{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Continuité, surfaces et courbes de niveau\n", "\n", "Soit $\\mathcal{D} \\subseteq \\mathbb{R}^n$ une région de l'espace (on peut penser que $n=2$), et $f:\\mathcal{D} \\to \\mathbb{R}$ une fonction. Soit en plus $\\bf{a}\\in \\mathcal{D}$. On dit que la fonction $f(\\bf{x})$ tend vers $L$ lorsque $\\bf{x}$ tend vers $\\bf{a}$ si pour tout réel $\\epsilon > 0 $ il existe un réel $\\delta >0$ tel que $|f(\\bf{x}) - L| < \\epsilon$ aussitôt que $|\\bf{x} - \\bf{a}| < \\delta$. Autrement dit, la distance entre $f(\\bf{x})$ et $L$ est aussi petite que l'on veut, pourvu que la distance entre $\\bf{x}$ et $\\bf{a}$ soit suffisament petite. On écrit dans ce cas $\\displaystyle \\lim_{\\bf{x} \\to \\bf{a}} f(\\bf{x} ) = L$\n", "\n", "La fonction $f$ est continue en $\\bf{a}$ si $\\displaystyle \\lim_{ \\bf{x} \\to \\bf{a} } f(x)= f( \\bf{a} )$. Ceci présuppose notamment que $\\bf{a}$ fait partie du domaine de $f$. Ceci signifie que les valeurs de $f$ ne varient pas brusquement lorsque $\\bf{x}$ varie aux alentours de $\\bf{a}$. Dans le cas où $n=2$ (deux variables) l'interprétation de ceci en termes de la surface $z=f(x,y)$ es essentiellement la même que celle de la contuité d'une fonction $y=f(x)$ en termes de sa courbe : il n'y a pas de déchirures. Par ailleurs, en plusieurs variables on dispose de l'outil supplémentaire qui sont les courbes de niveau.\n", "\n", "Étant donnée $k\\in \\mathbb{R}$, la courbe de niveau $k$ pour la fonction $f$ est l'ensemble $\\{(x,y)\\in \\mathbb{R}^2| f(x,y)=k\\}$. Ci bas on desine plusieurs surfaces et les siagrammes de courbes de niveau associés.\n", "\n", "Voyons quelques exemples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple 1.\n", "\n", "On considère la fonction\n", "\n", "$$ f(x,y) = \\frac{y}{x^2+y^2} $$\n", "Notons que cette fonction n'est pas définie pour $(x,y)=(0,0)$. La courbe de niveau $c$ est le cercle $x^+ (y-\\frac{1}{2c})^2 = \\frac{1}{4c^2}$, privé de l'origine. Il s'agit du cercle centré à $(0,\\frac{1}{2c})$, de rayon $\\frac{1}{2c}$ (mais il faut enlever l'origine : il appartient à tous ces cercles, ce qui n'a pas de sens si on les interprète comme courbes de niveau).\n", "\n", "\n", "On voit bien qu'il y a un problème à l'origine (le 11e commandement)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('x,y')\n", "f(x,y)=y/(x^2+y^2)\n", "S=plot3d(f,(x,-1,1),(y,-1,1),color='blue', opacity=0.35, mesh=0.2)\n", "show(S, aspect_ratio=[10,10,1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Voyons les courbes de niveau maintenant." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C=contour_plot(f, (x,-1, 1), (y,-1, 1),cmap='Blues',linestyles='solid', contours = [-5,-3,-2,-1,-1/2,-1/4,-1/10, 0,1/10, 1/4,1/2,1,2,3,5], colorbar=True)\n", "show(C,figsize=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Voir la fin du notebook, pour des meilleurs graphiques!" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "contour_plot?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple 2.\n", "\n", "On considère la fonction\n", "\n", "$$ f(x,y) = \\left\\{ \\begin{array}{lcl} \\frac{x^2-y^2}{x^2+y^2} & \\text{ si } & (x,y)\\ne (0,0)\\\\ 0& \\text{ si } & (x,y) =(0,0) \\end{array}\\right.$$\n", "\n", "\n", "On voit bien qu'il y a un problème à l'origine (le 11e commandement)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('x,y')\n", "f(x,y)=(x^2-y^2)/(x^2+y^2)\n", "S=plot3d(f,(x,-1,1),(y,-1,1),color='blue', opacity=0.55, mesh=0.2)\n", "show(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Voyons les courbes de niveau : on voit bien que si l'on se rapproche de l'origine par différentes droites, les valeurs de $f$ sont différentes aussi. La limite de $f$ en $(0,0)$ n'existe simplement pas, cette fonction ne peut pas être continue en ce point." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C=contour_plot(f, (x,-1, 1), (y,-1, 1),cmap='Blues',linestyles='solid', colorbar=True)\n", "show(C,figsize=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple 3 :\n", "Considérons la fonction $g(x,y) = \\arctan\\left( \\frac{y}{x}\\right)$ lorsque $x\\ne 0$.\n", "La présence du $x$ au dénominateur indique qu'il y aura des problèmes pour des valeurs de $x$ très petites." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g(x,y) = arctan(y/x)\n", "S=plot3d(g,(x,-1,1),(y,-1,1),color='blue', opacity=0.45, mesh= 1)\n", "show(S)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "C=contour_plot(g, (x,-1, 1), (y,-1, 1),cmap='Blues',linestyles='solid', colorbar=True)\n", "show(C)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple 4 :\n", "Voyons maintenant à quoi ressemble une surface continue. Soit $h$ la fonction définie par\n", "\n", "$$ h(x,y) = \\left\\{ \\begin{array}{lcl} \\frac{3x^2 y}{x^2+y^2} & \\text{ si } & (x,y)\\ne (0,0)\\\\ 0& \\text{ si } & (x,y) =(0,0) \\end{array}\\right.$$\n", "\n", "Ici on pourrait penser que le même problème que ci-haut va se présenter, mas ce n'est pas le cas, en fait, le numérateur est de degré 3, le dénominateur de degré 2. Le numérateur tend vers 0 plus vite que le dénominateur." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "h(x,y)= 3*x^2*y/(x^2+y^2)\n", "S=plot3d(h,(x,-1,1),(y,-1,1),color='blue', opacity=0.45, mesh = 1)\n", "show(S)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C=contour_plot(h, (x,-1, 1), (y,-1, 1),cmap='Blues',linestyles='solid', colorbar=True)\n", "show(C,figsize=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple 5\n", "Soit maintenant la fonction définie par $\\displaystyle h(x,y) = \\frac{xy^2}{x^2+y^4}$ pour $(x,y)\\ne (0,0)$ Nous avons vu en classe que si $\\mathcal{C}_m$ est la droite de pente $m$, alors $$\\lim_{\\stackrel{(x,y)\\to (0,0)}{\\mathcal{C}_m}} f(x,y) = 0$$\n", "mais sur la parabole $x=y^2$, la limite a une autre valeur. Ainsi, la limite de $f(x,y)$ lorsque $(x,y)$ tend vers $0$ n'existe pas. Voyons la surface, mais mieux encore, les courbes de niveau." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "h(x,y)= x*y^2/(x^2+y^4)\n", "S=plot3d(h,(x,-1,1),(y,-1,1),color='blue', opacity=0.45, mesh=0.3)\n", "show(S)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C=contour_plot(h, (x,-1, 1), (y,-1, 1),cmap='Blues',linestyles='solid', colorbar=True)\n", "show(C,figsize=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Retour à l'exemple 1" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var(\"x,y,z\")\n", "h(x,y)= y/(x^2+y^2)\n", "\n", "cm = colormaps.Spectral\n", "zmin, zmax = -2, 2\n", "def c(x,y,z):\n", " return float((h(x,y)-zmin)/(zmax-zmin)) # soustraire le min puis diviser par l'écart donne quelque chose entre 0 et 1.\n", "S = implicit_plot3d(z==h, (x,-1,1), (y,-1,1), (z,zmin,zmax), \n", " color = (cm,c), region=lambda x,y,z: x^2+y^2+z^2>0.001)\n", "show(S, aspect_ratio=[2,2,1], viewer=\"threejs\")\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C=contour_plot(h, (x,-1.5,1.5), (y,-1.5,1.5), cmap =\"Spectral\", \n", " contours = [-2,-1,-0.5,-0.25,0,0.25,0.5,1,2], \n", " colorbar = True, axes = True, \n", " labels = True, label_colors=\"black\", \n", " label_inline=True, label_fontsize=8, \n", " gridlines=True, axes_labels=[\"$x$\",\"$y$\"])\n", "show(C, figsize=8)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.0", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }