SciPy_SymPy/tutorial_exercises/Solvers.ipynb

{
 "metadata": {
  "name": "Solvers"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Solvers"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Boilerplate to make the doctester work. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys\n",
      "import os\n",
      "sys.path.insert(1, os.path.join(os.path.pardir, \"ipython_doctester\"))\n",
      "from sympy import *\n",
      "from ipython_doctester import test\n",
      "# Work around a bug in IPython. This will disable the ability to paste things with >>>\n",
      "def notransform(line): return line\n",
      "from IPython.core import inputsplitter\n",
      "inputsplitter.transform_classic_prompt = notransform\n",
      "init_printing()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For each exercise, fill in the function according to its docstring. Execute the cell to see if you did it right. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a, b, c, d, x, y, z, t = symbols('a b c d x y z t')\n",
      "f, g, h = symbols('f g h', cls=Function)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Algebraic Equations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Write a function that computes the [quadratic equation](http://en.wikipedia.org/wiki/Quadratic_equation)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def quadratic():\n",
      "    return ???\n",
      "quadratic()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "SyntaxError",
       "evalue": "invalid syntax (<ipython-input-7-99cd274c3f68>, line 2)",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-7-99cd274c3f68>\"\u001b[0;36m, line \u001b[0;32m2\u001b[0m\n\u001b[0;31m    return ???\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Write a function that computes the general solution to the cubic $x^3 + ax^2 + bx + c$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cubic():\n",
      "    return ???\n",
      "cubic()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "SyntaxError",
       "evalue": "invalid syntax (<ipython-input-10-258b5a2454f9>, line 2)",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-10-258b5a2454f9>\"\u001b[0;36m, line \u001b[0;32m2\u001b[0m\n\u001b[0;31m    return ???\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Differential Equations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A population that grows without bound is modeled by the differential equation\n",
      "\n",
      "$$f'(t)=af(t)$$\n",
      "\n",
      "Solve this differential equation using SymPy."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If the population growth is bounded, it is modeled by \n",
      "\n",
      "$$f'(t) = f(t)(1 - f(t))$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}