{ "cells": [ { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Approximation de l'intégrale d'une courbe par la méthode des rectangles\n", "\n", "[Fichier Geogebra : somme des rectangles pour la parabole $y=x^2$sur [0;1]](https://www.geogebra.org/m/n6javdkf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de la fonction sommeRectangle(a, b, n) du cours\n", "\n", "Que représentent les variables `u` et `v` dans la fonction ci-dessous ?" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "\n", "def f(x):\n", " return x ** 2\n", "\n", "def sommeRectangle(a, b, n):\n", " h = (b - a) / n\n", " x = a \n", " u = 0\n", " v = 0\n", " for k in range(0, n - 1): #n subdivisions => n tours\n", " u = u + h * f(x) \n", " x = x + h\n", " v = v + h * f(x)\n", " return (u, v)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.20399999999999996, 0.2849999999999999)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sommeRectangle(0, 1, 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exemple 3\n", "\n", "Compléter les fonctions Python ci-dessous pour qu'elles retournent une approximation de $\\int_{a}^{b}f(x) \\mathrm{dx}$ par la somme de rectangles à gauche construits sur $n$ subdivisions régulières de l'intervalle $[a;b]$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def rectangleGauche(f, a, b, n):\n", " s = 0\n", " pas = (b - a)/n\n", " x = a\n", " for k in range(n):\n", " s = '..............'\n", " x = '..............'\n", " return s\n", "\n", "\n", "def rectangleGauche2(f, a, b, n):\n", " s = 0\n", " pas = (b - a) / n\n", " for k in range(n):\n", " s = '..............'\n", " return s\n", "\n", "def rectangleGaucheDessin(f, a, b, n):\n", " s = 0\n", " pas = (b - a)/n\n", " x = a\n", " for k in range(n):\n", " s = s + f(x) * pas\n", " plt.fill([x, x + pas, x + pas, x, x], [0] * 2 + [f(x)] * 2 + [0], hatch='/',edgecolor='black', facecolor='none')\n", " x = x + pas \n", " lesx = np.linspace(a, b, 1000) \n", " fvect = np.vectorize(f)\n", " ax = plt.gca()\n", " ax.spines['top'].set_color('none')\n", " ax.spines['right'].set_color('none')\n", " ax.spines['bottom'].set_position(('data',0))\n", " ax.spines['left'].set_position(('data',a))\n", " plt.plot(lesx, fvect(lesx), color='black')\n", " plt.title(r\"Rectangles à gauche $\\int_{%d}^{%d}f(x)dx\\approx$%1.3f\"%(a,b,s))\n", " plt.savefig('methodeRectangleGauche-{}-{}-{}-{}subdivisions.eps'.format(f.__name__,a,b,n))\n", " plt.show()\n", " return s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Écrire une fonction `rectangleDroite(f, a, b, n)` qui retourne une approximation de $\\int_{a}^{b}f(x) \\mathrm{dx}$ par la somme de rectangles à droite construits sur $n$ subdivisions régulières de l'intervalle $[a;b]$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def rectangleDroite(f, a, b, n):\n", " s = 0\n", " pas = (b - a)/n\n", " x = a + pas\n", " for k in range(n):\n", " s = '..............'\n", " x = '..............'\n", " return s\n", "\n", "def rectangleDroite2(f, a, b, n):\n", " s = 0\n", " pas = (b - a) / n\n", " for k in range(1, n + 1):\n", " s = '..............'\n", " return s\n", "\n", "def rectangleDroiteDessin(f, a, b, n):\n", " s = 0\n", " pas = (b - a)/n\n", " x = a\n", " for k in range(n):\n", " s = s + f(x + pas) * pas\n", " plt.fill([x, x + pas, x + pas, x, x], [0] * 2 + [f(x+pas)] * 2 + [0], hatch='/',edgecolor='black', facecolor='none')\n", " x = x + pas \n", " lesx = np.linspace(a, b, 1000) \n", " fvect = np.vectorize(f)\n", " ax = plt.gca()\n", " ax.spines['top'].set_color('none')\n", " ax.spines['right'].set_color('none')\n", " ax.spines['bottom'].set_position(('data',0))\n", " ax.spines['left'].set_position(('data',a))\n", " plt.plot(lesx, fvect(lesx), color='black')\n", " plt.title(r\"Rectangles à droite $\\int_{%d}^{%d}f(x)dx\\approx$%1.3f\"%(a,b,s))\n", " plt.savefig('methodeRectangleDroite-{}-{}-{}-{}subdivisions.eps'.format(f.__name__,a,b,n))\n", " plt.show()\n", " return s" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def inverse(x):\n", " return 1 / x" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'inverse'" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "inverse.__name__" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'..............'" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rectangleGauche(inverse, 1, 2, 10)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'..............'" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rectangleGauche2(inverse, 1, 2, 10)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "0.7187714031754279" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rectangleGaucheDessin(inverse,1,2,10)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def carre(x):\n", " return x ** 2" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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