{"id":33554,"date":"2024-09-19T17:27:54","date_gmt":"2024-09-19T17:27:54","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33554"},"modified":"2025-07-27T00:23:03","modified_gmt":"2025-07-27T00:23:03","slug":"%e5%a4%89%e5%88%86%e6%b3%95%e3%81%ab%e3%82%88%e3%82%8b%e3%83%96%e3%83%a9%e3%82%ad%e3%82%b9%e3%83%88%e3%82%af%e3%83%ad%e3%83%bc%e3%83%8a%e3%81%a8%e3%82%aa%e3%82%a4%e3%83%a9%e3%83%bc%ef%bc%9d%e3%83%a9","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ja\/%e5%a4%89%e5%88%86%e6%b3%95%e3%81%ab%e3%82%88%e3%82%8b%e3%83%96%e3%83%a9%e3%82%ad%e3%82%b9%e3%83%88%e3%82%af%e3%83%ad%e3%83%bc%e3%83%8a%e3%81%a8%e3%82%aa%e3%82%a4%e3%83%a9%e3%83%bc%ef%bc%9d%e3%83%a9\/","title":{"rendered":"\u5909\u5206\u6cd5\u306b\u3088\u308b\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u3068\u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f"},"content":{"rendered":"<h1 style=\"text-align:center;\">\u53e4\u5178\u529b\u5b66\u306b\u304a\u3051\u308b\u5909\u5206\u6cd5\u3068\u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f<\/h1>\n<p style=\"text-align:center;\"><em><strong>Resumen:<\/strong><br \/>\u3053\u306e\u6388\u696d\u3067\u306f\u3001\u5909\u5206\u8a08\u7b97\u306e\u624b\u6cd5\u3092\u7528\u3044\u3066\u89e3\u6790\u529b\u5b66\u306e\u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa\u3092\u518d\u78ba\u8a8d\u3057\u3001\u305d\u306e\u7d50\u679c\u3092\u57fa\u306b\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c\u306e\u89e3\u6cd5\u3078\u306e\u5fdc\u7528\u3092\u8a73\u8ff0\u3059\u308b\u3002<\/em><\/p>\n<hr \/>\n<p style=\"text-align:center;\"><strong>Objetivos de Aprendizaje:<\/strong><br \/>\nAl concluir esta clase el estudiante ser\u00e1 capaz de:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong> \u30cf\u30df\u30eb\u30c8\u30f3\u306e\u6700\u5c0f\u4f5c\u7528\u306e\u539f\u7406<\/li>\n<li><strong>\u8a3c\u660e\u3059\u308b<\/strong> \u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f<\/li>\n<li><strong>\u89e3\u304f<\/strong> \u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c\u3092<\/li>\n<\/ol>\n<hr \/>\n<p style=\"text-align:center;\"><strong><u>\u76ee\u6b21<\/u>\uff1a<\/strong><br \/>\n<a href=\"#1\">\u53e4\u5178\u529b\u5b66\u306b\u304a\u3051\u308b\u5909\u5206\u6cd5\u306e\u610f\u7fa9<\/a><br \/>\n <a href=\"#2\">\u5909\u5206\u554f\u984c\u306e\u5b9a\u5f0f\u5316<\/a><br \/>\n <a href=\"#3\">\u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f<\/a><br \/>\n <a href=\"#4\">\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c<\/a><br \/>\n <a href=\"#5\">Wolfram \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u542b\u3080 GitHub \u30ea\u30dd\u30b8\u30c8\u30ea<\/a>\n<\/p>\n<hr \/>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/JyumifjGzM0\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/center><\/p>\n<hr \/>\n<p><a id=\"1\"><\/a><\/p>\n<h2>\u53e4\u5178\u529b\u5b66\u306b\u304a\u3051\u308b\u5909\u5206\u6cd5\u306e\u610f\u7fa9<\/h2>\n<p style=\"text-align:justify;\">\u30cb\u30e5\u30fc\u30c8\u30f3\u529b\u5b66\u3067\u306f\u3001\u5909\u5206\u6cd5\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3088\u308a\u52b9\u679c\u7684\u306b\u53d6\u308a\u7d44\u3080\u3053\u3068\u304c\u3067\u304d\u308b\u591a\u304f\u306e\u554f\u984c\u304c\u5b58\u5728\u3059\u308b\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u65b9\u7a0b\u5f0f\u304a\u3088\u3073\u30cf\u30df\u30eb\u30c8\u30f3\u306e\u6700\u5c0f\u4f5c\u7528\u306e\u539f\u7406\u306b\u3068\u3063\u3066\u57fa\u672c\u3067\u3042\u308b\u3002\u672c\u8cea\u7684\u306b\u3001\u3053\u306e\u65b9\u6cd5\u306f\u3042\u308b\u91cf\u3092\u6700\u5927\u5316\u307e\u305f\u306f\u6700\u5c0f\u5316\u3059\u308b\u8ecc\u9053\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306b\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001\u4e8c\u70b9\u9593\u306e\u8ecc\u9053\u306e\u3046\u3061\u79fb\u52d5\u8ddd\u96e2\u3084\u79fb\u52d5\u6642\u9593\u3092\u6700\u5c0f\u306b\u3059\u308b\u3082\u306e\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306e\u4f8b\u304c\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u539f\u7406\u3067\u3042\u308a\u3001\u3053\u308c\u306f\u5149\u304c\u5e38\u306b\u901a\u904e\u6642\u9593\u3092\u6700\u5c0f\u306b\u3059\u308b\u7d4c\u8def\u306b\u6cbf\u3063\u3066\u9032\u3080\u3053\u3068\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u3053\u308c\u304b\u3089\u5149\u306e\u5c48\u6298\u306b\u95a2\u3059\u308b <a href=\"http:\/\/toposuranos.com\/material\/es\/la-refraccion-de-la-luz-y-la-ley-de-snell\/\" target=\"_blank\" rel=\"noopener\">\u30b9\u30cd\u30eb\u306e\u6cd5\u5247<\/a> \u304c\u5c0e\u304b\u308c\u308b\u3002<\/p>\n<p style=\"text-align:justify;\">\u5909\u5206\u6cd5\u306f\u53e4\u5178\u529b\u5b66\u306b\u304a\u3044\u3066\u591a\u304f\u306e\u5229\u70b9\u3092\u6709\u3059\u308b\u3002\u4f8b\u3048\u3070\u3001\u5bfe\u79f0\u6027\u3092\u6301\u3064\u7cfb\u306b\u5bfe\u3057\u3066\u306f\u89e3\u6790\u7684\u306a\u53b3\u5bc6\u89e3\u304c\u5f97\u3089\u308c\u3001\u3088\u308a\u8907\u96d1\u306a\u7cfb\u306b\u5bfe\u3057\u3066\u306f\u5909\u5206\u6442\u52d5\u7406\u8ad6\u3092\u901a\u3058\u3066\u8fd1\u4f3c\u89e3\u304c\u5f97\u3089\u308c\u308b\u3002\u307e\u305f\u3001\u529b\u3092\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u5f62\u3067\u8868\u3059\u3053\u3068\u304c\u56f0\u96e3\u306a\u72b6\u6cc1\u3067\u306f\u3001\u6700\u5c0f\u4f5c\u7528\u306e\u539f\u7406\u304c\u53e4\u5178\u529b\u5b66\u306e\u554f\u984c\u3092\u3088\u308a\u52b9\u7387\u7684\u306b\u89e3\u304f\u65b9\u6cd5\u3092\u63d0\u4f9b\u3059\u308b\u3002\u8981\u3059\u308b\u306b\u3001\u5909\u5206\u6cd5\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u6cd5\u5247\u306e\u4ee3\u66ff\u7684\u306a\u5b9a\u5f0f\u5316\u3001\u7269\u7406\u6cd5\u5247\u306e\u7d71\u4e00\u3001\u554f\u984c\u89e3\u6c7a\u306e\u52b9\u7387\u5411\u4e0a\u3001\u5b9f\u9a13\u7d50\u679c\u4e88\u6e2c\u306e\u7cbe\u5ea6\u5411\u4e0a\u3092\u3082\u305f\u3089\u3059\u57fa\u672c\u7684\u306a\u30c4\u30fc\u30eb\u3067\u3042\u308b\u3002<\/p>\n<p><a id=\"2\"><\/a><\/p>\n<h2>\u5909\u5206\u554f\u984c\u306e\u5b9a\u5f0f\u5316<\/h2>\n<p style=\"text-align:justify;\">\u5909\u5206\u6cd5\u3067\u306f\u3001\u6c4e\u95a2\u6570\u306e\u5024\u3092\u6975\u5024\u3068\u3059\u308b\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u91cd\u70b9\u3092\u7f6e\u304f\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">J(x,y(x))=\\displaystyle \\int_{x_1}^{x_2} f\\left(x,y(x),\\frac{dy(x)}{dx}\\right)dx,<\/span>\n<p style=\"text-align:justify;\">\u305d\u306e\u6700\u5927\u5024\u307e\u305f\u306f\u6700\u5c0f\u5024\u3092\u6c42\u3081\u308b\u305f\u3081\u3067\u3042\u308b\u3002\u3053\u306e\u5f0f\u306b\u304a\u3044\u3066\u3001\u6c4e\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u306f\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u3068\u305d\u306e\u5c0e\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">dy(x)\/dx<\/span> \u306b\u4f9d\u5b58\u3057\u3001\u7a4d\u5206\u7bc4\u56f2\u306e\u4e0a\u4e0b\u9650\u306f\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u3002\u7a4d\u5206\u3092\u6975\u5024\u3068\u3059\u308b\u305f\u3081\u306b\u3001\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u306b\u5909\u5206\u3092\u52a0\u3048\u3001\u6c4e\u95a2\u6570\u306e\u5024\u3092\u6975\u3068\u3059\u308b\u95a2\u6570\u3092\u6c42\u3081\u308b\u3002\u4f8b\u3048\u3070\u3001\u7a4d\u5206\u304c\u6700\u5c0f\u5024\u3068\u306a\u308b\u5834\u5408\u306b\u306f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u306b\u3069\u308c\u307b\u3069\u8fd1\u3044\u95a2\u6570\u3067\u3042\u3063\u3066\u3082\u3001\u305d\u306e\u8fd1\u508d\u306e\u4efb\u610f\u306e\u95a2\u6570\u306f\u6c4e\u95a2\u6570\u306e\u5024\u3092\u5897\u5927\u3055\u305b\u308b\u3002<\/p>\n<p style=\"text-align:justify;\">\u300c\u8fd1\u63a5\u95a2\u6570\u300d\u306e\u6982\u5ff5\u3092\u5b9a\u5f0f\u5316\u3059\u308b\u305f\u3081\u306b\u3001\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u306b\u5bfe\u3057\u3066\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306a\u8868\u793a <span class=\"katex-eq\" data-katex-display=\"false\">y=(\\alpha,x)<\/span> \u3092\u5272\u308a\u5f53\u3066\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\alpha=0<\/span> \u306e\u3068\u304d <span class=\"katex-eq\" data-katex-display=\"false\">y(0,x)=y(x)<\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u3092\u6975\u5024\u3068\u3059\u308b\u95a2\u6570\u3067\u3042\u308b\u3068\u3059\u308b\u3002\u3053\u306e\u3053\u3068\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u73fe\u3067\u304d\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y(\\alpha, x) = y(x) + \\alpha \\eta(x),<\/span>\n<p style=\"text-align:justify;\">\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span> \u306f <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{C}^1<\/span> \u7d1a\u306e\u95a2\u6570\u3067\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">x_2<\/span> \u3067\u6d88\u3048\u308b\u3082\u306e\u3067\u3042\u308a\u3001\u3053\u306e\u5909\u5206\u3092\u542b\u3080\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">y(\\alpha,x)<\/span> \u306f\u7a4d\u5206\u306e\u59cb\u70b9\u3068\u7d42\u70b9\u306b\u304a\u3044\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u3068\u4e00\u81f4\u3059\u308b\u3002<\/p>\n<p style=\"text-align:justify;\">\u3053\u306e\u5909\u5206 <span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span> \u3092\u542b\u3080\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">y(\\alpha,x)<\/span> \u3092 <span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span> \u306e\u4ee3\u308f\u308a\u306b\u6c4e\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u3092\u5b9a\u7fa9\u3059\u308b\u7a4d\u5206\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001\u30d1\u30e9\u30e1\u30fc\u30bf <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> \u306b\u4f9d\u5b58\u3059\u308b\u65b0\u305f\u306a\u6c4e\u95a2\u6570\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">J(x,y(\\alpha, x)) = \\displaystyle \\int_{x_1}^{x_2} f\\left(x,y(\\alpha,x), \\dfrac{d}{dx}y(\\alpha,x)\\right)dx<\/span>\n<p style=\"text-align:justify;\">\u5c40\u6240\u7684\u306a\u6975\u304c\u5b58\u5728\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u6b21\u306e\u6761\u4ef6\u304c\u6e80\u305f\u3055\u308c\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\dfrac{\\partial J(x,y(\\alpha,x))}{\\partial \\alpha}\\right|_{\\alpha=0} = 0<\/span>\n<p style=\"text-align:justify;\">\u4efb\u610f\u306e\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span> \u306b\u5bfe\u3057\u3066\u3002<\/p>\n<p><a id=\"3\"><\/a><\/p>\n<h2>\u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f<\/h2>\n<p style=\"text-align:justify;\">\u5c0e\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">\\partial J(x,y(\\alpha,x))\/\\partial \\alpha<\/span> \u3092\u89e3\u6790\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n{}\\dfrac{\\partial J(x,y(\\alpha,x))}{\\partial \\alpha}\n\n&amp;=&amp;\\dfrac{\\partial}{\\partial \\alpha} \\displaystyle \\int_{x_1}^{x_2} f\\left(x,y(\\alpha,x),\\dfrac{dy(\\alpha, x)}{dx}\\right)dx \\\\ \\\n\n&amp;=&amp;\\displaystyle \\int_{x_1}^{x_2} \\left(\\dfrac{\\partial f}{\\partial x}\\dfrac{\\partial x}{\\partial  \\alpha} + \\dfrac{\\partial f}{\\partial y(\\alpha, x)}\\dfrac{\\partial y(\\alpha, x)}{\\partial  \\alpha}  + \\dfrac{\\partial f }{ \\partial \\frac{dy(\\alpha,x)}{dx}} \\dfrac{\\partial \\frac{dy(\\alpha,x)}{dx}}{\\partial \\alpha}\\right)dx\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3053\u3053\u304b\u3089\u3001\u6b21\u306e\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3042\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\\dfrac{\\partial x}{\\partial \\alpha} &amp;=&amp; 0 \\\\ \\\\\n\n\\dfrac{\\partial y(\\alpha,x)}{\\partial \\alpha} &amp;=&amp; \\dfrac{\\partial}{\\partial \\alpha} \\left(y(x) + \\alpha \\eta(x) \\right) = \\eta(x) \\\\ \\\\\n\n\\dfrac{\\partial}{\\partial \\alpha}\\left( \\dfrac{dy(\\alpha, x)}{dx} \\right)&amp;=&amp; \\dfrac{\\partial}{\\partial \\alpha} \\left(\\dfrac{dy(x)}{dx} + \\alpha\\dfrac{d\\eta(x)}{dx} \\right) = \\dfrac{d\\eta}{dx}\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u7c21\u7565\u5316\u3055\u308c\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n{} \\dfrac{\\partial J(x,y(\\alpha,x))}{\\partial \\alpha} &amp;=&amp; \\displaystyle \\int_{x_1}^{x_2} \\left(\\dfrac{\\partial f}{\\partial y(\\alpha,x)}\\eta(x) + \\dfrac{\\partial f}{\\partial  \\frac{dy(\\alpha,x)}{dx}} \\dfrac{d\\eta(x)}{dx} \\right)dx \\\\ \\\\\n\n&amp;=&amp;\\displaystyle \\int_{x_1}^{x_2} \\dfrac{\\partial f}{\\partial y(\\alpha,x)}\\eta(x) dx +  \\int_{x_1}^{x_2} \\dfrac{\\partial f}{\\partial  \\frac{dy(\\alpha,x)}{dx}} \\dfrac{d\\eta(x)}{dx} dx\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u6b21\u306b\u3001\u7b2c2\u306e\u7a4d\u5206\u3092\u898b\u308b\u3068\u3001\u90e8\u5206\u7a4d\u5206\u3092\u7528\u3044\u3066\u7c21\u7565\u5316\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\\displaystyle \\int_{x_1}^{x_2} \\dfrac{\\partial f}{\\partial  \\frac{dy(\\alpha,x)}{dx}} \\dfrac{d\\eta}{dx} dx\n\n&amp;=&amp; \\left. \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha,x)}{dx}} \\eta(x)\\right|_{x_1}^{x_2} - \\displaystyle \\int_{x_1}^{x_2}\\eta(x) \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha, x)}{dx}} \\right) dx\\\\ \\\\\n\n&amp;=&amp; - \\displaystyle \\int_{x_1}^{x_2}\\eta(x) \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha, x)}{dx}} \\right)dx\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3088\u3063\u3066<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n{} \\dfrac{\\partial J(x,y(\\alpha,x))}{\\partial \\alpha}\n\n&amp;=&amp; \\displaystyle \\int_{x_1}^{x_2} \\left[ \\eta(x) \\dfrac{\\partial f}{\\partial y(\\alpha, x)}  - \\eta(x) \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha,x)}{dx}} \\right) \\right]dx \\\\ \\\\\n\n&amp;=&amp; \\displaystyle \\int_{x_1}^{x_2} \\left[ \\dfrac{\\partial f}{\\partial y(\\alpha, x)}  -  \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(\\alpha,x)}{dx}} \\right) \\right] \\eta(x) dx\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3057\u305f\u304c\u3063\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\dfrac{\\partial J (x,y(\\alpha, x))}{\\partial \\alpha}\\right|_{\\alpha=0} = 0<\/span> \u3068\u3044\u3046\u6761\u4ef6\u3068\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\eta(x)<\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">x_2<\/span> \u3067\u6d88\u3048\u308b\u3068\u3044\u3046\u552f\u4e00\u306e\u6761\u4ef6\u306b\u5f93\u3046\u4efb\u610f\u306e\u95a2\u6570\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u3001\u6b21\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\dfrac{\\partial f}{\\partial y(0, x)}  -  \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(0,x)}{dx}}\\right) = \\dfrac{\\partial f}{\\partial y(x)}  -  \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial \\frac{dy(x)}{dx}}\\right) = 0.\n\n<\/span>\n<p style=\"text-align:justify;\">\u6700\u5f8c\u306b\u3001\u3053\u306e\u8868\u73fe\u306b\u304a\u3044\u3066\u8868\u8a18\u3092\u7c21\u7565\u5316\u3059\u308b\u3068\u3001\u3044\u308f\u3086\u308b\u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f\u306b\u81f3\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\dfrac{\\partial f}{\\partial y}= \\dfrac{d}{dx}\\left( \\dfrac{\\partial f}{\\partial y^\\prime} \\right)},<\/span>\n<p style=\"text-align:justify;\">\u3053\u308c\u306f\u3001\u6c4e\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u304c\u6975\u5024\u3092\u53d6\u308b\u305f\u3081\u306e\u5fc5\u8981\u6761\u4ef6\u3092\u306f\u308b\u304b\u306b\u7c21\u6f54\u306b\u8868\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002<\/p>\n<p><a id=\"4\"><\/a><\/p>\n<h2>\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c<\/h2>\n<h3>\u554f\u984c\u306e\u5b9a\u5f0f\u5316<\/h3>\n<p style=\"text-align:justify;\">\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c\u306f\u5909\u5206\u8a08\u7b97\u306b\u3088\u3063\u3066\u89e3\u304b\u308c\u308b\u6a5f\u68b0\u529b\u5b66\u306e\u53e4\u5178\u7684\u306a\u554f\u984c\u3067\u3042\u308b\u3002\u72b6\u6cc1\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002\u4e00\u5b9a\u306e\u529b\u5834\u306e\u4f5c\u7528\u4e0b\u3067\u904b\u52d5\u3059\u308b\u7269\u4f53\u304c\u3001\u521d\u671f\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span> \u304b\u3089\u7d42\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span> \u3078\u79fb\u52d5\u3059\u308b\u3068\u3057\u3001\u521d\u671f\u70b9\u306e\u9ad8\u3055\u304c\u7d42\u70b9\u3088\u308a\u3082\u9ad8\u3044\u5834\u5408\u3001\u7c92\u5b50\u304c\u53ef\u80fd\u306a\u9650\u308a\u77ed\u6642\u9593\u3067\u7d42\u70b9\u306b\u5230\u9054\u3059\u308b\u305f\u3081\u306b\u306f\u3069\u306e\u3088\u3046\u306a\u8ecc\u8de1\u3092\u8fbf\u308b\u3079\u304d\u304b\u3001\u3068\u3044\u3046\u554f\u3044\u3067\u3042\u308b\u3002<\/p>\n<h3>\u89e3\u306e\u5b9a\u5f0f\u5316<\/h3>\n<p style=\"text-align:justify;\">\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c\u3092\u89e3\u304f\u306b\u306f\u3001\u72b6\u6cc1\u3092\u5358\u7d14\u5316\u3057\u3066\u8003\u3048\u308b\u3068\u5f79\u306b\u7acb\u3064\u3002\u305d\u3053\u3067\u3001\u51fa\u767a\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1, y_1)<\/span> \u3092\u5ea7\u6a19\u306e\u539f\u70b9\u306b\u56fa\u5b9a\u3057\u3001\u5230\u9054\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span> \u306f\u539f\u70b9\u306e\u53f3\u5074\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> \u8ef8\u306e\u4e0b\u306b\u3042\u308b\u3082\u306e\u3068\u3059\u308b\u3002<\/p>\n<div style=\"text-align:center;\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/probbraquistocrona.png\" alt=\"c\u00e1lculo variacional - problema de la braquist\u00f3crona\" width=\"711\" height=\"505\" class=\"aligncenter size-full wp-image-28729 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/probbraquistocrona.png\" alt=\"c\u00e1lculo variacional - problema de la braquist\u00f3crona\" width=\"711\" height=\"505\" class=\"aligncenter size-full wp-image-28729 lazyload\" srcset=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/probbraquistocrona.png 711w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/probbraquistocrona-300x213.png 300w\" sizes=\"(max-width: 711px) 100vw, 711px\" \/><\/noscript><\/div>\n<p style=\"text-align:justify;\">\u3053\u306e\u5834\u5408\u3001\u91cd\u529b\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u308b <span class=\"katex-eq\" data-katex-display=\"false\">-\\hat{y}<\/span> \u65b9\u5411\u306b\u50cd\u304f\u4e0b\u5411\u304d\u306e\u529b\u5834\u3092\u8003\u3048\u3001\u904b\u52d5\u304c\u6469\u64e6\u306a\u3057\u3067\u884c\u308f\u308c\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3002\u3053\u306e\u6587\u8108\u3067\u306f\u3001\u7c92\u5b50\u304c\u51fa\u767a\u70b9\u3068\u5230\u9054\u70b9\u3092\u7d50\u3076\u3055\u307e\u3056\u307e\u306a\u8ecc\u9053\u306b\u5f93\u3046\u3082\u306e\u3068\u3057\u3066\u3001\u305d\u308c\u3089\u306e\u4e2d\u3067\u79fb\u52d5\u6642\u9593\u3092\u6700\u5c0f\u306b\u3059\u308b\u8ecc\u9053\u3092\u6c42\u3081\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3059\u308b\u3002<\/p>\n<h3>\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u691c\u8a0e<\/h3>\n<p style=\"text-align:justify;\">\u3053\u306e\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u3001\u91cd\u529b\u7cfb\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u3092\u5229\u7528\u3067\u304d\u308b\u3002\u7c92\u5b50\u306e\u8cea\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u3068\u901f\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">v<\/span> \u306b\u5bfe\u3059\u308b\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc <span class=\"katex-eq\" data-katex-display=\"false\">E_{cin}=\\frac{1}{2}mv^2<\/span> \u3068\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc <span class=\"katex-eq\" data-katex-display=\"false\">E_{pot,g}<\/span> \u306e\u53cc\u65b9\u3092\u8003\u616e\u3059\u308b\u3068\u3001\u7cfb\u306e\u5168\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u4e00\u5b9a\u3067\u3042\u308b\u3002\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u57fa\u6e96\u306f\u539f\u70b9\u306b\u7f6e\u304d\u3001<span class=\"katex-eq\" data-katex-display=\"false\">E_{pot,g}(y=0)=0<\/span> \u3068\u3057\u3001\u4efb\u610f\u306e\u9ad8\u3055 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u3067\u306f <span class=\"katex-eq\" data-katex-display=\"false\">E_{pot,g}(y)=mgy<\/span> \u3068\u306a\u308b\u3002<\/p>\n<p style=\"text-align:justify;\">\u7c92\u5b50\u306f\u539f\u70b9\u304b\u3089\u901f\u5ea6\u30bc\u30ed\u3067\u51fa\u767a\u3059\u308b\u306e\u3067\u3001\u305d\u306e\u5168\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u96f6\u306b\u7b49\u3057\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">E_{cin} + E_{pot,g}=0<\/span>\n<p style=\"text-align:justify;\">\u7c92\u5b50\u304c\u57fa\u6e96\u70b9\u3088\u308a\u4e0b\u306b\u843d\u4e0b\u3059\u308b\u306e\u3067\u3001\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u8ca0\u3067\u3042\u308a\u3001\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u6b63\u3067\u3042\u308b\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u306e\u5f0f\u304b\u3089\u901f\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">v<\/span> \u3092\u89e3\u304f\u3068\u6b21\u306e\u7d50\u679c\u3092\u5f97\u308b\u3002<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} &amp;\\dfrac{1}{2}mv^2 + (-mgy) = 0 \\\\ \\\\\n\n\\vdash &amp;\\dfrac{1}{2}mv^2 = mgy \\\\ \\\\\n\n\\vdash &amp;v^2 = 2gy \\\\ \\\\\n\n\\vdash &amp;v = \\sqrt{2gy}\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u4efb\u610f\u306e\u9ad8\u3055 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u3067\u306e\u7c92\u5b50\u306e\u901f\u5ea6\u3092\u305d\u306e\u8ecc\u9053\u4e0a\u306e\u4f4d\u7f6e\u306b\u5fdc\u3058\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<h3>\u79fb\u52d5\u6642\u9593\u306e\u691c\u8a0e<\/h3>\n<p style=\"text-align:justify;\">\u901f\u5ea6\u3092\u6c42\u3081\u305f\u5f8c\u3001\u79fb\u52d5\u8981\u7d20 <span class=\"katex-eq\" data-katex-display=\"false\">ds=\\sqrt{dx^2 + dy^2}<\/span> \u3092\u5229\u7528\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u79fb\u52d5\u6642\u9593\u306e\u5fae\u5c0f\u8981\u7d20\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} dt &amp;= \\dfrac{ds}{v} = \\dfrac{\\sqrt{dx^2 + dy^2}}{\\sqrt{2gy}}\\\\ \\\\\n\n&amp;= \\sqrt{\\dfrac{dx^2 + dy^2}{2gy} }\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3057\u305f\u304c\u3063\u3066\u3001<span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span> \u304b\u3089 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span> \u307e\u3067\u306e\u79fb\u52d5\u6642\u9593\u306f\u6b21\u306e\u7a4d\u5206\u306b\u3088\u3063\u3066\u6c42\u3081\u3089\u308c\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} t &amp;= \\displaystyle \\int_{(x_1,y_1)}^{(x_2,y_2)} dt \\\\ \\\\\n\n&amp;= \\displaystyle \\int_{(x_1,y_1)}^{(x_2,y_2)} \\sqrt{\\dfrac{dx^2 + dy^2}{2gy}} \\\\ \\\\\n\n&amp;= \\displaystyle \\dfrac{1}{\\sqrt{2g}}\\int_{y_1}^{y_2} \\sqrt{\\dfrac{1+ \\left(\\dfrac{dx}{dy}\\right)^2 }{y}}dy \\\\ \\\\\n\n\\end{array}<\/span>\n<h3>\u5909\u5206\u554f\u984c\u306e\u5b9a\u5f0f\u5316<\/h3>\n<p style=\"text-align:justify;\">\u3053\u306e\u6700\u5f8c\u306e\u5f0f\u306b\u3088\u308a\u3001\u6642\u9593\u3092\u6b21\u306e\u5f62\u306e\u6c4e\u95a2\u6570\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u305f\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n{}t = J(y,x(y)) = \\displaystyle \\int_{y_1}^{y_2} f\\left(y,x(y),\\dfrac{dx(y)}{dy} \\right) dy\n\n<\/span>\n<p style=\"text-align:justify;\">\u3053\u3053\u3067<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f\\left(y,x(y), \\dfrac{dx(y)}{dy}\\right) = \\sqrt{\\dfrac{1+ \\left(\\dfrac{dx(y)}{dy} \\right)^2}{y}} <\/span>\n<p style=\"text-align:justify;\">\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{2g}<\/span> \u3068\u3044\u3046\u56e0\u5b50\u306f\u7121\u8996\u3067\u304d\u308b\u3002\u3068\u3044\u3046\u306e\u3082\u3001<span class=\"katex-eq\" data-katex-display=\"false\">J<\/span> \u3092\u6700\u9069\u5316\u3059\u308b\u3053\u3068\u306f <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{2g}J<\/span> \u3092\u6700\u9069\u5316\u3059\u308b\u306e\u3068\u5168\u304f\u540c\u3058\u3060\u304b\u3089\u3067\u3042\u308b\u3002<\/p>\n<p style=\"text-align:justify;\">\u4ee5\u4e0a\u3092\u8e0f\u307e\u3048\u3001\u5148\u307b\u3069\u3068\u540c\u3058\u624b\u9806\u306b\u5f93\u3063\u3066\u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f\u3092\u69cb\u6210\u3059\u308b\u3068\u3001\u6700\u7d42\u7684\u306b\u6b21\u306e\u5f0f\u306b\u5230\u9054\u3059\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\partial f}{\\partial x} = \\dfrac{d}{dy} \\dfrac{\\partial f}{\\partial x^\\prime}<\/span>\n<p style=\"text-align:justify;\">\u3057\u304b\u3057\u3001\u3053\u3053\u3067\u306f <span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\partial f}{\\partial x} = 0<\/span> \u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u306e\u3067\u3001<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dy}\\dfrac{\\partial f}{\\partial x^\\prime} = 0,<\/span>\n<p style=\"text-align:justify;\">\u8a00\u3044\u63db\u3048\u308b\u3068<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\partial f}{\\partial x^\\prime} = \\dfrac{1}{\\sqrt{2a}},<\/span>\n<p style=\"text-align:justify;\">\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u306f\u4efb\u610f\u306e\u5b9a\u6570\u3067\u3042\u308a\u3001\u5f8c\u306e\u5c55\u958b\u306b\u3068\u3063\u3066\u300c\u4fbf\u5229\u300d\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u3053\u306e\u3088\u3046\u306b\u8a18\u3057\u305f\u3002<\/p>\n<h3>\u5909\u5206\u554f\u984c\u306e\u89e3\u6cd5<\/h3>\n<p style=\"text-align:justify;\">\u3053\u306e\u6700\u5f8c\u306e\u5f0f\u306b <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u3092\u4ee3\u5165\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} &amp;\\dfrac{\\partial }{\\partial x^\\prime} \\sqrt{\\dfrac{1+ x^{\\prime 2}}{y}}  = \\dfrac{1}{\\sqrt{2a}} \\\\ \\\\\n\n\\vdash &amp; \\dfrac{1}{2}\\left( \\dfrac{1 + x^{\\prime 2} }{y} \\right)^{-1\/2} \\left(\\dfrac{2x^\\prime}{y} \\right) = \\dfrac{1}{\\sqrt{2a}} \\\\ \\\\\n\n\\vdash &amp; \\dfrac{1}{2}\\sqrt{\\dfrac{y}{1 + x^{\\prime 2}}} \\left(\\dfrac{2x^\\prime}{y} \\right) = \\dfrac{1}{\\sqrt{2a}} \\\\ \\\\\n\n\\vdash &amp; \\sqrt{\\dfrac{4x^{\\prime 2} y}{4y^2 (1 + x^{\\prime 2})} }  = \\sqrt{\\dfrac{1}{2a}} \\\\ \\\\\n\n\\vdash &amp;  \\dfrac{y x^{\\prime 2} }{y^2 (1 + x^{\\prime 2})}   = \\dfrac{1}{ 2a} \\\\ \\\\\n\n\\vdash &amp; 2ayx^{\\prime 2} = y^2 + y^2 x^{\\prime 2} \\\\ \\\\\n\n\\vdash &amp;  x^{\\prime 2} (2ay - y^2) = y^2 \\\\ \\\\\n\n\\vdash &amp; \\left(\\dfrac{dx}{dy}\\right)^2 = \\dfrac{y^2}{2ay - y^2} \\\\ \\\\\n\n\\vdash &amp; \\dfrac{dx}{dy} = \\pm \\sqrt{\\dfrac{y^2}{2ay - y^2}} \\\\ \\\\\n\n\\vdash &amp; dx = \\pm \\dfrac{y\\,dy}{\\sqrt{2ay - y^2}} \\\\ \\\\\n\n\\vdash &amp; x = \\displaystyle  \\pm \\int \\dfrac{y}{\\sqrt{2ay - y^2}}\\,dy\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3053\u306e\u7a4d\u5206\u3092\u89e3\u304f\u306b\u306f\u3001\u6b21\u306e\u7f6e\u63db\u3092\u884c\u3046\u65b9\u6cd5\u3092\u691c\u8a0e\u3067\u304d\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} y &amp;= a[1-\\cos(\\theta)] \\\\\n\n dy &amp;= a\\sin(\\theta) d\\theta\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3053\u308c\u306b\u3088\u308a\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} x= &amp; \\pm \\displaystyle \\int \\dfrac{y}{\\sqrt{2ay - y^2}}\\,dy = \\displaystyle \\int \\dfrac{a[1-\\cos(\\theta)]a\\sin(\\theta)}{\\sqrt{2a^2[1-\\cos(\\theta)] - a^2[1-\\cos(\\theta)]^2 }}\\,d\\theta \\\\ \\\\\n\n&amp; = \\pm \\displaystyle \\int \\dfrac{a^2[1-\\cos(\\theta)]\\sin(\\theta)}{\\sqrt{a^2[1-\\cos(\\theta)]\\left\\{ 2 - [1-\\cos(\\theta)] \\right\\} }}\\,d\\theta \\\\ \\\\\n\n&amp; = \\pm \\displaystyle \\int \\dfrac{a[1-\\cos(\\theta)]\\sin(\\theta)}{\\sqrt{[1-\\cos(\\theta)]  [1 + \\cos(\\theta)]  }}\\,d\\theta \\\\ \\\\\n\n&amp; = \\pm \\displaystyle \\int \\dfrac{a[1-\\cos(\\theta)]\\sin(\\theta)}{\\sqrt{ 1-\\cos^2(\\theta)}}\\,d\\theta \\\\ \\\\\n\n&amp; = \\pm \\displaystyle \\int \\dfrac{a[1-\\cos(\\theta)]\\sin(\\theta)}{\\sin(\\theta)}\\,d\\theta \\\\ \\\\\n\n&amp; = \\pm \\displaystyle \\int a[1-\\cos(\\theta)]\\,d\\theta \\\\ \\\\\n\n&amp; = \\pm a(\\theta - \\sin(\\theta)) + C\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u66f2\u7dda\u306f\u6975\u5ea7\u6a19\u306b\u304a\u3051\u308b\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u66f2\u7dda\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u3001\u539f\u70b9\u3092\u51fa\u767a\u70b9\u3068\u3059\u308b\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u3068\u4e00\u81f4\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} x(\\theta) &amp;= \\pm a(\\theta - \\sin(\\theta)) \\\\\n\n   y(\\theta) &amp;= a(1-\\cos(\\theta))\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u7a4d\u5206\u5b9a\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u306f\u3001\u8ecc\u9053\u304c\u539f\u70b9\u304b\u3089\u59cb\u307e\u308b\u3068\u3044\u3046\u521d\u671f\u6761\u4ef6\u3092\u6e80\u305f\u3059\u305f\u3081\u306b\u6d88\u53bb\u3055\u308c\u305f\u3002\u307e\u305f\u3001\u5b9a\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u3092\u8abf\u6574\u3057\u3066\u66f2\u7dda\u304c\u6700\u5f8c\u306b <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span> \u3092\u901a\u308b\u3088\u3046\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u4e8c\u3064\u306e\u65b9\u7a0b\u5f0f\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><strong>\u9078\u629e\u80a2 1\uff1a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\begin{array}{rl}\n\n{} x(\\theta) &amp;= a(\\theta - \\sin(\\theta)) \\\\\n\n   y(\\theta) &amp;= a(1-\\cos(\\theta))\n\n\\end{array}}<\/span>\n<p style=\"text-align:center;\"><strong>\u9078\u629e\u80a2 2\uff1a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\begin{array}{rl}\n\n{} x(\\theta) &amp;= - a(\\theta - \\sin(\\theta)) \\\\\n\n   y(\\theta) &amp;= a(1-\\cos(\\theta))\n\n\\end{array}}<\/span> <\/p>\n<p style=\"text-align:justify;\">\u3053\u306e\u554f\u984c\u306b\u5bfe\u3059\u308b\u5b9f\u884c\u53ef\u80fd\u306a\u89e3\u306f\u7b2c\u4e8c\u306e\u9078\u629e\u80a2\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u3001\u5b9a\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u3092\u8ca0\u306e\u5024\u306b\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u89e3\u3068\u3057\u3066\u5fc5\u8981\u306a\u6761\u4ef6\u3092\u6e80\u305f\u3059\u66f2\u7dda\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/solbraquis.png\" alt=\"Ejemplo de soluci\u00f3n posible, un arco de cicloide\" width=\"497\" height=\"329\" class=\"aligncenter size-full wp-image-28731 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/solbraquis.png\" alt=\"Ejemplo de soluci\u00f3n posible, un arco de cicloide\" width=\"497\" height=\"329\" class=\"aligncenter size-full wp-image-28731 lazyload\" srcset=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/solbraquis.png 497w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/solbraquis-300x199.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/noscript><\/center><\/p>\n<h3>\u89e3\u306e\u6700\u7d42\u8abf\u6574<\/h3>\n<p style=\"text-align:justify;\">\u6700\u5f8c\u306e\u8abf\u6574\u3092\u65bd\u3057\u305f\u5f8c\u3001\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u66f2\u7dda\u306f\u6b21\u306e\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u5f62\u5f0f\u3092\u3068\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nx(\\theta) &amp;= b(\\theta - \\sin(\\theta)) \\\\\n\ny(\\theta) &amp;= -b(1-\\cos(\\theta))\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3053\u3053\u3067\u306f <span class=\"katex-eq\" data-katex-display=\"false\">a=-b<\/span> \u3068\u7f6e\u304d\u63db\u3048\u3001<span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt b<\/span> \u3068\u3057\u305f\u3002\u3053\u306e\u66f2\u7dda\u306e\u5468\u671f\u306f <span class=\"katex-eq\" data-katex-display=\"false\">2b\\pi<\/span> \u3067\u3042\u308a\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x_2 \\in ]0,2b\\pi[[<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">y_2 \\in ]-2b,0[[<\/span> \u3068\u3044\u3046\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002\u3053\u308c\u306f\u6975\u3081\u3066\u91cd\u8981\u3067\u3042\u308a\u3001\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u66f2\u7dda\u304c\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306e1\u672c\u306e\u30a2\u30fc\u30af\u3068\u3057\u3066\u8868\u3055\u308c\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u3068\u3044\u3046\u306e\u3082\u3001\u7c92\u5b50\u304c\u9ad8\u3055\u30bc\u30ed\u306e\u70b9\u306b\u623b\u3063\u3066\u5b89\u5b9a\u3059\u308b\u3068\u89e3\u304c\u6709\u52b9\u3067\u306a\u304f\u306a\u308b\u304b\u3089\u3067\u3042\u308b\u3002<\/p>\n<p style=\"text-align:justify;\">\u3053\u306e\u65b9\u7a0b\u5f0f\u3092\u554f\u984c\u306b\u9069\u7528\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3059 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u306e\u5024\u3092\u6c42\u3081\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} x_2 &amp;= b(\\theta - \\sin(\\theta))\\\\\n\n y_2 &amp;= - b(1-\\cos(\\theta))\n\n\\end{array}<\/span>\n<p style=\"text-align:justify;\">\u3053\u306e\u975e\u7dda\u5f62\u30b7\u30b9\u30c6\u30e0\u306f\u89e3\u6790\u7684\u306a\u89e3\u3092\u6301\u305f\u306a\u3044\u3088\u3046\u306b\u898b\u3048\u308b\u306e\u3067\u3001Wolfram Mathematica \u306b\u3088\u308b\u6570\u5024\u7684\u624b\u6cd5\u3092\u7528\u3044\u308b\u3053\u3068\u306b\u3059\u308b\u3002\u4ee5\u4e0b\u306b\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306e\u624b\u9806\u3092\u793a\u3059\u3002<\/p>\n<h4>\u30b9\u30c6\u30c3\u30d7 1: \u30b7\u30b9\u30c6\u30e0\u306e\u8a2d\u5b9a<\/h4>\n<p style=\"text-align:justify;\">\u89e3\u304f\u3079\u304d\u30b7\u30b9\u30c6\u30e0\u3092\u69cb\u6210\u3059\u308b\u65b9\u7a0b\u5f0f\u3092\u8a2d\u5b9a\u3059\u308b<\/p>\n<p><code>eq1 = x2 == b*(theta - Sin[theta])<br \/>\neq2 = y2 == -b*(1 - Cos[theta])<\/code><\/p>\n<h4>\u30b9\u30c6\u30c3\u30d7 2: \u5230\u9054\u70b9\u3092\u5b9a\u7fa9\u3059\u308b<\/h4>\n<p style=\"text-align:justify;\">\u7c92\u5b50\u304c\u8ecc\u9053\u306e\u7d42\u7aef\u3067\u5230\u9054\u3059\u308b\u70b9\u3092\u8a2d\u5b9a\u3059\u308b\u3002\u3053\u3053\u3067\u306f <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)=(1,-2)<\/span> \u3068\u3059\u308b\u3002\u3053\u308c\u3089\u306e\u5024\u3092\u5909\u66f4\u3057\u3066\u540c\u69d8\u306e\u5225\u306e\u8a2d\u5b9a\u3092\u8a66\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p><code>x2val = 1; y2val = -2;<\/code><\/p>\n<h4>\u30b9\u30c6\u30c3\u30d7 3: \u6c42\u3081\u308b\u5024\u3092\u6570\u5024\u7684\u306b\u8a08\u7b97\u3059\u308b<\/h4>\n<p style=\"text-align:justify;\">\u554f\u984c\u306e\u89e3\u3092\u6570\u5024\u7684\u306b\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b \u300cFindRoot\u300d \u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b<\/p>\n<p><code>sol = FindRoot[{eq1, eq2} \/. {x2 -> x2val, y2 -> y2val}, {{b,1}, {theta, 1}}]<\/code><\/p>\n<p style=\"text-align:justify;\">\u3053\u3053\u3067\u306f\u6570\u5024\u89e3\u306e\u521d\u671f\u8fd1\u4f3c\u3068\u3057\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">b=1<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta=1<\/span> \u3092\u4f7f\u7528\u3057\u305f\u3002\u305d\u306e\u7d50\u679c\u3001<span class=\"katex-eq\" data-katex-display=\"false\">b\\approx 2.4056<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta \\approx 1.40138<\/span> \u3068\u3044\u3046\u89e3\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n<h4>\u30b9\u30c6\u30c3\u30d7 4: \u7d50\u679c\u306e\u691c\u8a3c<\/h4>\n<p style=\"text-align:justify;\">\u3053\u308c\u3089\u306e\u89e3\u304c\u7269\u7406\u7684\u306b\u610f\u5473\u3092\u6301\u3064\u305f\u3081\u306b\u306f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x_2 \\in ]0,2b\\pi[[<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">y_2 \\in ]-2b, 0[[<\/span> \u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u3092\u601d\u3044\u51fa\u305d\u3046\u3002\u6b21\u306e\u624b\u9806\u306b\u3088\u308a\u3053\u308c\u3092\u8fc5\u901f\u306b\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/p>\n<p style=\"text-align:justify;\">\u307e\u305a\u3001\u6c42\u3081\u305f\u89e3\u304b\u3089 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u306e\u5024\u3092\u62bd\u51fa\u3059\u308b\u3002<\/p>\n<p><code>bval = sol[[1, 2]]; thetaval = sol[[2, 2]];<\/code><\/p>\n<p style=\"text-align:justify;\">\u6b21\u306b\u3001\u78ba\u8a8d\u51e6\u7406\u3092\u5b9f\u884c\u3059\u308b\u3088\u3046\u6307\u793a\u3059\u308b\u3002<\/p>\n<p><code>If[0 < x2val < 2*Pi*bval &#038;&#038; -2*bval < y2val < 0, \"Valores v\u00e1lidos\", \"Valores inv\u00e1lidos\"]<\/code><\/p>\n<p style=\"text-align:justify;\">\u3046\u307e\u304f\u3044\u3051\u3070\u51fa\u529b\u306f\u300cValores v\u00e1lidos\u300d\u3068\u306a\u308b\u306f\u305a\u3067\u3042\u308b\u3002\u3053\u306e\u30b3\u30fc\u30c9\u7247\u306f\u3001\u7269\u7406\u72b6\u6cc1\u304c\u6b63\u3057\u304f\u30e2\u30c7\u30eb\u5316\u3055\u308c\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308b\u306e\u306b\u5f79\u7acb\u3064\u3002<\/p>\n<p style=\"text-align:justify;\">\u3053\u308c\u3089\u306e\u624b\u9806\u306b\u3088\u308a\u3001\u51fa\u767a\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)=(0,0)<\/span> \u3068\u5230\u9054\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)=(1,-2)<\/span> \u3092\u7d50\u3076\u89e3\u66f2\u7dda\u3092\u5b8c\u5168\u306b\u8abf\u6574\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u3002\u5f97\u3089\u308c\u305f\u66f2\u7dda\u306f\u6b21\u306e\u901a\u308a\u3067\u3042\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} x(\\theta) &amp;\\approx 2.4056(\\theta - \\sin(\\theta)) \\\\\n\n y(\\theta) &amp;\\approx -2.4056(1-\\cos(\\theta))\n\n\\end{array}\\;\\;;\\theta\\in [0, 1.40138]<\/span>\n<p style=\"text-align:justify;\">\u305d\u306e\u30b0\u30e9\u30d5\u306f\u6b21\u306e\u3088\u3046\u306b\u898b\u3048\u308b\u3002<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/sol2braquis.png\" alt=\"\" width=\"296\" height=\"345\" class=\"aligncenter size-full wp-image-28733 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/sol2braquis.png\" alt=\"\" width=\"296\" height=\"345\" class=\"aligncenter size-full wp-image-28733 lazyload\" srcset=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/sol2braquis.png 296w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/sol2braquis-257x300.png 257w\" sizes=\"(max-width: 296px) 100vw, 296px\" \/><\/noscript><\/center><\/p>\n<p><a id=\"5\"><\/a><\/p>\n<h2>Wolfram \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u542b\u3080 GitHub \u30ea\u30dd\u30b8\u30c8\u30ea<\/h2>\n<p style=\"text-align:justify;\">\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c\u306e\u89e3\u6c7a\u306b\u7528\u3044\u305f\u5b8c\u5168\u306a\u30b3\u30fc\u30c9\uff08Wolfram Mathematica \u3067\u958b\u767a\u3055\u308c\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u542b\u3080\uff09\u306f\u3001\u79c1\u306e GitHub \u30ea\u30dd\u30b8\u30c8\u30ea\u304b\u3089\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u304a\u3088\u3073\u95b2\u89a7\u304c\u53ef\u80fd\u3067\u3042\u308b\u3002\u3053\u306e\u30ea\u30dd\u30b8\u30c8\u30ea\u306b\u306f\u30a4\u30f3\u30bf\u30e9\u30af\u30c6\u30a3\u30d6\u306a\u30ce\u30fc\u30c8\u30d6\u30c3\u30af\u5f62\u5f0f\u306e\u30b3\u30fc\u30c9\u304c\u683c\u7d0d\u3055\u308c\u305f <code>.nb<\/code> \u30d5\u30a1\u30a4\u30eb\u3068\u3001\u30b3\u30fc\u30c9\u3092\u76f4\u63a5\u898b\u305f\u3044\u4eba\u5411\u3051\u306e\u30d7\u30ec\u30fc\u30f3\u30c6\u30ad\u30b9\u30c8\u7248\u3067\u3042\u308b <code>.m<\/code> \u30d5\u30a1\u30a4\u30eb\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3002<\/p>\n<p style=\"text-align:justify;\"><strong>GitHub \u304b\u3089\u30ea\u30dd\u30b8\u30c8\u30ea\u3092 <a href=\"https:\/\/github.com\/girebz\/Braquist-crona\" target=\"_blank\" rel=\"noopener\">\u3053\u3061\u3089<\/a> \u304b\u3089\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3067\u304d\u308b\u3002<\/strong><\/p>\n<p style=\"text-align:justify;\">\u30b3\u30fc\u30c9\u306b\u52a0\u3048\u3066\u3001\u3053\u306e\u30ea\u30dd\u30b8\u30c8\u30ea\u306b\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4f7f\u7528\u65b9\u6cd5\u3084\u7406\u89e3\u65b9\u6cd5\u306b\u95a2\u3059\u308b\u8a73\u7d30\u306a\u8aac\u660e\u3092\u542b\u3080\u300cREADME\u300d\u30d5\u30a1\u30a4\u30eb\u3068\u3001\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c\u306e\u89e3\u6cd5\u3092\u6bb5\u968e\u7684\u306b\u89e3\u8aac\u3057\u305f\u8cc7\u6599\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3002\u5f79\u306b\u7acb\u3066\u3070\u5e78\u3044\u3067\u3042\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u53e4\u5178\u529b\u5b66\u306b\u304a\u3051\u308b\u5909\u5206\u6cd5\u3068\u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f Resumen:\u3053\u306e\u6388\u696d\u3067\u306f\u3001\u5909\u5206\u8a08\u7b97\u306e\u624b\u6cd5\u3092\u7528\u3044\u3066\u89e3\u6790\u529b\u5b66\u306e\u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa\u3092\u518d\u78ba\u8a8d\u3057\u3001\u305d\u306e\u7d50\u679c\u3092\u57fa\u306b\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c\u306e\u89e3\u6cd5\u3078\u306e\u5fdc\u7528\u3092\u8a73\u8ff0\u3059\u308b\u3002 Objetivos de Aprendizaje: Al concluir esta clase el estudiante ser\u00e1 capaz de: \u7406\u89e3\u3059\u308b \u30cf\u30df\u30eb\u30c8\u30f3\u306e\u6700\u5c0f\u4f5c\u7528\u306e\u539f\u7406 \u8a3c\u660e\u3059\u308b \u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f \u89e3\u304f \u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c\u3092 \u76ee\u6b21\uff1a \u53e4\u5178\u529b\u5b66\u306b\u304a\u3051\u308b\u5909\u5206\u6cd5\u306e\u610f\u7fa9 \u5909\u5206\u554f\u984c\u306e\u5b9a\u5f0f\u5316 \u30aa\u30a4\u30e9\u30fc\uff1d\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f \u30d6\u30e9\u30ad\u30b9\u30c8\u30af\u30ed\u30fc\u30ca\u554f\u984c Wolfram \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u542b\u3080 GitHub \u30ea\u30dd\u30b8\u30c8\u30ea \u53e4\u5178\u529b\u5b66\u306b\u304a\u3051\u308b\u5909\u5206\u6cd5\u306e\u610f\u7fa9 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