LópezFrancisco_TrabajoFinalMetNum.ipynb

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  "metadata": {
    "colab": {
      "name": "LópezFrancisco_TrabajoFinalMetNum.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/roilhi/MetNum_ITECI_2020/blob/gh-pages/L%C3%B3pezFrancisco_TrabajoFinalMetNum.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1NZZSavuVTCd",
        "colab_type": "text"
      },
      "source": [
        "#**Metodos Numericos**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M11eVuwGyaFr",
        "colab_type": "text"
      },
      "source": [
        "## Universidad de Ensenada ITECI Ingeniería Industrial"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H6gfkR8i8K8W",
        "colab_type": "text"
      },
      "source": [
        "ALUMNO: Francisco Javier López Rodríguez"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xDVaIfzHgfuc",
        "colab_type": "text"
      },
      "source": [
        "Introduccion\n",
        "\n",
        "\n",
        "*   En esta libreta de python podran encontrar un ejercicio de cada unidad vista durante la materia, se pueden encontrar ejercicios de ecuaciones y distintos metodos como el metodo de newton, interpolacion de newton, metodo de simpson 1/3 y metodo de Eliminación por Gauss-Jordan. cada uno con su error relatico como tambien podran observar la grafica de cada problema."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FV1MC7MRf59N",
        "colab_type": "text"
      },
      "source": [
        "Objetivos\n",
        "\n",
        "\n",
        "*   Aprender\n",
        "*   Practicar\n",
        "*   Programar"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T5djQsmsmE54",
        "colab_type": "text"
      },
      "source": [
        "**2) Seleccionar un ejercicio de cada unidad:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BVvaKVN5yx9D",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Primero importamos las librerías necesarias\n",
        "import numpy as np #librería numérica \n",
        "import matplotlib.pyplot as plt #librería para las gráficas\n",
        "import pandas as pd"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LG9WoQpbV7EB",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "1. **Unidad 1:** RAÍCES O SOLUCIONES DE ECUACIONES NO LINEALES:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iTLZuHY2Vkxp",
        "colab_type": "text"
      },
      "source": [
        "**Metodo de Biseccion:** Hemos observado en el método gráfico que existe\n",
        "una raíz entre los valores a y b si entre f(a) y f(b)\n",
        "hay un cambio de signo.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ogf_AHDfpIWs",
        "colab_type": "text"
      },
      "source": [
        "En el método de bisección se divide a la mitad un intervalo [a, b]. Si hay un cambio\n",
        "de signo se evalúa la función en el punto medio."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PYHVGLC-3xjb",
        "colab_type": "text"
      },
      "source": [
        "Cálculo del error relativo porcentual: \n",
        "$$\\epsilon_r = \\left \\lvert \\frac{V_r-Vn}{Vr}\\right\\rvert \\times 100 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SND0dUe27Ro5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((vreal-vnum)/vreal)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tK86iFu9zrVb",
        "colab_type": "text"
      },
      "source": [
        "*   Método de bisección\n",
        "Estimar la raíz de la función $f(x)=x-\\cos(x)$ en el intervalo $[0.5, 1]$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YY2aIq4wzzNO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Valores iniciales\n",
        "a =0.5\n",
        "b = 1\n",
        "Vanalitico = 0.73909\n",
        "def fx(x_int):\n",
        "  fx = x_int-np.cos(x_int)\n",
        "  return fx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Szy2bKbQ2iue",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "outputId": "e036f372-1715-4d23-b23f-cc122e6eb7bd"
      },
      "source": [
        "numIter = 0\n",
        "N = int(input('Defina un numero N de iteraciones '))\n",
        "x_old = 0\n",
        "while numIter<N: \n",
        "  x_i = (a+b)/2\n",
        "  if fx(a)*fx(x_i)<0:\n",
        "    b = x_i\n",
        "  elif fx(a)*fx(x_i)==0:\n",
        "    raizAproxBisec = x_i\n",
        "  else: \n",
        "    a = x_i\n",
        "  numIter = numIter+1\n",
        "  raizAproxBisec = x_i\n",
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"La raíz estimada por el método de bisección es =\",+raizAproxBisec, \"iteración i=\",+numIter)\n",
        "  print(\"El error relativo es =\",+ErrorBisec, \"iteración i=\",+numIter)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Defina un numero N de iteraciones 5\n",
            "La raíz estimada por el método de bisección es = 0.75 iteración i= 1\n",
            "El error relativo es = 100.0 iteración i= 1\n",
            "La raíz estimada por el método de bisección es = 0.625 iteración i= 2\n",
            "El error relativo es = 20.0 iteración i= 2\n",
            "La raíz estimada por el método de bisección es = 0.6875 iteración i= 3\n",
            "El error relativo es = 9.090909090909092 iteración i= 3\n",
            "La raíz estimada por el método de bisección es = 0.71875 iteración i= 4\n",
            "El error relativo es = 4.3478260869565215 iteración i= 4\n",
            "La raíz estimada por el método de bisección es = 0.734375 iteración i= 5\n",
            "El error relativo es = 2.127659574468085 iteración i= 5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ID1doyBsOIgh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "01a4aa68-92c3-4423-84e4-ca99845370e4"
      },
      "source": [
        "# Datos para la graficación \n",
        "ejeX = np.linspace(0,2*np.pi,101)\n",
        "# Graficando la función\n",
        "plt.plot(ejeX,fx(ejeX), label='$f(x)$')\n",
        "# Graficar la raíz encontrada en el método\n",
        "plt.plot(raizAproxBisec,fx(raizAproxBisec),'o',label='raíz encontrada $x_i$')\n",
        "plt.xlabel('$x$')\n",
        "plt.ylabel('$f(x)$')\n",
        "plt.title('Raíz de la función $f(x)=x-cos(x)$ método de bisección')\n",
        "plt.legend() #muestra la leyenda\n",
        "plt.grid() #muestra la cuadrícula\n",
        "plt.show() #Muestra la gráfica"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9MiegzQ6aiKq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "122d0132-b2b4-44a5-e5e9-e3c30ddbd040"
      },
      "source": [
        "%%html\n",
        "<a href=\"https://classroom.google.com/c/MTE2ODQ2NjE3NTcz/m/MTI2MDQ4OTAyODI1/details\" target=\"_blank\">video aquí sobre la explicacion de este tema en classroom</a>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<a href=\"https://classroom.google.com/c/MTE2ODQ2NjE3NTcz/m/MTI2MDQ4OTAyODI1/details\" target=\"_blank\">video aquí sobre la explicacion de este tema en classroom</a>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X7MZHnIoJ6iq",
        "colab_type": "text"
      },
      "source": [
        "2. **Unidad 2:** INTERPOLACIÓN Y REGRESIÓN NUMÉRICAS:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BqVrF_hdLJ8m",
        "colab_type": "text"
      },
      "source": [
        "**Interpolacion de Newton:** Es de gran utilidad para la ingeniería el concepto de “interpolación”. Se\n",
        "trata de trazar curvas que puedan “ajustar” o predecir una función\n",
        "continua dado un registro de valores discretos."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XtL1w9NAicCh",
        "colab_type": "text"
      },
      "source": [
        "Datos Discretos:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tnqlz5trihZ1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 235
        },
        "outputId": "f3ef00c1-239c-4535-84de-b13b816ef44f"
      },
      "source": [
        "import pandas as pd\n",
        "datos = pd.DataFrame({ \"i\": [0, 1, 2, 3, 4, 5], \"Xi\" : [1.6, 2, 2.5, 3.2, 4, 4.5], \"F(Xi)\" : [2, 8, 14, 15, 8, 2]}, index=[\"X1\", \"X2\", \"X3\", \"X4\", \"X5\", \"X6\"])\n",
        "datos"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>i</th>\n",
              "      <th>Xi</th>\n",
              "      <th>F(Xi)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X1</th>\n",
              "      <td>0</td>\n",
              "      <td>1.6</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X2</th>\n",
              "      <td>1</td>\n",
              "      <td>2.0</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X3</th>\n",
              "      <td>2</td>\n",
              "      <td>2.5</td>\n",
              "      <td>14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X4</th>\n",
              "      <td>3</td>\n",
              "      <td>3.2</td>\n",
              "      <td>15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X5</th>\n",
              "      <td>4</td>\n",
              "      <td>4.0</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X6</th>\n",
              "      <td>5</td>\n",
              "      <td>4.5</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    i   Xi  F(Xi)\n",
              "X1  0  1.6      2\n",
              "X2  1  2.0      8\n",
              "X3  2  2.5     14\n",
              "X4  3  3.2     15\n",
              "X5  4  4.0      8\n",
              "X6  5  4.5      2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 113
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7awMsP1ix8Bk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "762f1f97-c7c0-4d24-fbc0-3b98ac136034"
      },
      "source": [
        "datos.plot.bar()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fe2a1360390>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 114
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ARf3CRh5yD6b",
        "colab_type": "text"
      },
      "source": [
        "*   Método de Interpolacíon de Newton:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SEMz7eApzPe6",
        "colab_type": "text"
      },
      "source": [
        "N=1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zeInNMPXMzuE",
        "colab_type": "text"
      },
      "source": [
        "Evaluar en la función $f(x)=f[x_1,x_0]=\\frac{f(x_1)-f(x_0)}{x_1-x_0}=\\frac{8-2}{2-1.6}=\\frac{6}{0.4}=15$   "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G1TNGCe3yA_C",
        "colab_type": "text"
      },
      "source": [
        "Evaluar en la función $f(x)=f[x_2,x_1]=\\frac{f(x_2)-f(x_1)}{x_2-x_1}=\\frac{14-8}{2.5-2}=\\frac{6}{0.5}=12$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "amZDSHYkzSuy",
        "colab_type": "text"
      },
      "source": [
        "Evaluar en la función $f(x)=f[x_3,x_2]=\\frac{f(x_3)-f(x_2)}{x_3-x_2}=\\frac{15-14}{3.2-2.5}=\\frac{1}{0.7}=1.4285$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dzx4VQ-pzZvq",
        "colab_type": "text"
      },
      "source": [
        "N=2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-4opMCv2zZ4q",
        "colab_type": "text"
      },
      "source": [
        "Evaluar en la función $f(x)=f[x_2,x_1,x_0]=\\frac{f(x_2,x_1)-f(x_1,x_0)}{x_2-x_0}=\\frac{12-15}{12.5-1.6}=\\frac{-3}{0.9}=-3.3333$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L_vlIYeJzaBX",
        "colab_type": "text"
      },
      "source": [
        "Evaluar en la función $f(x)=f[x_3,x_2,x_1]=\\frac{f(x_3,x_2)-f(x_2,x_1)}{x_3-x_1}=\\frac{1.4285-12}{3.2-2}=\\frac{-10.5715}{1.2}=-8.8095$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nya7D0YPzgZS",
        "colab_type": "text"
      },
      "source": [
        "N=3"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3MschdzuzgyZ",
        "colab_type": "text"
      },
      "source": [
        "Evaluar en la función  $f(x)=f[x_3,x_2,x_1,x_0]=\\frac{f(x_3,x_2,x_1)-f(x_2,x_1,x_0)}{x_3-x_0}=\\frac{-8.8095-(-3.3333)}{3.2-1.6}=\\frac{-8.8095+3.3333}{1.6}=\\frac{-5.4762}{1.6}-3.4226$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CRswsC42zmyb",
        "colab_type": "text"
      },
      "source": [
        "$b_1=f[x_1,x_0]=15$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PP5sGZr6znAq",
        "colab_type": "text"
      },
      "source": [
        "$b_2=f[x_2,x_1,x_0]=-3.3333$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wg373EvhznLb",
        "colab_type": "text"
      },
      "source": [
        "$b_3=f[x_3,x_2,x_1,x_0]=-3.4226$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_6mDOKak0g1p",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 336
        },
        "outputId": "d646380b-d37f-485a-85e5-c8d0855c8a21"
      },
      "source": [
        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/watch?v=tzNWBdAWiao&t=1505s\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyr\"<br>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/watch?v=tzNWBdAWiao&t=1505s\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyr\"<br>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4OX7RHHP98Eq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9f8fcc79-bab9-433d-eb40-4b168dbb6bd7"
      },
      "source": [
        "%%html\n",
        "<a href=\"https://classroom.google.com/c/MTE2ODQ2NjE3NTcz/m/MTE4MzY5NzY3NTc2/details\" target=\"_blank\">video aquí sobre la explicacion de este tema en classroom</a>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<a href=\"https://classroom.google.com/c/MTE2ODQ2NjE3NTcz/m/MTE4MzY5NzY3NTc2/details\" target=\"_blank\">video aquí sobre la explicacion de este tema en classroom</a>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O0XsxSt3_c9a",
        "colab_type": "text"
      },
      "source": [
        "3. **Unidad 3:** INTEGRACIÓN Y DIFERENCIACIÓN NUMERICAS:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ACEctEmEAyIE",
        "colab_type": "text"
      },
      "source": [
        "**Método de simpson 1/3:** Se toma la ecuación de Newton-Cotes pero ahora la aproximación es\n",
        "con un polinomio de orden 2 (parábola), este puede ser representado\n",
        "por un polinomio de Lagrange."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bNHHxo1GLLMF",
        "colab_type": "text"
      },
      "source": [
        "$I=(b-a)\\frac{f(x_0)+4f(x_1)+f(x_2)}{6}=$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8YFa6tW8PuC7",
        "colab_type": "text"
      },
      "source": [
        "$x_1=\\frac{b-a}{2}=$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JJWBpAIKPjE7",
        "colab_type": "text"
      },
      "source": [
        "$x_1=\\frac{1.57-0}{2}=\\frac{1.57}{2}=0.785$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vtj2tAVvADIk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 142
        },
        "outputId": "3a27e0f1-9d8b-4c14-83a2-9cf75053bec6"
      },
      "source": [
        "import pandas as pd\n",
        "datos = pd.DataFrame({ \"X\" : [0, 1.57, 0.785], \"F(X)\" : [9, 6, 8.12]}, index=[\"X0=\",\"X2=\", \"X1=\"])\n",
        "datos"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X</th>\n",
              "      <th>F(X)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X0=</th>\n",
              "      <td>0.000</td>\n",
              "      <td>9.00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X2=</th>\n",
              "      <td>1.570</td>\n",
              "      <td>6.00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X1=</th>\n",
              "      <td>0.785</td>\n",
              "      <td>8.12</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         X  F(X)\n",
              "X0=  0.000  9.00\n",
              "X2=  1.570  6.00\n",
              "X1=  0.785  8.12"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 117
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ofMh9NMQQnOq",
        "colab_type": "text"
      },
      "source": [
        "$I=(1.57-0)\\frac{9+4(8.12)+6}{6}= 12.4239$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tVoWe7neRcuh",
        "colab_type": "text"
      },
      "source": [
        "$I= 12.4239$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DYRygKXfSJT_",
        "colab_type": "text"
      },
      "source": [
        "Cálculo del error relativo porcentual: \n",
        "$$\\epsilon_r = \\left \\lvert \\frac{V_r-Vn}{Vr}\\right\\rvert \\times 100 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l4GaPF-HRWwz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((12.4247-12.4239)/12.4247)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sVMbLGKHSVs3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "1bfe6a63-ef51-48c8-c627-ea6b82c4237f"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "El error relativo es = 0.006438787254419921\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "se1vU7IrSx6i",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "6387e89c-6b0d-49c0-e775-5b51b9aa8bff"
      },
      "source": [
        "# Datos para la graficación \n",
        "ejeX = (7.9133*1.57,20)\n",
        "# Graficando la función\n",
        "plt.plot(ejeX,fx(ejeX), label='$I$')\n",
        "# Graficar la raíz encontrada en el método\n",
        "plt.plot(raizAproxBisec,fx(raizAproxBisec),'o',label='funcion $x_1$')\n",
        "plt.xlabel('$x$')\n",
        "plt.ylabel('$f(x)$')\n",
        "plt.title(\"$I=(b-a)\\frac{f(x_0)+4f(x_1)+f(x_2)}{6}=$ método de simpson 1/3\")\n",
        "plt.legend() #muestra la leyenda\n",
        "plt.grid() #muestra la cuadrícula\n",
        "plt.show() #Muestra la gráfica"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3tXlOVpRpZQn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 336
        },
        "outputId": "2347c34a-bd13-49d4-b628-b809cc4591eb"
      },
      "source": [
        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/watch?v=oDrpEQtf7Hc\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyr\"<br>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/watch?v=oDrpEQtf7Hc\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyr\"<br>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5_sNvDUhvi2m",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "128a0ed0-7970-433a-e949-1183029bae67"
      },
      "source": [
        "%%html\n",
        "<img width=\"500px\" src=\"https://www.youtube.com/watch?v=oDrpEQtf7Hc&t=1s\"></img>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<img width=\"500px\" src=\"https://www.youtube.com/watch?v=oDrpEQtf7Hc&t=1s\"></img>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cK2vG0Y2ZPOe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a92b8090-48e8-4d9d-e177-d5ab7260ff08"
      },
      "source": [
        "%%html\n",
        "<a href=\"https://drive.google.com/file/d/1f43vOSorWx2JNkcli7lZfCjCY2DqtOwh/view\" target=\"_blank\">video aquí sobre la explicacion de este tema en classroom</a>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<a href=\"https://drive.google.com/file/d/1f43vOSorWx2JNkcli7lZfCjCY2DqtOwh/view\" target=\"_blank\">video aquí sobre la explicacion de este tema en classroom</a>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "byiBfQrkZGSU",
        "colab_type": "text"
      },
      "source": [
        "4. **Unidad 4:** SOLUCIÓN DE SISTEMAS DE ECUACIONES LINEALES:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NAC_VFCy9LOC",
        "colab_type": "text"
      },
      "source": [
        "Los sistemas de ecuaciones lineales están conformados por un conjunto\n",
        "de expresiones de primer grado. Encontrar su solución, en ingeniería,\n",
        "resuelve los siguientes problemas:\n",
        "\n",
        "\n",
        "\n",
        "*   Encontrar las magnitudes de las fuerzas de reacción en un objeto o tensión de las cuerdas que sujetan a una masa para mantenerla en equilibro.\n",
        "\n",
        "*   Encontrar las magnitudes de las corrientes eléctricas que\n",
        "circulan a través de las mallas de un circuito eléctrico.\n",
        "\n",
        "*   Encontrar la transformación de rotación en una imagen para girarla con cierto ángulo."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K5PLu9gwAP5N",
        "colab_type": "text"
      },
      "source": [
        "Sistema de Ecuaciones Visto en Clase:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hp3lcQw9-ztQ",
        "colab_type": "text"
      },
      "source": [
        "$3x_1-0.1x_2-0.2x_3=7.85$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HQDMwRye_3ez",
        "colab_type": "text"
      },
      "source": [
        "$0.1x_1+7x_2-0.3x_3=-19.3$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wi_oNzw3_3nq",
        "colab_type": "text"
      },
      "source": [
        "$0.3x_1-0.2x_2-10x_3=71.4$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I-S0VKWUB5Gx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 142
        },
        "outputId": "af3a977e-0d84-4c7d-bcdd-03eb2ced4d87"
      },
      "source": [
        "import pandas as pd\n",
        "datos = pd.DataFrame({ \"X1\" : [3, -0.1, -0.2], \"X2\" : [0.1, 7, -0.3], \"X3\" : [0.3, -0.2, -10]}, index=[\"A\", \"A\", \"A\"])\n",
        "datos"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X1</th>\n",
              "      <th>X2</th>\n",
              "      <th>X3</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>A</th>\n",
              "      <td>3.0</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>A</th>\n",
              "      <td>-0.1</td>\n",
              "      <td>7.0</td>\n",
              "      <td>-0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>A</th>\n",
              "      <td>-0.2</td>\n",
              "      <td>-0.3</td>\n",
              "      <td>-10.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    X1   X2    X3\n",
              "A  3.0  0.1   0.3\n",
              "A -0.1  7.0  -0.2\n",
              "A -0.2 -0.3 -10.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 124
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "15xtLJJJDLa_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 142
        },
        "outputId": "3d30b8b3-6eb8-4033-ffb0-0fe9e7d99449"
      },
      "source": [
        "import pandas as pd\n",
        "datos = pd.DataFrame({ \"X\" : [\"X1\", \"X2\", \"X3\"]}, index=[\"X=\", \"X=\", \"X=\"])\n",
        "datos"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>X</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X=</th>\n",
              "      <td>X1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X=</th>\n",
              "      <td>X2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X=</th>\n",
              "      <td>X3</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     X\n",
              "X=  X1\n",
              "X=  X2\n",
              "X=  X3"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 125
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d24X-4K4GBbh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 142
        },
        "outputId": "57fee06d-d89c-4bcc-97e4-7a3ecd52b0a0"
      },
      "source": [
        "import pandas as pd\n",
        "datos = pd.DataFrame({ \"b\": [7.85, -19.3, 71.4]}, index=[\"b=\", \"b=\", \"b=\"])\n",
        "datos"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>b</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>b=</th>\n",
              "      <td>7.85</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b=</th>\n",
              "      <td>-19.30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>b=</th>\n",
              "      <td>71.40</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        b\n",
              "b=   7.85\n",
              "b= -19.30\n",
              "b=  71.40"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 126
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CalHHJTIHNz6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 142
        },
        "outputId": "bf253965-80eb-4d09-b73b-84735b6e26ca"
      },
      "source": [
        "import pandas as pd\n",
        "datos = pd.DataFrame({ \"(0)\" : [0, 0, 0]}, index=[\"X1\", \"X2\", \"X3\"])\n",
        "datos"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>(0)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>X1</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X2</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>X3</th>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    (0)\n",
              "X1    0\n",
              "X2    0\n",
              "X3    0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 127
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j6RQ7iHlJYIr",
        "colab_type": "text"
      },
      "source": [
        "(1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Gf58LN_HEAW",
        "colab_type": "text"
      },
      "source": [
        "$X_1(1)=\\frac{-(-0.1)(0)-(-0.2)(0)+7.85}3=2.61$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WafbeXFrIrdF",
        "colab_type": "text"
      },
      "source": [
        "$X_2(1)=\\frac{-(0.1)(0)-(-0.3)(0)-19.3}7=-2.75$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nsv8cgdpIrla",
        "colab_type": "text"
      },
      "source": [
        "$X_3(1)=\\frac{-(0.3)(0)-(-0.2)(0)+71.4}{10}=7.14$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l949xcmLIruS",
        "colab_type": "text"
      },
      "source": [
        "(2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rHzFe1_RIr4j",
        "colab_type": "text"
      },
      "source": [
        "$X_1(2)=\\frac{-(-0.1)(-2.75)-(-0.2)(7.14)+7.85}3=3.00$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZntulEnDIsDq",
        "colab_type": "text"
      },
      "source": [
        "$X_2(2)=\\frac{-(0.1)(2.61)-(-0.3)(7.14)-19.3}7=-2.48$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EH7Rk8H8KL0V",
        "colab_type": "text"
      },
      "source": [
        "$X_3(2)=\\frac{-(0.3)(2.61)-(-0.2)(-2.75)+71.4}{10}=7.05$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nYiERz6TLdyt",
        "colab_type": "text"
      },
      "source": [
        "Cálculo del error relativo porcentual: \n",
        "$$\\epsilon_r = \\left \\lvert \\frac{V_r-Vn}{Vr}\\right\\rvert \\times 100 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U72gNrYbLSHM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((3-2.61)/3)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LMsU335cLwcG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "8130ef2e-0dcd-409c-9c61-220adc11d280"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"Er1= El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Er1= El error relativo es = 13.000000000000004\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MEVzaztoPQTW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((-2.48+2.75)/-2.48)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oIrA_65cPQci",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9c356365-5c1e-4ae7-c319-1fce55470f67"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"Er2= El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Er2= El error relativo es = 10.88709677419355\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bZxVIn50P0Hn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((7-7.14)/7)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0KFrIb4mQKkV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "80ebcd1b-e50c-4afc-ca53-564f57ca6b54"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"Er3= El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Er3= El error relativo es = 1.9999999999999956\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9R073SD-L9b7",
        "colab_type": "text"
      },
      "source": [
        "(3)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "scd0jdpBMC1Y",
        "colab_type": "text"
      },
      "source": [
        "$X_1(3)=\\frac{-(-0.1)(-2.48)-(-0.2)(7)+7.85}3=3.00$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wzfj3fqyMEKD",
        "colab_type": "text"
      },
      "source": [
        "$X_2(3)=\\frac{-(0.1)(3)-(-0.3)(7)-19.3}7=-2.5$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "isPmDgIVMEY0",
        "colab_type": "text"
      },
      "source": [
        "$X_3(3)=\\frac{-(0.3)(3)-(-0.2)(-2.48)+71.4}{10}=7$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NHUlJZE5MGHc",
        "colab_type": "text"
      },
      "source": [
        "Cálculo del error relativo porcentual: \n",
        "$$\\epsilon_r = \\left \\lvert \\frac{V_r-Vn}{Vr}\\right\\rvert \\times 100 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hRmbxYx8Qnaj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((3.7690-3)/3.7690)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B-9UjuBHQnjp",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "be23196b-72c7-4ac2-b895-a727ad548163"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"Er1= El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Er1= El error relativo es = 20.40328999734678\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3HwFXkOyQ51L",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((-2.48+2.5)/-2.48)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cnGXYIKqQ5_C",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3f394d8f-d711-44c2-a9f1-8303b0e11cc2"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"Er2= El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Er2= El error relativo es = 0.8064516129032264\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DFnhixADQ6Ir",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((7.05-7)/7.05)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dg--soxBQ6Sb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3b448c10-d15f-4197-b3e9-0fde35f49ff0"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"Er3= El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Er3= El error relativo es = 0.7092198581560258\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RN5KhNVTM7Gk",
        "colab_type": "text"
      },
      "source": [
        "(4)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nO9ghz86TFB7",
        "colab_type": "text"
      },
      "source": [
        "$X_1(4)=\\frac{-(-0.1)(-2.5)-(-0.2)(7)+7.85}3=3.76$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P24ZANJ3TFlT",
        "colab_type": "text"
      },
      "source": [
        "$X_2(4)=\\frac{-(0.1)(3.76)-(-0.3)(7)-19.3}7=-2.5$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9JSGWO7yTFwx",
        "colab_type": "text"
      },
      "source": [
        "$X_3(4)=\\frac{-(0.3)(3.76)-(-0.2)(-2.5)+71.4}{10}=6.9772$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uPApcuE3VaCQ",
        "colab_type": "text"
      },
      "source": [
        "Cálculo del error relativo porcentual: \n",
        "$$\\epsilon_r = \\left \\lvert \\frac{V_r-Vn}{Vr}\\right\\rvert \\times 100 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NfADOp6kVRF_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((3-3.76)/3)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2fVkj-ZeVeMD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "281f2731-7189-48a0-d78d-1061739fea6c"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"Er1= El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Er1= El error relativo es = 25.333333333333325\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h4F29057VhNX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((-2.5+2.503)/-2.5)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ClqKcGnZV4nc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3648aa8c-5e96-4b94-be1d-772ab61ea79b"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"Er2= El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Er2= El error relativo es = 0.12000000000000455\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F8RYpmcEV76b",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Función que calcule el error relativo porcentual\n",
        "def ErrorRelativo(vreal,vnum):\n",
        "  epsilon = abs((6.97-7)/6.97)*100\n",
        "  return epsilon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ndl97DmZV8Nr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6aac7f4e-b0b8-4ba6-e09b-67c79fbdb751"
      },
      "source": [
        "  ErrorBisec = ErrorRelativo(raizAproxBisec,x_old)\n",
        "  x_old = x_i\n",
        "  print(\"Er= El error relativo es =\",+ErrorBisec)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Er= El error relativo es = 0.43041606886657463\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ONC6Zmhyqp6a",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 336
        },
        "outputId": "67bf1bda-5b4b-461b-f2ff-5b2d0a918112"
      },
      "source": [
        "%%html\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/watch?v=UV6WYhthq7k\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyr\"<br>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/watch?v=UV6WYhthq7k\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyr\"<br>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "frtIYoCBswfl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "15ece7fb-9d5a-4c67-f2ff-db1c61d98275"
      },
      "source": [
        "%%html\n",
        "<img width=\"500px\" src=\"https://www.youtube.com/watch?v=UV6WYhthq7k\"></img>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<img width=\"500px\" src=\"https://www.youtube.com/watch?v=UV6WYhthq7k\"></img>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4AP9miq6oxNc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "1a5655ad-4306-49c7-b26e-c95bbe88132b"
      },
      "source": [
        "%%html\n",
        "<a href=\"https://drive.google.com/file/d/1K7d7cEYDo17i0L49UTXkNIJFe2o2TJs5/view\" target=\"_blank\">video aquí sobre la explicacion de este tema en classroom</a>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<a href=\"https://drive.google.com/file/d/1K7d7cEYDo17i0L49UTXkNIJFe2o2TJs5/view\" target=\"_blank\">video aquí sobre la explicacion de este tema en classroom</a>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "blwuQEivWtmf",
        "colab_type": "text"
      },
      "source": [
        "#Tipos de Variables#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0l4klXcLad1I",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   print (\"hola\")\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MsU0H5DsbwjN",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Celda\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZwLlCahacHBW",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Todo lo que esta entre comillas (\" \")\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VGWSq0hucaD0",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Ha estos se les conoce como punto flotante\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "69cOza7Ncxf2",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Ha estos se les conoce como numeros enteros\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9ejGuHZ0dBmz",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Los booleanos son\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mIS58zMmdXN2",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Esta es la forma correcta para agregar una ecuacion\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vqpX7dNpdxAW",
        "colab_type": "text"
      },
      "source": [
        "Los superindices se ponen con este simbolo ^"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SVhZa1CzeVBF",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Los Subindices se ponen con el guion bajo (_)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3c7xy5Upe1wr",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   La diagonal invertida $\\pi\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KtRjRABcgPKO",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Para las fracciones \\frac\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JeOUExlZhFY9",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   \\pm\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WaAc9RTbhXea",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   \\sqrt\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YZbkzWQRiKk_",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   \\times\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uliT3T9Miky1",
        "colab_type": "text"
      },
      "source": [
        "*   \\geq"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6CC02-rLjAQs",
        "colab_type": "text"
      },
      "source": [
        "*   \\leq"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SBSy9SrhjY20",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   \\int\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3_EHsoWqktfv",
        "colab_type": "text"
      },
      "source": [
        "#Conclusión:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7dWNgp2wk3Wc",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Mi conclusión es que para ser un buen programador se necesita más que 1 mes de clases, creo que cumplí con los objetivos de este trabajo, aunque es muy importante mencionar que me hace falta mucho por aprender. Google colab es una herramienta de programación muy interesante, me gustaría no dejar esto por terminado, si no, seguir buscando información o tutoriales de programación en este tipo de programas, ya que son de demasiada utilidad en la carrera como ingeniero industrial, creo que tener una buena habilidad en esta herramienta me dará un plus en mi experiencia laboral.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gb_vNoidmR4q",
        "colab_type": "text"
      },
      "source": [
        "#Observaciones del curso:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hGmsMw8ImZED",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Logré observar que fue un curso muy rápido, pero bien aprovechado, al principio le batallé un poco, pero a como fueron pasando los días pude mejorar en mis trabajos. Es muy importante mencionar que el docente que impartió este curso estuvo con toda la disponibilidad de aclararnos dudas y fue muy tolerante con la entrega de trabajos. Por ultimo quiero dar gracias por el esfuerzo del profe de apoyarnos en sus tiempos libres para contestar dudas y resolver las mismas.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6gshUFYNoWDL",
        "colab_type": "text"
      },
      "source": [
        "#FIN DEL DOCUMENTO"
      ]
    }
  ]
}