MathWithSumpy_SERIES_LIMITS_082918.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Just about any math equation !!!\n",
    "\n",
    "### For ADVANCED ALGETRA: sympy library in Jupyter Notebook allows you to:\n",
    " \n",
    " - Series\n",
    " - Limits\n",
    " - Sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "from __future__ import division\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x, y, z = symbols(\"x, y, z\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a, b,c,d = symbols ('a b c d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVwAAAAwBAMAAACved+KAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$1 - \\frac{x^{2}}{2} + \\frac{x^{4}}{24} - \\frac{x^{6}}{720} + \\frac{x^{8}}{40320} + \\mathcal{O}\\left(x^{10}\\right)$$"
      ],
      "text/plain": [
       "     2    4     6      8          \n",
       "    x    x     x      x      ⎛ 10⎞\n",
       "1 - ── + ── - ─── + ───── + O⎝x  ⎠\n",
       "    2    24   720   40320         "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Simple Expansion  -- LaTeX printing\n",
    "cos(x).series(n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAAwBAMAAAAP5rdkAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nr0z/AhTvONtXUJeUAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$x - \\frac{x^{3}}{6} + \\frac{x^{5}}{120} - \\frac{x^{7}}{5040} + \\frac{x^{9}}{362880} + \\mathcal{O}\\left(x^{10}\\right)$$"
      ],
      "text/plain": [
       "     3     5     7       9           \n",
       "    x     x     x       x       ⎛ 10⎞\n",
       "x - ── + ─── - ──── + ────── + O⎝x  ⎠\n",
       "    6    120   5040   362880         "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Simple Expansion  -- LaTeX printing\n",
    "sin(x).series(n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWkAAAAwBAMAAAAho5b2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n+Bty1QnGumwQZgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$x - \\frac{2 x^{3}}{3} + \\frac{2 x^{5}}{15} - \\frac{4 x^{7}}{315} + \\frac{2 x^{9}}{2835} + \\mathcal{O}\\left(x^{10}\\right)$$"
      ],
      "text/plain": [
       "       3      5      7      9         \n",
       "    2⋅x    2⋅x    4⋅x    2⋅x     ⎛ 10⎞\n",
       "x - ──── + ──── - ──── + ──── + O⎝x  ⎠\n",
       "     3      15    315    2835         "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Simple Expansion  -- LaTeX printing\n",
    "(sin(x)*cos(x)).series(n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJkAAAAyBAMAAAC9qWSkAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMqvNiRDvuyJ2mUTd\nZlSFEfbmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAD8klEQVRIDZ1XTWgUSRR+ncz/9PTMSfDiNHpR\nWZzoQUURG0EkEUkbxcVTgiCyLOic/Je0XjyoZNB4iEHSyh4WRJyrIDigIAqugYXdi5JcDHtY2DEg\n+K+v/rqrq3p6ZrbQeu9976tvXnVVV1cAktve5HSQHQu8BCflJyTlVHFIjjr4uzrgOvynDqmIdZQi\nS66a0OOso2MKcqiJQHp9rQe19HFlrB6eZdBcD2qwpA+PItb7PtRMJzpYi0yfQT3VZn3QxkeBBa8P\nNXgRHaxFzzjSU22wkPx0jc99qY03tHJkoDDRl9rgkDxY8zN2X2r55GWozvellvuq1SMDc15fanBE\nHqz5Jzly98QmUWWEk+NoyWPweWaMNQ6saESYJDimIRChXRb5tcwZ5fEhG6qOyAmb/iQ8ycq0rQI/\nwJyFJrNZWyQka3yUghi35AswxeZV5dOLVbO+CXa8NT2BpyeoN+4zANUuVpgb9qV3oR94Eu1qAMJ2\n6pZthmTt3KRtbL4zs644c06QtN248s0NQSOcW/j/8PUr0zi/ETqmXKcGsLZBG8wzMDULfzEIIKXs\n7XQdTEHzkHQBj2Wn9NwcAmAfhQx6pKEa+TcBKF/1KARQ4GclD6F4FPKCNo/gH/iDbuq9hfx/KSfT\nokaoDUHZgWqFYTDQpk75O2nEf3XGo0ykNTD8FWuDwTohVUkH5gQ1Qq1OaKoaY5D+4M5PlElpVA2Y\nbi9q6kxzLiw0yQPhajhTrKpC+kekA7NFTXxt6ipYDRiYl9RwFSx3DvKutgp18ovsR4OZ5pX9hp/q\nrBfQ6LZ4vDgJ17Cg32hRGfoMwagtX6wt768tr5o8knr1lNULpc/c4aa47/ZeZDIaYji9sZnD9+fR\n3UgpZZ+a+M5S1FRW+GblWjQ37qgUKf7fb72kgW6Kh3Enksw8LQJ+Iv23KABup6fRKfDgiZJUw+C0\n5LKjXpRRciw7VHsQTWqRepLXFIbZBHw5RW38452eWftwWCHGhpGTvwkwXoHjhdU/rd5A2dVFag7C\n60a3SRNijpzVw3euV+ioWXxPPHgZ1paxKb4bRt1/qJfckfMw767B+ZH2M6q58DxUK7Qp7sIWart1\n2RaAATs4zThNavslVCuK7dvlc8PHs1sNFrjnFGlfPHxuqCBWQdzIDOWF7VAkvZcZbYOlSw6wNeUx\n8BvZ23wbbnZQkGFycZhKtfjev4QP0Sf7LWgZH93it2xb7KwgE+PQm+rY7PBulvsdzciIKxHpLTq9\n7uatNxLYyR30IxlZhye2RQjJwVLM+OiIqUo0TojS+NHp0qxWF0KYzvqh38m72ymh4X9riA4MNHQs\nFunpL0q4FztWB8foGvwALYXjkJdOLKYAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\lim_{x \\to 0^+}\\left(\\frac{1}{x} \\sin{\\left (x \\right )}\\right)$$"
      ],
      "text/plain": [
       "     sin(x)\n",
       " lim ──────\n",
       "x─→0⁺  x   "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Simple Limit -- check syntax\n",
    "Limit(sin(x)/x, x, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAHlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAACGjDitAAAACXRSTlMAVO8Qq5l2zWYZcMvdAAAACXBIWXMAAA7EAAAOxAGV\nKw4bAAAAHUlEQVQIHWNgAANGZQYGk5DJQDYbqQSr03QPsBkAJYgIYEZbtZEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Simple Limit\n",
    "limit(sin(x)/x, x, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOBAMAAADkjZCYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJZjLNVN0i77ur\nRHZ72Yd1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAVElEQVQIHWNgEDIxZWBgSGeQmMDAsoCBOYGB\n+wAD+0cG/gMMvN8Z5BUYeP8xzDdgYP3MMF8BREJEgLLs3xm4NzCwfATpYkpgYGhnkApgYBB+d5QB\nAPogE3QldevOAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$0$$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Simple Limit to INFINITY\n",
    "limit(1/x, x, oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAAA5BAMAAAB9gZCeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nKPkGIR+PaDm/XvwAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\sum_{x=1}^{\\infty} x^{- x}$$"
      ],
      "text/plain": [
       "  ∞      \n",
       " ___     \n",
       " ╲       \n",
       "  ╲    -x\n",
       "  ╱   x  \n",
       " ╱       \n",
       " ‾‾‾     \n",
       "x = 1    "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Confirm Syntax of Infinite Series Limit\n",
    "Sum(1/x**x, (x, 1, oo))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ8AAAAPBAMAAAAIUwCQAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nEZjDGspEAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$1.29128599706266$$"
      ],
      "text/plain": [
       "1.29128599706266"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Infinite Series Limit\n",
    "Sum(1/x**x, (x, 1, oo)).evalf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ8AAAAPBAMAAAAIUwCQAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nEZjDGspEAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$1.29128599706266$$"
      ],
      "text/plain": [
       "1.29128599706266"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Infinite Series Limit\n",
    "N(Sum(1/x**x, (x, 1, oo)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Integral?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGoAAAAuBAMAAAAyxpHeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAmYkQdqvvRN27IjJm\nVM1kwppwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACkUlEQVRIDZ1UTWgTQRh9ySZmN5tkS696iD9g\nQaFLqV4Es7UpIorJIRd7SaCIIII5FPGWHvSo2UPpQcQsgqgopAfxJsnRQ7EBL+Kl8aKoB6MxFn+q\nfvszkyls02QHJt9773svM5nMLuCO0AHdQ6OUueP5UeyuV9qUjdFTkc7oGUA2g6TqAfYH5MpB1qrp\nQVI/goTUXpBU5HuQlLIZJKV1g6QaS76peNOVE5Zvez3P5ecGh3jM4LwH1JUxJlEtGpw00hziE4Mn\nGdBaDFGtlgXCYYJ/cdjwxIrOu5D+CaQvyxbDUslDE0yhmhSuxpNV3njEET548F1fQvinS56tnY/X\n8ur7vdmCLczQnJ57eMoA9hNEfPzsFqTs/OIhmyH1zSmSCRmpPORl1C1S7gJSOnFDbgOvbMM1S+li\nCi+N2zaDtuWU2AIiUPJQStCapNwCwnq4m7SAN0SlKwi1cRCT+ltiQP2XU1BdtpxUG5pByiVyImXa\nvQbNUBdyGjo+2gKNjY5bp758dVImT9E+DLtnp/aYyJSpsps+2SZCv1bHetneoZeiHZLfOdPrhDJp\nbFBRf9syjdqYU5IGok0hRaeR1HOI6O5pZFq4l7Re0+ts1rFfbbmpBSgWLcTWouOutGp4Ss1xmikj\ncTMc21I67qVmVyN29Nxhtdg7Uey9qF0kG23rWHZ6X5PgZ5pS4ciD01JhdmaNCBATroYjeB+yxVh8\niaF+jezw1vC5vf0Qon8EIsI7jPAnhQlUZXaWguZA/lTyuODQOgIR4cA3QMMUrcPiXHpYp+grlkU2\nLK4Oa9zm+7uNDUlU90ke0s1siZ3+LmbwrdGSr7yLqKV3Mfi2K6u+8kBxAhcG9v2bK+pl/8ZA9f6Z\nABv8D0kSjCii1SJoAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\int \\sin{\\left (x \\right )}\\, dx$$"
      ],
      "text/plain": [
       "⌠          \n",
       "⎮ sin(x) dx\n",
       "⌡          "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Integral(sin(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEwAAAAUBAMAAADVZMaCAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$- \\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "-cos(x)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(sin(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC0AAAArBAMAAAAebRy0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMrvvmVREEIndzSJ2\nZqtw62vAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABGElEQVQ4EWNgAANGZQcIA53kD0AXgfDzC7CL\nd2IXZliCTZzb4+BXbOLJG5i+YxFnt2VgWYBFnOU7A2cDFnFmBYb6BCRxDid3MK++gSEeSZihm+EV\nRDyAQYt1A0JmNoM8mMd1gHceB0KYYRrD/gQQl/1N475jSOIMDPE4QmUOiio4h8MBzkRhXEHhwTls\nDWwCcA4SQyo0CM1e9jOvc3oY7P//R1IFYlYw3DwwC00MxG1n6C+IxiJewLAIJvofAT4Axf7AxFFp\nxo+ofCgvnOcDw3FMGbavTB+4L2CKs785fuQupjC6yAAmWkgAozgInGgxAxiSaDEDGJJokQIYahgs\n0aIHMDTRYgRwPTjRYgYwONFiCWBwosUMYADzqGBAhq3jCAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{d}{d x} x^{2}$$"
      ],
      "text/plain": [
       "d ⎛ 2⎞\n",
       "──⎝x ⎠\n",
       "dx    "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Derivative(x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAOBAMAAADd6iHDAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAf0lEQVQIHWNgVDJ2YICAMAb2H1BmKgPDTChz\nFgNDvgOEvT8AzgQKrA9gPZPYUwNkcXxnCGd4dWA1kMmVwFDKUB9wEchUYmAIYNgMZDDwKIDIPyDi\nEgOjAAPLFyCLRYGBR+AqzweGowxS5UVZHH+ZPzA+YNj///8v1pyjh94xAABbhSE1xl33oAAAAABJ\nRU5ErkJggg==\n",
      "text/latex": [
       "$$2 x$$"
      ],
      "text/plain": [
       "2⋅x"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANQAAAAPBAMAAABuCfzHAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n7f97/gMctmFMGwwYsQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$0.0005072143046136395$$"
      ],
      "text/plain": [
       "0.0005072143046136395"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate Expression from Symbols\n",
    "expr = sin(x)/x\n",
    "f = lambdify(x, expr)\n",
    "f(3.14)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:Anaconda3]",
   "language": "python",
   "name": "conda-env-Anaconda3-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}