{"id":33471,"date":"2022-03-15T13:00:59","date_gmt":"2022-03-15T13:00:59","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33471"},"modified":"2025-07-26T06:25:17","modified_gmt":"2025-07-26T06:25:17","slug":"%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%b8%e3%81%ae%e5%b0%8e%e5%85%a5","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ja\/%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%b8%e3%81%ae%e5%b0%8e%e5%85%a5\/","title":{"rendered":"\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3078\u306e\u5c0e\u5165"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3078\u306e\u5c0e\u5165<\/h1>\n<p style=\"text-align:center;\"><em>\u3053\u306e\u6388\u696d\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u3092\u652f\u914d\u3059\u308b\u57fa\u672c\u7684\u306a\u30a2\u30a4\u30c7\u30a2\u3068\u305d\u308c\u3089\u306e\u3055\u307e\u3056\u307e\u306a\u5206\u91ce\u3067\u306e\u5fdc\u7528\u3092\u8a73\u3057\u304f\u63a2\u7a76\u3057\u307e\u3059\u3002\u79c1\u305f\u3061\u3092\u53d6\u308a\u5dfb\u304f\u4e16\u754c\u306b\u304a\u3051\u308b\u7d76\u3048\u9593\u306a\u3044\u5909\u5316\u306e\u6027\u8cea\u306e\u5206\u6790\u304b\u3089\u59cb\u3081\u3001\u95a2\u6570\u3001\u5c0e\u95a2\u6570\u306a\u3069\u306e\u57fa\u672c\u7684\u306a\u6982\u5ff5\u3068\u3001\u305d\u308c\u3089\u304c\u9023\u7d9a\u7684\u304a\u3088\u3073\u96e2\u6563\u7684\u306a\u5909\u5316\u3068\u3069\u306e\u3088\u3046\u306b\u95a2\u9023\u3059\u308b\u304b\u3092\u63d0\u793a\u3057\u307e\u3059\u3002\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f (EDP) \u3068\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u3068\u306e\u533a\u5225\u3092\u5c0e\u5165\u3057\u3001EDO \u306e\u7814\u7a76\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002\u30b3\u30fc\u30d2\u30fc\u306e\u30ab\u30c3\u30d7\u306e\u51b7\u5374\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u6cd5\u5247\u3001\u4eba\u53e3\u30e2\u30c7\u30eb\u306a\u3069\u306e\u5b9f\u7528\u7684\u306a\u4f8b\u3067\u6982\u5ff5\u3092\u793a\u3057\u307e\u3059\u3002\u5b66\u751f\u306f\u3001\u81ea\u7136\u304a\u3088\u3073\u7269\u7406\u7684\u306a\u73fe\u8c61\u3092\u652f\u914d\u3059\u308b\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u89aa\u3057\u307f\u3001\u305d\u308c\u3089\u3092\u6570\u5b66\u7684\u306b\u8868\u73fe\u3059\u308b\u65b9\u6cd5\u3092\u767a\u898b\u3057\u3001\u305d\u306e\u89e3\u3092\u7814\u7a76\u3059\u308b\u305f\u3081\u306e\u3044\u304f\u3064\u304b\u306e\u6280\u8853\u3092\u7406\u89e3\u3059\u308b\u6a5f\u4f1a\u3092\u5f97\u307e\u3059\u3002\u3053\u306e\u521d\u671f\u306e\u77e5\u8b58\u306f\u3001\u5fae\u5206\u65b9\u7a0b\u5f0f\u304a\u3088\u3073\u305d\u306e\u79d1\u5b66\u3084\u5de5\u5b66\u3078\u306e\u5fdc\u7528\u306b\u304a\u3051\u308b\u3088\u308a\u9ad8\u5ea6\u306a\u7814\u7a76\u306e\u57fa\u790e\u3092\u5f62\u6210\u3057\u307e\u3059..<\/em><\/p>\n<p style=\"text-align:center;\"><strong><u>\u5b66\u7fd2\u76ee\u6a19<\/u>:<\/strong><br \/>\u3053\u306e\u6388\u696d\u3092\u7d42\u3048\u308b\u3068\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059:<\/p>\n<ol>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong> \u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u95a2\u9023\u3059\u308b\u57fa\u672c\u6982\u5ff5\u3001\u4f8b\u3048\u3070\u5909\u5316\u306e\u672c\u8cea\u3001\u95a2\u6570\u3001\u5c0e\u95a2\u6570\u3001\u304a\u3088\u3073\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f (EDP) \u3068\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u306e\u9055\u3044<\/li>\n<\/ul>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/bYwm6NAEvVA\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><br \/>\n<center><\/p>\n<p style=\"text-align:center;\"><strong>\u76ee\u6b21<\/strong><br \/>\n<a href=\"#LasEcuacionesDiferencialesYLaNaturalezaDeLasCosas\"><strong>\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u4e8b\u7269\u306e\u672c\u8cea<\/strong><\/a><br \/>\n<a href=\"#ElCambioIncesante\">\u7d76\u3048\u9593\u306a\u3044\u5909\u5316<\/a><br \/>\n<a href=\"#FuncionesDerivadasYSusCambios\">\u95a2\u6570\u3001\u5c0e\u95a2\u6570\u3068\u305d\u306e\u5909\u5316<\/a><br \/>\n<a href=\"#EDOyEDP\">EDO \u3068 EDP<\/a><br \/>\n<a href=\"#EjemplosDeEcuacionesDiferencialesOrdinarias\"><strong>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u4f8b<\/strong><\/a><br \/>\n<a href=\"#ElEnfriamientoDeUnaTazaDeCafe\">\u30b3\u30fc\u30d2\u30fc\u30ab\u30c3\u30d7\u306e\u51b7\u5374<\/a><br \/>\n<a href=\"#LasLeyesDeNewton\">\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u6cd5\u5247<\/a><br \/>\n<a href=\"#ModeloDePoblaciones\">\u4eba\u53e3\u30e2\u30c7\u30eb<\/a>\n<\/p>\n<p><\/center><\/p>\n<p><a name=\"LasEcuacionesDiferencialesYLaNaturalezaDeLasCosas\"><\/a><br \/>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/KgUDA2Q1qaA\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<h2>\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u4e8b\u7269\u306e\u672c\u8cea<\/h2>\n<p><a name=\"ElCambioIncesante\"><\/a><\/p>\n<h3>\u7d76\u3048\u9593\u306a\u3044\u5909\u5316<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=133s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u81ea\u7136\u754c\u3067\u306f\u3001\u3059\u3079\u3066\u304c\u5e38\u306b\u5909\u5316\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/strong><\/a> \u5909\u5316\u3057\u306a\u3044\u3088\u3046\u306b\u898b\u3048\u308b\u3082\u306e\u3001\u305f\u3068\u3048\u3070\u592a\u967d\u306e\u8f1d\u304d\u3067\u3055\u3048\u3001\u9069\u5207\u306a\u6642\u9593\u5c3a\u5ea6\u3067\u89b3\u5bdf\u3059\u308c\u3070\u5909\u5316\u3057\u3066\u3044\u307e\u3059\u3002\u3059\u3079\u3066\u304c\u5909\u5316\u3057\u307e\u3059\u3002\u661f\u306e\u8f1d\u304d\u3001\u30b3\u30fc\u30d2\u30fc\u30ab\u30c3\u30d7\u306e\u6e29\u5ea6\u3001\u7269\u4f53\u306e\u4f4d\u7f6e\u3001\u4eba\u53e3\u306e\u5927\u304d\u3055\u306a\u3069\u304c\u305d\u306e\u4f8b\u3067\u3042\u308a\u3001\u3053\u308c\u3089\u306e\u5909\u5316\u7387\u306f\u4e00\u822c\u306b\u3001\u305d\u306e\u5909\u5316\u304c\u8d77\u3053\u3063\u3066\u3044\u308b\u9593\u306b\u5909\u5316\u3059\u308b\u3082\u306e\u306e\u72b6\u614b\u3068\u95a2\u4fc2\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u5909\u5316\u3092\u76f4\u611f\u7684\u306b\u7406\u89e3\u3059\u308b\u65b9\u6cd5\u306e\u4e00\u3064\u306f\u3001\u6642\u9593\u306e\u7d4c\u904e\u3068\u3068\u3082\u306b\u7269\u4e8b\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u89b3\u5bdf\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u6642\u9593\u306b\u95a2\u3057\u3066\u8d77\u3053\u308b\u5909\u5316\u3092\u79c1\u305f\u3061\u306f\u9032\u5316\u3068\u547c\u3073\u3001\u79c1\u305f\u3061\u304c\u89b3\u5bdf\u3067\u304d\u308b\u3059\u3079\u3066\u306e\u3082\u306e\u306f\u7d76\u3048\u305a\u9032\u5316\u3057\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u9032\u5316\u306f\u5909\u5316\u306e\u552f\u4e00\u306e\u5f62\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u4f8b\u3048\u3070\u3001\u6d77\u629c\u306b\u5bfe\u3059\u308b\u79c1\u305f\u3061\u306e\u9ad8\u3055\u306f\u6642\u9593\u306e\u7d4c\u904e\u3068\u3068\u3082\u306b\u5909\u5316\u3059\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u3080\u3057\u308d\u79c1\u305f\u3061\u306e\u4f4d\u7f6e\uff08\u307e\u305f\u306f\u5730\u7406\u7684\u5ea7\u6a19\uff09\u306b\u3088\u3063\u3066\u5909\u5316\u3059\u308b\u53ef\u80fd\u6027\u306e\u307b\u3046\u304c\u9ad8\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n<p><a name=\"FuncionesDerivadasYSusCambios\"><\/a><\/p>\n<h3>\u95a2\u6570\u3001\u5c0e\u95a2\u6570\u3068\u305d\u306e\u5909\u5316<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=301s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u3088\u308a\u4e00\u822c\u7684\u306b\u306f\u3001<\/span><\/strong><\/a> \u8907\u6570\u306e\u5909\u6570\u3092\u6301\u3064\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_1,x_2, \\cdots, x_n)<\/span><\/span> \u306f\u3001\u3044\u305a\u308c\u304b\u306e\u5909\u6570\u304c\u5909\u5316\u3059\u308b\u3068\u5909\u308f\u308b\u3053\u3068\u304c\u3042\u308a\u3001\u305d\u306e\u5909\u5316\u306f\u9023\u7d9a\u7684\u307e\u305f\u306f\u96e2\u6563\u7684\u3067\u3042\u308a\u5f97\u307e\u3059\u3002\u8907\u6570\u5909\u6570\u306e\u95a2\u6570\u306b\u5bfe\u3057\u3066\u3001\u9023\u7d9a\u7684\u306a\u5909\u5316\u306f <strong>\u504f\u5fae\u5206:<\/strong> \u3092\u901a\u3058\u3066\u7814\u7a76\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial f(x_1, \\cdots, x_n)}{\\partial x_1} = \\lim_{\\Delta x_1 \\to 0} \\frac{ f(x_1 + \\Delta x_1, \\cdots, x_n) -  f(x_1, \\cdots, x_n)}{\\Delta x_1} <\/span>\n<p>\u95a2\u6570\u304c\u4e00\u3064\u306e\u5909\u6570\u306e\u3082\u306e\u3067\u3042\u308c\u3070\u3001<strong>\u901a\u5e38\u306e\u5c0e\u95a2\u6570:<\/strong>\u3092\u7528\u3044\u307e\u3059\u3002<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{df(x)}{dx} = \\lim_{\\Delta x \\to 0} \\frac{ f(x + \\Delta x) -  f(x)}{\\Delta x} <\/span>\n<p>\u5909\u5316\u304c\u9023\u7d9a\u3067\u306f\u306a\u304f\u96e2\u6563\u7684\u3067\u3042\u308b\u5834\u5408\u306b\u306f\u3001\u5c0e\u95a2\u6570\u306b\u73fe\u308c\u308b\u6975\u9650\u306e\u8a08\u7b97\u3092\u5358\u306b\u7701\u7565\u3057\u307e\u3059.<\/p>\n<p><a name=\"EDOyEDP\"><\/a><\/p>\n<h3>EDO \u3068 EDP<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=624s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u95a2\u6570\u3068\u305d\u306e\u3055\u307e\u3056\u307e\u306a\u5c0e\u95a2\u6570\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u306f<\/span><\/strong><\/a> \u306f <strong>\u5fae\u5206\u65b9\u7a0b\u5f0f<\/strong> \u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5c0e\u95a2\u6570\u304c\u504f\u5fae\u5206\u304b\u901a\u5e38\u306e\u5c0e\u95a2\u6570\u304b\u306b\u3088\u3063\u3066\u3001\u305d\u308c\u305e\u308c <strong>\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f (EDP)<\/strong> \u307e\u305f\u306f <strong>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO)<\/strong> \u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u7814\u7a76\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001\u305d\u308c\u304c\u73fe\u308c\u308b\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<p><a name=\"EjemplosDeEcuacionesDiferencialesOrdinarias\"><\/a><\/p>\n<h2>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u4f8b<\/h2>\n<p><a name=\"ElEnfriamientoDeUnaTazaDeCafe\"><\/a><\/p>\n<h3>\u30b3\u30fc\u30d2\u30fc\u30ab\u30c3\u30d7\u306e\u51b7\u5374<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=680s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u30b3\u30fc\u30d2\u30fc\u30ab\u30c3\u30d7\u306e\u51b7\u5374\u901f\u5ea6\u306f<\/span><\/strong><\/a> \u5468\u56f2\u3068\u30b3\u30fc\u30d2\u30fc\u306e\u6e29\u5ea6\u5dee\u306b\u6bd4\u4f8b\u3057\u307e\u3059\u3002\u7a7a\u6c17\u306e\u6e29\u5ea6\u3001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_a<\/span><\/span> \u304c\u4e00\u5b9a\u3067\u3001\u30b3\u30fc\u30d2\u30fc\u306e\u6e29\u5ea6\u304c\u6642\u9593\u306e\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_c=T_c(t),<\/span><\/span> \u3067\u3042\u308b\u3068\u3059\u308b\u3068\u3001\u5404\u77ac\u9593\u306b\u304a\u3051\u308b\u30b3\u30fc\u30d2\u30fc\u306e\u6e29\u5ea6\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u521d\u671f\u7684\u306b\u6b21\u306e\u5f0f\u304c\u3042\u308a\u307e\u3059:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{dT_c(t)}{dt} = -\\alpha^2(T_c(t) - T_a) <\/span>\n<p>\u3053\u3053\u3067 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u306f\u6bd4\u4f8b\u5b9a\u6570\u3067\u3042\u308a\u3001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_a \\lt T_c(t)<\/span><\/span> \u3067\u3001\u8ca0\u306e\u7b26\u53f7\u306f\u30b3\u30fc\u30d2\u30fc\u306e\u6e29\u5ea6\u304c\u6e1b\u5c11\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u5f8c\u3067\u3001\u3053\u306e\u65b9\u7a0b\u5f0f\u304c\u6b21\u306e\u5f62\u306e\u89e3\u3092\u6301\u3064\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_c(t) = T_a + Be^{-\\alpha^2 t}<\/span>\n<p>\u3053\u3053\u3067 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u306f\u6c7a\u5b9a\u3059\u3079\u304d\u5b9a\u6570\u3067\u3059\u3002<\/p>\n<p><a name=\"LasLeyesDeNewton\"><\/a><\/p>\n<h3>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u6cd5\u5247<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=885s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u7b2c\u4e8c\u6cd5\u5247\u306f\u672c\u8cea\u7684\u306b\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\u3001<\/span><\/strong><\/a> \u306a\u305c\u306a\u3089\u3001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F=ma<\/span><\/span> \uff08\u529b\u306f\u8cea\u91cf\u3068\u52a0\u901f\u5ea6\u306e\u7a4d\uff09\u3068\u3044\u3046\u5f0f\u306b\u304a\u3044\u3066\u3001\u52a0\u901f\u5ea6\u3001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a=d^2x(t)\/dt^2,<\/span><\/span> \u306f\u7269\u4f53\u306e\u4f4d\u7f6e\u306e\u6642\u9593\u306b\u95a2\u3059\u308b\u4e8c\u968e\u5c0e\u95a2\u6570\u3060\u304b\u3089\u3067\u3059\u3002\u3053\u306e\u6cd5\u5247\u306b\u3088\u3063\u3066\u3001\u7269\u4f53\u306e\u904b\u52d5\u3092\u8a18\u8ff0\u3059\u308b\u95a2\u4fc2\u5f0f\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u305d\u308c\u306f\u5b9f\u969b\u306b\u306f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3059\u3002\u5358\u7d14\u306a\u4f8b\u306f\u3070\u306d\u306e\u7814\u7a76\u3067\u3059\u3002\u7247\u65b9\u304c\u56fa\u5b9a\u3055\u308c\u305f\u58c1\u306b\u53d6\u308a\u4ed8\u3051\u3089\u308c\u3001\u3082\u3046\u7247\u65b9\u304c\u8cea\u91cf\u306b\u7d50\u5408\u3055\u308c\u305f\u3070\u306d\u304c\u5e73\u8861\u4f4d\u7f6e\u306b\u3042\u308b\u3068\u304d\u3001\u305d\u306e\u8cea\u91cf\u3092\u305d\u306e\u4f4d\u7f6e\u304b\u3089\u8ddd\u96e2 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u3060\u3051\u79fb\u52d5\u3055\u305b\u308b\u3068\u3001\u30d5\u30c3\u30af\u306e\u6cd5\u5247\u306b\u3088\u308a\u8cea\u91cf\u306b\u306f\u5fa9\u5143\u529b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F=-kx<\/span><\/span> \u304c\u4f5c\u7528\u3057\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u7b2c\u4e8c\u6cd5\u5247\u306b\u3088\u308a\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle -kx(t) = m\\frac{d^2x(t)}{dt^2} <\/span>\n<p>\u5f8c\u3067\u3001\u305d\u306e\u89e3\u304c\u6b21\u306e\u5f62\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle x(t) = A\\sin\\left(\\sqrt{\\frac{k}{m}}t + \\phi \\right)<\/span>\n<p>\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">\\phi<\/span> \u306f\u3001<strong>\u554f\u984c\u306e\u521d\u671f\u6761\u4ef6<\/strong>\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u308b\u5b9a\u6570\u3067\u3059\u3002<\/p>\n<p><a name=\"ModeloDePoblaciones\"><\/a><\/p>\n<h3>\u4eba\u53e3\u30e2\u30c7\u30eb<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=1184s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">1 \u4eba\u3042\u305f\u308a\u306e\u6210\u9577\u7387<\/span><\/strong><\/a> \u306f\u51fa\u751f\u7387\u3068\u6b7b\u4ea1\u7387\u306e\u5dee\u306b\u7b49\u3057\u304f\u3001\u3064\u307e\u308a:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{1}{x(t)} \\frac{dx(t)}{dt} = N - M<\/span>\n<p>\u51fa\u751f\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u304c\u6642\u9593\u306b\u5bfe\u3057\u3066\u4e00\u5b9a\u3067\u3001\u6b7b\u4ea1\u6570\u304c\u4eba\u53e3\u306b\u6bd4\u4f8b\u3059\u308b\u3068\u3059\u308b\u3068\u3001\u3064\u307e\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M=\\alpha^2 x(t),<\/span><\/span> \u3067\u3042\u308c\u3070\u3001\u4e0a\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u5f62\u306b\u306a\u308a\u307e\u3059:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{dx(t)}{dt} = x(t) (N - \\alpha^2 x(t))<\/span>\n<p>\u3053\u308c\u306f <strong>\u300c\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u65b9\u7a0b\u5f0f\u300d<\/strong> \u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u65b9\u7a0b\u5f0f\u304b\u3089\u3001\u591a\u6570\u306e\u4eba\u53e3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1(t), x_2(t), \\cdots, x_n(t)<\/span><\/span> \u304c\u4e92\u3044\u306b\u5b58\u5728\u3092\u7af6\u3044\u5408\u3046\u3088\u3046\u306a\u4e00\u822c\u5316\u3092\u6b21\u306e\u3088\u3046\u306b\u69cb\u7bc9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{dx_i(t)}{dt} = x_i(t) \\left(N_i - \\displaystyle \\sum_{j=1}^n\\alpha^2_{ij} x_j(t)  \\right)<\/span>\n<p>\u3053\u3053\u3067 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">i\\in\\{1,\\cdots, n\\}<\/span><\/span> \u3067\u3059\u3002\u3053\u308c\u306f <strong>\u30ed\u30c8\u30ab=\u30f4\u30a9\u30eb\u30c6\u30e9\u65b9\u7a0b\u5f0f<\/strong> \u3068\u547c\u3070\u308c\u308b\u3082\u306e\u3067\u3059\u3002<\/p>\n<h2>\u7d50\u8ad6<\/h2>\n<p>\u3053\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u5165\u9580\u3092\u901a\u3058\u3066\u3001\u6570\u5b66\u304c\u81ea\u7136\u754c\u3067\u8d77\u3053\u308b\u5909\u5316\u3092\u3069\u306e\u3088\u3046\u306b\u6b63\u78ba\u304b\u3064\u512a\u96c5\u306b\u6349\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3092\u63a2\u3063\u3066\u304d\u307e\u3057\u305f\u3002\u30b3\u30fc\u30d2\u30fc\u30ab\u30c3\u30d7\u306e\u51b7\u5374\u304b\u3089\u3070\u306d\u306e\u904b\u52d5\u3084\u4eba\u53e3\u306e\u6210\u9577\u306b\u81f3\u308b\u307e\u3067\u3001\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306f\u8907\u96d1\u306a\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u3092\u7406\u89e3\u3057\u3084\u3059\u3044\u6570\u5b66\u7684\u95a2\u4fc2\u306b\u7ffb\u8a33\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u306e\u69cb\u9020\u3068\u610f\u5473\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u306f\u3001\u7269\u7406\u5b66\u3001\u751f\u7269\u5b66\u3001\u7d4c\u6e08\u5b66\u3001\u5de5\u5b66\u306a\u3069\u306e\u591a\u304f\u306e\u5206\u91ce\u3078\u306e\u6249\u3092\u958b\u304d\u307e\u3059\u3002\u3053\u306e\u6388\u696d\u306f\u3001\u89e3\u6cd5\u6280\u8853\u3001\u5b9a\u6027\u7684\u5206\u6790\u3001\u6570\u5024\u7684\u624b\u6cd5\u3092\u6df1\u3081\u308b\u3088\u3046\u306a\u3088\u308a\u9ad8\u5ea6\u306a\u7814\u7a76\u3092\u7d9a\u3051\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u6982\u5ff5\u7684\u57fa\u76e4\u3092\u7bc9\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u6700\u3082\u91cd\u8981\u306a\u306e\u306f\u3001\u5909\u5316\u306e\u8a00\u8a9e \u2014 \u5fae\u5206\u65b9\u7a0b\u5f0f \u2014 \u304c\u52d5\u7684\u30b7\u30b9\u30c6\u30e0\u306e\u632f\u308b\u821e\u3044\u3092\u8a18\u8ff0\u3057\u3001\u7406\u89e3\u3057\u3001\u4e88\u6e2c\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u3068\u3044\u3046\u3053\u3068\u306b\u3064\u3044\u3066\u306e\u521d\u6b69\u7684\u306a\u76f4\u611f\u3092\u8eab\u306b\u3064\u3051\u305f\u3053\u3068\u3067\u3059\u3002<\/p>\n<p>\u6b21\u306e\u6388\u696d\u3067\u306f\u3001\u3088\u308a\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3092\u958b\u767a\u3057\u3001\u305d\u308c\u3089\u3092\u65b0\u3057\u3044\u6587\u8108\u306b\u9069\u7528\u3057\u7d9a\u3051\u307e\u3059\u3002\u5fae\u5206\u65b9\u7a0b\u5f0f\u306f\u3001\u73fe\u5b9f\u3092\u5206\u6790\u3059\u308b\u65b9\u6cd5\u3092\u63d0\u4f9b\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u7570\u306a\u308b\u6761\u4ef6\u4e0b\u3067\u3069\u306e\u3088\u3046\u306b\u9032\u5316\u3059\u308b\u304b\u3092\u60f3\u50cf\u3059\u308b\u65b9\u6cd5\u3082\u63d0\u4f9b\u3057\u3066\u304f\u308c\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3078\u306e\u5c0e\u5165 \u3053\u306e\u6388\u696d\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u3092\u652f\u914d\u3059\u308b\u57fa\u672c\u7684\u306a\u30a2\u30a4\u30c7\u30a2\u3068\u305d\u308c\u3089\u306e\u3055\u307e\u3056\u307e\u306a\u5206\u91ce\u3067\u306e\u5fdc\u7528\u3092\u8a73\u3057\u304f\u63a2\u7a76\u3057\u307e\u3059\u3002\u79c1\u305f\u3061\u3092\u53d6\u308a\u5dfb\u304f\u4e16\u754c\u306b\u304a\u3051\u308b\u7d76\u3048\u9593\u306a\u3044\u5909\u5316\u306e\u6027\u8cea\u306e\u5206\u6790\u304b\u3089\u59cb\u3081\u3001\u95a2\u6570\u3001\u5c0e\u95a2\u6570\u306a\u3069\u306e\u57fa\u672c\u7684\u306a\u6982\u5ff5\u3068\u3001\u305d\u308c\u3089\u304c\u9023\u7d9a\u7684\u304a\u3088\u3073\u96e2\u6563\u7684\u306a\u5909\u5316\u3068\u3069\u306e\u3088\u3046\u306b\u95a2\u9023\u3059\u308b\u304b\u3092\u63d0\u793a\u3057\u307e\u3059\u3002\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f (EDP) \u3068\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (EDO) \u3068\u306e\u533a\u5225\u3092\u5c0e\u5165\u3057\u3001EDO 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