Fourier_x_squared.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = Symbol('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = Symbol ('n', integer=True, positive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANwAAABGBAMAAABVieeXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n+FfOK1emo+P1H8MiOAizTMaCAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{1}{\\sqrt{\\pi}} \\int_{- \\pi}^{\\pi} x^{2} \\sin{\\left (n x \\right )}\\, dx = 0$$"
      ],
      "text/plain": [
       "π                    \n",
       "⌠                    \n",
       "⎮   2                \n",
       "⎮  x ⋅sin(n⋅x) dx    \n",
       "⌡                    \n",
       "-π                   \n",
       "───────────────── = 0\n",
       "        √π           "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a= Integral(x*x*sin(n*x),(x,-pi,pi))/sqrt(pi)\n",
    "Eq(a,simplify(a.doit()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATwAAABGBAMAAACj5TUmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nwS8A7f/HNTijPL39/zh+NLzs/wGe+dMl+uZzUgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{1}{\\sqrt{\\pi}} \\int_{- \\pi}^{\\pi} x^{2} \\cos{\\left (n x \\right )}\\, dx = \\frac{4 \\left(-1\\right)^{n}}{n^{2}} \\sqrt{\\pi}$$"
      ],
      "text/plain": [
       "π                             \n",
       "⌠                             \n",
       "⎮   2                         \n",
       "⎮  x ⋅cos(n⋅x) dx             \n",
       "⌡                         n   \n",
       "-π                  4⋅(-1) ⋅√π\n",
       "───────────────── = ──────────\n",
       "        √π               2    \n",
       "                        n     "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b= Integral(x*x*cos(n*x),(x,-pi,pi))/sqrt(pi)\n",
    "Eq(b,simplify(b.doit()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMwAAABGBAMAAAByJ2Z/AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nXd2KYU7Z/2UbwlD/AjUPdt6An3S2AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{2 \\sqrt{\\pi}} \\int_{- \\pi}^{\\pi} x^{2}\\, dx = \\frac{\\sqrt{2} \\pi^{\\frac{5}{2}}}{3}$$"
      ],
      "text/plain": [
       "   π                 \n",
       "   ⌠                 \n",
       "   ⎮   2             \n",
       "√2⋅⎮  x  dx          \n",
       "   ⌡              5/2\n",
       "   -π         √2⋅π   \n",
       "─────────── = ───────\n",
       "    2⋅√π         3   "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g=Integral(x*x,(x,-pi,pi))/sqrt(2*pi)\n",
    "Eq(g,g.doit())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAvBAMAAAAV7ydtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdpmJMlQiZrurEN1E\n782PMUhmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVQoFWNggACjpgVQFgNzAucDGJs7geUb\nnH2A7Q+MzcDA+gvB5hZAsI0QTHYFBPswwxEYh+VpaBeQLf////9PvP//f2BgYDYJTBdLgMi7Mpgx\nOkCYQLKBcwGMzTKBG8ZkYCrgh4uvX8B/ACYhzcBrAGO3M3DC2TAxGtFAn8AAxTYkG7fCzGBTYIgv\ngHIYvzLwb4Cyee4wrH8AU8SAUMPAwLUZLsxmrQVnMzDYHkBweG9B2WwJDBxfoWz+Xwg2bwMDNyzW\n2QsY4gVgeg8p9YCYAANRNjeM9yhhAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{\\pi^{2}}{3}$$"
      ],
      "text/plain": [
       " 2\n",
       "π \n",
       "──\n",
       "3 "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_zero=g.doit()/sqrt(2*pi)\n",
    "c_zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAI8AAAAuBAMAAADjDVfrAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRKVQdhpaQSiT8IZe6dGzSXhDy2arUv8HmeHYTtHQGFQAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{4 \\left(-1\\right)^{n}}{n^{2}} \\cos{\\left (n x \\right )}$$"
      ],
      "text/plain": [
       "      n         \n",
       "4⋅(-1) ⋅cos(n⋅x)\n",
       "────────────────\n",
       "        2       \n",
       "       n        "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=simplify(b.doit())/(sqrt(pi))*cos(n*x)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAACnsAAAA9BAMAAACdR1O5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\sum_{n=1}^{20} \\frac{4 \\left(-1\\right)^{n}}{n^{2}} \\cos{\\left (n x \\right )} + \\frac{\\pi^{2}}{3} = - 4 \\cos{\\left (x \\right )} + \\cos{\\left (2 x \\right )} - \\frac{4}{9} \\cos{\\left (3 x \\right )} + \\frac{1}{4} \\cos{\\left (4 x \\right )} - \\frac{4}{25} \\cos{\\left (5 x \\right )} + \\frac{1}{9} \\cos{\\left (6 x \\right )} - \\frac{4}{49} \\cos{\\left (7 x \\right )} + \\frac{1}{16} \\cos{\\left (8 x \\right )} - \\frac{4}{81} \\cos{\\left (9 x \\right )} + \\frac{1}{25} \\cos{\\left (10 x \\right )} - \\frac{4}{121} \\cos{\\left (11 x \\right )} + \\frac{1}{36} \\cos{\\left (12 x \\right )} - \\frac{4}{169} \\cos{\\left (13 x \\right )} + \\frac{1}{49} \\cos{\\left (14 x \\right )} - \\frac{4}{225} \\cos{\\left (15 x \\right )} + \\frac{1}{64} \\cos{\\left (16 x \\right )} - \\frac{4}{289} \\cos{\\left (17 x \\right )} + \\frac{1}{81} \\cos{\\left (18 x \\right )} - \\frac{4}{361} \\cos{\\left (19 x \\right )} + \\frac{1}{100} \\cos{\\left (20 x \\right )} + \\frac{\\pi^{2}}{3}$$"
      ],
      "text/plain": [
       "  20                                                                          \n",
       "_____                                                                         \n",
       "╲                                                                             \n",
       " ╲          n                                                                 \n",
       "  ╲   4⋅(-1) ⋅cos(n⋅x)    2                                                   \n",
       "   ╲  ────────────────   π                           4⋅cos(3⋅x)   cos(4⋅x)   4\n",
       "   ╱          2        + ── = -4⋅cos(x) + cos(2⋅x) - ────────── + ──────── - ─\n",
       "  ╱          n           3                               9           4        \n",
       " ╱                                                                            \n",
       "╱                                                                             \n",
       "‾‾‾‾‾                                                                         \n",
       "n = 1                                                                         \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "⋅cos(5⋅x)   cos(6⋅x)   4⋅cos(7⋅x)   cos(8⋅x)   4⋅cos(9⋅x)   cos(10⋅x)   4⋅cos(\n",
       "───────── + ──────── - ────────── + ──────── - ────────── + ───────── - ──────\n",
       "   25          9           49          16          81           25          12\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "11⋅x)   cos(12⋅x)   4⋅cos(13⋅x)   cos(14⋅x)   4⋅cos(15⋅x)   cos(16⋅x)   4⋅cos(\n",
       "───── + ───────── - ─────────── + ───────── - ─────────── + ───────── - ──────\n",
       "1           36          169           49          225           64          28\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                \n",
       "                                                \n",
       "                                                \n",
       "                                                \n",
       "                                               2\n",
       "17⋅x)   cos(18⋅x)   4⋅cos(19⋅x)   cos(20⋅x)   π \n",
       "───── + ───────── - ─────────── + ───────── + ──\n",
       "9           81          361          100      3 \n",
       "                                                \n",
       "                                                \n",
       "                                                \n",
       "                                                "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d=Sum(c,(n,1,20))\n",
    "Eq(d+c_zero,d.doit()+c_zero)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f=d.doit()+c_zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWAAAAETCAYAAAAI19wjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nB6xlwrERFbsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1141063c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1140beac8>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(f,(x,-pi,pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}