlRQCBwr1Ursr7bnrNSygH4CBhbWgWVAnN+zk4YUzP3YfzvbIdSqrXW+qqVa7MWc855JLBCaz1bKXUnRne31lrrbOuXZxNWza+yfOVelMbcWLsxdykx55xRSvUA3gYGaa3TS6k2aynsnKsArYFtSqkzGHOTweX8TVVz/2z/T2udqbU+DURihH15Zc45jwO+BdBa7wFcMfZgsVdm/X0vrrIc7hWxMXeh55wzRbEYI9jL+zwsFHLOWutkrbWX1tpPa+2H8T7DIK31QduUaxHm/Nn+CePNc5RSXhjTNKdKtUrLMueczwLdAZRSLTHCPaFUqyxdwcDjOatm7gCStdYXLHZ0W7+jXMi7zf2AKIx32d/O+d5UjL/cYPzwVwPRwH6gsa1rLoVz3gxcAg7nfAXbumZrn3Oesdso56tlzPw5K2AOEA78Doywdc2lcM4BwC6MlTSHgV62rrmE5/sVcAHIxLhKHwdMACbk+hkvzPn9+N3Sf67lE6pCCGGHyvK0jBBCiGKScBdCCDsk4S6EEHZIwl0IIeyQhLsQQtghCXchhLBDEu5CCGGHJNyFEMIO/T+zxc+x2or7JgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x ,y)\n",
    "plt.plot(x ,yn)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.49206389052044364\n",
      "0.49206389052044364\n",
      "0.48975011902324056\n"
     ]
    }
   ],
   "source": [
    "print(np.trapz(yn, x=x))\n",
    "print(integrate.trapz(yn, x=x))\n",
    "print(integrate.simps(yn, x=x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2-D Integration\n",
    "\n",
    "Now for a 2-D case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def z(x, y):\n",
    "    return np.cos(x)+np.sin(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(-3,3,.05)\n",
    "y = np.arange(-3,3,.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.0000000e+00, -2.9500000e+00, -2.9000000e+00, -2.8500000e+00,\n",
       "       -2.8000000e+00, -2.7500000e+00, -2.7000000e+00, -2.6500000e+00,\n",
       "       -2.6000000e+00, -2.5500000e+00, -2.5000000e+00, -2.4500000e+00,\n",
       "       -2.4000000e+00, -2.3500000e+00, -2.3000000e+00, -2.2500000e+00,\n",
       "       -2.2000000e+00, -2.1500000e+00, -2.1000000e+00, -2.0500000e+00,\n",
       "       -2.0000000e+00, -1.9500000e+00, -1.9000000e+00, -1.8500000e+00,\n",
       "       -1.8000000e+00, -1.7500000e+00, -1.7000000e+00, -1.6500000e+00,\n",
       "       -1.6000000e+00, -1.5500000e+00, -1.5000000e+00, -1.4500000e+00,\n",
       "       -1.4000000e+00, -1.3500000e+00, -1.3000000e+00, -1.2500000e+00,\n",
       "       -1.2000000e+00, -1.1500000e+00, -1.1000000e+00, -1.0500000e+00,\n",
       "       -1.0000000e+00, -9.5000000e-01, -9.0000000e-01, -8.5000000e-01,\n",
       "       -8.0000000e-01, -7.5000000e-01, -7.0000000e-01, -6.5000000e-01,\n",
       "       -6.0000000e-01, -5.5000000e-01, -5.0000000e-01, -4.5000000e-01,\n",
       "       -4.0000000e-01, -3.5000000e-01, -3.0000000e-01, -2.5000000e-01,\n",
       "       -2.0000000e-01, -1.5000000e-01, -1.0000000e-01, -5.0000000e-02,\n",
       "       -1.0658141e-14,  5.0000000e-02,  1.0000000e-01,  1.5000000e-01,\n",
       "        2.0000000e-01,  2.5000000e-01,  3.0000000e-01,  3.5000000e-01,\n",
       "        4.0000000e-01,  4.5000000e-01,  5.0000000e-01,  5.5000000e-01,\n",
       "        6.0000000e-01,  6.5000000e-01,  7.0000000e-01,  7.5000000e-01,\n",
       "        8.0000000e-01,  8.5000000e-01,  9.0000000e-01,  9.5000000e-01,\n",
       "        1.0000000e+00,  1.0500000e+00,  1.1000000e+00,  1.1500000e+00,\n",
       "        1.2000000e+00,  1.2500000e+00,  1.3000000e+00,  1.3500000e+00,\n",
       "        1.4000000e+00,  1.4500000e+00,  1.5000000e+00,  1.5500000e+00,\n",
       "        1.6000000e+00,  1.6500000e+00,  1.7000000e+00,  1.7500000e+00,\n",
       "        1.8000000e+00,  1.8500000e+00,  1.9000000e+00,  1.9500000e+00,\n",
       "        2.0000000e+00,  2.0500000e+00,  2.1000000e+00,  2.1500000e+00,\n",
       "        2.2000000e+00,  2.2500000e+00,  2.3000000e+00,  2.3500000e+00,\n",
       "        2.4000000e+00,  2.4500000e+00,  2.5000000e+00,  2.5500000e+00,\n",
       "        2.6000000e+00,  2.6500000e+00,  2.7000000e+00,  2.7500000e+00,\n",
       "        2.8000000e+00,  2.8500000e+00,  2.9000000e+00,  2.9500000e+00])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3.  , -2.95, -2.9 , ...,  2.85,  2.9 ,  2.95],\n",
       "       [-3.  , -2.95, -2.9 , ...,  2.85,  2.9 ,  2.95],\n",
       "       [-3.  , -2.95, -2.9 , ...,  2.85,  2.9 ,  2.95],\n",
       "       ...,\n",
       "       [-3.  , -2.95, -2.9 , ...,  2.85,  2.9 ,  2.95],\n",
       "       [-3.  , -2.95, -2.9 , ...,  2.85,  2.9 ,  2.95],\n",
       "       [-3.  , -2.95, -2.9 , ...,  2.85,  2.9 ,  2.95]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, Y = np.meshgrid(x, y)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolor(X, Y, z(X, Y), cmap='jet')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Put this example in 3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%matplotlib notebook\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "\n",
    "# Make data.\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "# Plot the surface.\n",
    "surf = ax.plot_surface(X, Y, z(X, Y), cmap='jet',\n",
    "                       linewidth=0, antialiased=False)\n",
    "\n",
    "# Customize the z axis.\n",
    "ax.set_zlim(-1.01, 1.01)\n",
    "\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "\n",
    "# Add a color bar which maps values to colors.\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral = 1.6934400967184076\n",
      "Error = 2.6428245051366776e-13\n"
     ]
    }
   ],
   "source": [
    "I, err = nquad(z, [[-3, 3],[-3, 3]])\n",
    "print(\"Integral = \"+str(I))\n",
    "print(\"Error = \"+str(err))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can we do something more complicated?\n",
    "\n",
    "Consider (from the scipy example):\n",
    "\n",
    "$$\\Large{I_N = \\int_{0}^{+\\infty}\\int_{1}^{+\\infty} \\frac{e^{-xt}}{t^{N}} \\mathrm{d}t\\mathrm{d}x}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral = 0.09999999999998103\n",
      "Error = 1.2479337063157417e-09\n"
     ]
    }
   ],
   "source": [
    "N = 10.0\n",
    "def f2(t, x):\n",
    "    return np.exp(-x*t)/(t**N)\n",
    "\n",
    "I, err = nquad(f2, [[1, np.inf],[0, np.inf]])\n",
    "print(\"Integral = \"+str(I))\n",
    "print(\"Error = \"+str(err))"
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}