{
 "metadata": {
  "name": "",
  "signature": "sha256:90a0a9f9d3180d1ade2be17ea7934c31c7dc857b9e3b70e59178e4c656b03396"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# gr\u00e1ficas incluidas en el notebook\n",
      "%pylab inline\n",
      "# carga biblioteca c\u00e1lculo simb\u00f3lico\n",
      "from sympy import * \n",
      "# genera expresiones matem\u00e1ticas \"l\u00edndas\"\n",
      "init_printing(use_unicode=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Ki1, Ki2, rho1, rho2, x= symbols('Ki1 Ki2 rho1 rho2 x')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "R= (1- sqrt(Ki2/ Ki1)* sqrt(rho2/ rho1) )/ (1+ sqrt(Ki2/ Ki1)* sqrt(rho2/ rho1) )\n",
      "T= 1-R\n",
      "R"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{- \\sqrt{\\frac{Ki_{2}}{Ki_{1}}} \\sqrt{\\frac{\\rho_{2}}{\\rho_{1}}} + 1}{\\sqrt{\\frac{Ki_{2}}{Ki_{1}}} \\sqrt{\\frac{\\rho_{2}}{\\rho_{1}}} + 1}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJYAAABWBAMAAADfx3JlAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nMd5H+L9Hk7+DNb7CPdq/IB8P9FXmv30AAAAASUVORK5CYII=\n",
       "prompt_number": 3,
       "text": [
        "      _____     ____    \n",
        "     \u2571 Ki\u2082     \u2571 \u03c1\u2082     \n",
        "-   \u2571  \u2500\u2500\u2500 \u22c5  \u2571  \u2500\u2500  + 1\n",
        "  \u2572\u2571   Ki\u2081  \u2572\u2571   \u03c1\u2081     \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "     _____     ____     \n",
        "    \u2571 Ki\u2082     \u2571 \u03c1\u2082      \n",
        "   \u2571  \u2500\u2500\u2500 \u22c5  \u2571  \u2500\u2500  + 1 \n",
        " \u2572\u2571   Ki\u2081  \u2572\u2571   \u03c1\u2081      "
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Para graficar en funci\u00f3n de la raz\u00f3n rho2/rho1= x\n",
      "Ri= R.subs([(Ki1,1), (Ki2, 1)]) # Igual valor a los Ki1 y Ki2\n",
      "Ri=Ri.subs([(rho2,x), (rho1,1)])\n",
      "Ti= 1+Ri"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p= plot((Ri,(x, -0.5,99)), (Ti,(x, -0.5,99)), show=False, ylim=(-1.2,2.2))\n",
      "p[1].line_color= 'red' # Coeficiente de transmisi\u00f3n en rojo\n",
      "p.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Q1QXccAOQkCA9iWnTZPA5Pp73LBDRtWEAjBFOJ1BdDZw9K62yUkJCCwe7XQad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\nBgARkUkxAIiITOr/Ab8IHVcGrkTiAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x43ecb10>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Se ve que en $\\frac{\\rho_2}{\\rho_1}=0$, $R=1$ y $T=2$ en tanto que cuando $\\frac{\\rho_2}{\\rho_1} \\rightarrow \\infty$, $R\\rightarrow -1$ y $T\\rightarrow 0$. Por supuesto cuando $\\rho_2= \\rho_1$, $R=0$ y $T=1$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# En escala logar\u00edtimica (rho2/rho1= 1 aqui es x=0)\n",
      "pl= plot((Ri,(x, -10,99)), (Ti,(x, -10,99)), show=False, ylim=(-1.2,2.2), xscale='log')\n",
      "pl[1].line_color= 'red'\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x43e92d0>"
       ]
      }
     ],
     "prompt_number": 15
    }
   ],
   "metadata": {}
  }
 ]
}