{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "Funciones_python.ipynb", "provenance": [], "collapsed_sections": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "XWUUQdZuI0AP" }, "source": [ "En primer lugar importamos las librerias necesarias para graficar funciones. Una libreria de Python son módulos que contienen distintas funciones que nos ayudan a programar." ] }, { "cell_type": "code", "metadata": { "id": "mI9jUEeKFbKx" }, "source": [ "import numpy as np #Numpy contiene distintas funciones que nos ayudan a operar con listas o matrices.\r\n", "import matplotlib.pyplot as plt #Matplotlib contiene funciones que nos permiten realizar distintos tipos de gráficos.\r\n", "import math #Math contiene funciones matemáticas que necesitamos, como raiz(x)" ], "execution_count": 1, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "gl9etcqeMCmW" }, "source": [ "Definimos nuestra primera función a graficar $f(x) = 1/x$" ] }, { "cell_type": "code", "metadata": { "id": "TQCm-PbdGJwZ" }, "source": [ "def f1(x): #Nombre de la función\r\n", " return 1/x #Valor que entrega" ], "execution_count": 2, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "82m3Zyqd02T4" }, "source": [ "Creamos un arreglo de números (lista de números desde 0 hasta 100).\r\n", "\r\n", "A cada elemento de la lista le aplicamos la función y creamos una lista con las imagenes de la función." ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "c2Vib3oyHGtJ", "outputId": "f17fb5a9-394f-4d26-d10a-844403af11a7" }, "source": [ "X = np.arange(0,100,1) #Creamos lista de números\r\n", "Y = [] #Creamos lista vacia\r\n", "for x in X: #Tomamos los elementos de nuestra lista X\r\n", " Y.append(f1(x)) #y llenamos la lista Y1 con los valores de f1(x)" ], "execution_count": 3, "outputs": [ { "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in long_scalars\n", " \n" ], "name": "stderr" } ] }, { "cell_type": "markdown", "metadata": { "id": "x8l3OMBV2C-O" }, "source": [ "Graficamos usando la librería Matplotlib" ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 312 }, "id": "eYGtjzyOH_a2", "outputId": "51af5f83-4289-43d7-ef9e-743904f0c11b" }, "source": [ "plt.plot(X,Y) #Graficamos el arreglo de números y las imagenes de la función\r\n", "plt.xlabel('x') #Nombre eje x\r\n", "plt.ylabel('y') #Nombre eje y\r\n", "plt.title('Función 1/x') #Título del gráfico\r\n", "plt.show #Mostrar el gráfico" ], "execution_count": 4, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": { "tags": [] }, "execution_count": 4 }, { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "tags": [], "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "VKPhkcviEVre" }, "source": [ "Realizamos el mismo procedimiento ahora con la función $\\sqrt x $" ] }, { "cell_type": "code", "metadata": { "id": "sabPLaJ5Is8Q" }, "source": [ "#funcion raiz(x)\r\n", "def f2(x):\r\n", " return math.sqrt(x)" ], "execution_count": 5, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "1wkOfPDDLEHP" }, "source": [ "X2 = np.arange(0,100,1) \r\n", "Y2 = []\r\n", "for x in X2:\r\n", " Y2.append(f2(x))" ], "execution_count": 6, "outputs": [] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 312 }, "id": "I8dGt4YlLK2J", "outputId": "cee2748e-fa94-473d-878c-cde6a045ab8e" }, "source": [ "plt.plot(X2,Y2)\r\n", "plt.xlabel('x')\r\n", "plt.ylabel('y')\r\n", "plt.title('Función raiz(x)')\r\n", "plt.show" ], "execution_count": 7, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": { "tags": [] }, "execution_count": 7 }, { "output_type": "display_data", "data": { "image/png": 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\n", 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