{"id":32866,"date":"2022-04-28T13:00:43","date_gmt":"2022-04-28T13:00:43","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=32866"},"modified":"2025-04-03T23:15:02","modified_gmt":"2025-04-03T23:15:02","slug":"%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/","title":{"rendered":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?"},"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>\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?<\/h1>\n<p style=\"text-align:center;\" dir=\"ltr\"><em><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><\/br>\u0412 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u044b\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f (\u041e\u0414\u0423) \u043f\u043e\u0440\u044f\u0434\u043a\u0430 k, \u043d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 \u0438\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0432 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u0438 \u043e\u0431\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0435. \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0442\u0430\u043a\u0438\u0445 \u043f\u043e\u043d\u044f\u0442\u0438\u0439, \u043a\u0430\u043a \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438 \u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0435\u044f\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0437\u0430\u043a\u043b\u0430\u0434\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0441\u043d\u043e\u0432\u044b \u0434\u043b\u044f \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0439 \u044d\u0442\u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0438 \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u044b\u0445 \u0441 \u043d\u0438\u043c\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432, \u0442\u0430\u043a\u0438\u0445 \u043a\u0430\u043a \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u044f\u0432\u043d\u044b\u0435 \u0438 \u043d\u0435\u044f\u0432\u043d\u044b\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f.<\/em><\/p>\n<p style=\"text-align:center\"><strong>\u0426\u0415\u041b\u0418 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u042f<\/strong><\/p>\n<p>\u041f\u043e \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u0437\u0430\u043d\u044f\u0442\u0438\u044f \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0441\u043c\u043e\u0436\u0435\u0442:<\/p>\n<ol>\n<li><strong>\u0412\u0441\u043f\u043e\u043c\u043d\u0438\u0442\u044c<\/strong> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f (\u041e\u0414\u0423).<\/li>\n<li><strong>\u041e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c<\/strong> \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u041e\u0414\u0423 \u0438 \u0435\u0433\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u043c\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438.<\/li>\n<\/ol>\n<p style=\"text-align:center;\" dir=\"ltr\"><strong>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><br \/>\n<a href=\"#LaEcuacionDiferencialOrdinariaDeOrdenK\"><strong>\u041e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423) \u043f\u043e\u0440\u044f\u0434\u043a\u0430 k<\/strong><\/a><br \/>\n<a href=\"#TeoremaDeLaFuncionImplicita\">\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0435\u044f\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/a><br \/>\n<a href=\"#LaSolucionDeUnaEcuacionDiferencialOrdinaria\"><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong><\/a><br \/>\n<a href=\"#CuidadoConElDominioDeDefinicionDeLasSoluciones\">\u0412\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043a \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0439<\/a><br \/>\n<a href=\"#SolucionExtendidaYSolucionMaximal\">\u0420\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u043d\u043e\u0435 \u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/a><br \/>\n<a href=\"#SolucionExplicitaYSolucionImplicita\">\u042f\u0432\u043d\u043e\u0435 \u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/zE29azRIKng\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u041d\u0430 \u0434\u0430\u043d\u043d\u043e\u043c \u044d\u0442\u0430\u043f\u0435 \u0443 \u043d\u0430\u0441 \u0443\u0436\u0435 \u0435\u0441\u0442\u044c \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u044f\u0441\u043d\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043e \u0442\u043e\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438 \u043a\u0430\u043a\u0438\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043e\u043d\u043e \u043c\u043e\u0436\u0435\u0442 \u0438\u043c\u0435\u0442\u044c. \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043e\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u043c\u0441\u044f, \u0447\u0442\u043e\u0431\u044b \u0438\u0437\u0443\u0447\u0438\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0441 \u0446\u0435\u043b\u044c\u044e \u0437\u0430\u043b\u043e\u0436\u0438\u0442\u044c \u043f\u0440\u043e\u0447\u043d\u0443\u044e \u043e\u0431\u0449\u0443\u044e \u043e\u0441\u043d\u043e\u0432\u0443 \u0434\u043b\u044f \u0434\u0430\u043b\u044c\u043d\u0435\u0439\u0448\u0435\u0433\u043e \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f.<\/p>\n<p><a name=\"LaEcuacionDiferencialOrdinariaDeOrdenK\"><\/a><\/p>\n<h3>\u041e\u0414\u0423 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 k<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=163s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u041e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)<\/span><\/strong><\/a> \u2014 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0443\u0447\u0430\u0441\u0442\u0432\u0443\u044e\u0442 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u0430\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>, \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span> \u0438 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0435\u0451 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435. \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u043e\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x)<\/span><\/span> \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442\u0441\u044f \u0441\u0438\u043c\u0432\u043e\u043b\u0430\u043c\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{dy(x)}{dx}<\/span><\/span> \u0438\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y&#039;(x)<\/span><\/span>, \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u2014 \u043a\u0430\u043a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{d^2y(x)}{dx^2}<\/span><\/span> \u0438\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y&#039;&#039;(x)<\/span><\/span>, \u0438 \u0432 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u2014 \u043a\u0430\u043a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{d^ny(x)}{dx^n}<\/span><\/span> \u0438\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(n)}(x)<\/span><\/span>. \u041d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0435\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(k)}(x)<\/span><\/span> \u043f\u043e\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438, \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u043f\u043e\u0440\u044f\u0434\u043a\u043e\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong>. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, <strong>\u043e\u0431\u0449\u0430\u044f \u0444\u043e\u0440\u043c\u0430 \u041e\u0414\u0423 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/strong> \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0442\u0430\u043a:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F\\left(x,y(x),y&#039;(x), \\cdots, y^{(k)}(x)\\right)=0.<\/span>\n<p>\u0413\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e \u041e\u0414\u0423 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432 <strong>\u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u0435<\/strong>, \u0435\u0441\u043b\u0438 \u043e\u043d\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u043e \u044f\u0432\u043d\u043e \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(k)}(x)<\/span><\/span>, \u0442\u043e \u0435\u0441\u0442\u044c:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(k)}(x) = f\\left(x,y(x),y&#039;(x), \\cdots, y^{(k-1)}(x)\\right).<\/span>\n<p>\u0412 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R} \\longrightarrow \\mathbb{R}^n,<\/span><\/span> \u0442\u0430\u043a \u0447\u0442\u043e \u043e\u043d\u0430 \u0438 \u0432\u0441\u0435 \u0435\u0451 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0432 \u0442\u043e\u0447\u043a\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in\\mathbb{R}<\/span><\/span> \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u0438\u0437 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span>. \u0421 \u0443\u0447\u0451\u0442\u043e\u043c \u044d\u0442\u043e\u0433\u043e, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>, \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0449\u0430\u044f \u041e\u0414\u0423 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>, \u0438\u043c\u0435\u0435\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1+(k+1)<\/span><\/span> \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Dom}(F)\\subset \\mathbb{R}^{1+n(k+1)}<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Rec}(F)\\subset \\mathbb{R}<\/span><\/span>; \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Dom}(f) = \\mathbb{R}^{1+nk}<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text{Rec}(f)\\subset \\mathbb{R}^n<\/span><\/span>.<\/p>\n<p>\u041f\u0435\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u043e\u0431\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u044b \u041e\u0414\u0423 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u043a \u0435\u0451 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u0435\u043d \u0431\u043b\u0430\u0433\u043e\u0434\u0430\u0440\u044f <strong>\u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u043d\u0435\u044f\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong><\/p>\n<p><a name=\"TeoremaDeLaFuncionImplicita\"><\/a><\/p>\n<h4>\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0435\u044f\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=887s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u041f\u0443\u0441\u0442\u044c <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043b\u0430\u0441\u0441\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{C}^1<\/span><\/span> \u043d\u0430 \u043e\u0442\u043a\u0440\u044b\u0442\u043e\u043c \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U \\subset \\mathbb{R}^n<\/span><\/span><\/span><\/strong><\/a> \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438 \u0432 \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0447\u0438\u0441\u043b\u0430\u0445. \u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1,\\cdots, a_n) \\in U<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(a_1,\\cdots, a_n) = 0<\/span><\/span> \u0438<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial F(a_1,\\cdots, a_n)}{\\partial x_n} \\neq 0<\/span>\n<p>\u0422\u043e\u0433\u0434\u0430 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043e\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0441\u0442\u044c <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> \u0442\u043e\u0447\u043a\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1, \\cdots, a_{n-1}) \\in \\mathbb{R}^{n-1}<\/span><\/span> \u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi:V \\longrightarrow \\mathbb{R}<\/span><\/span> \u0442\u0430\u043a\u0430\u044f, \u0447\u0442\u043e:<\/p>\n<ol>\n<li type=\"i\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V \\times \\varphi(V) \\subset U<\/span><\/span><\/li>\n<li type=\"i\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x_1,\\cdots,x_{n-1},x_n) = 0 \\leftrightarrow x_n = \\varphi(x_1,\\cdots, x_{n-1})<\/span><\/span><\/li>\n<li type=\"i\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi<\/span> \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u0438\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\dfrac{\\partial \\varphi (a_1,\\cdots, a_{n-1})}{\\partial x_i} = - \\dfrac{ \\dfrac{\\partial F (a_1,\\cdots, a_n)}{\\partial x_i} }{ \\dfrac{\\partial F (a_1,\\cdots, a_n)}{\\partial x_n} }<\/span>\n<\/li>\n<\/ol>\n<h4>\u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u043d\u0435\u044f\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/h4>\n<h5>\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438<\/h5>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=1101s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi(x_1,\\cdots,x_{n-1}, x_n) = (x_1,\\cdots,x_{n-1}, F(x_1,\\cdots, x_n)).<\/span><\/span><\/span><\/strong><\/a> \u0415\u0441\u043b\u0438 \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0435\u0451 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0430 \u043d\u0438\u0436\u0435:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left( \\dfrac{\\partial \\psi(x_1,\\cdots, x_n)}{\\partial(x_1,\\cdots, x_n)} \\right) = \\left( \\begin{array}{cccc}\n\n1 &amp; 0 &amp;  \\cdots &amp; 0 \\\\\n\n0 &amp; 1 &amp;  \\cdots &amp; \\vdots \\\\\n\n\\vdots &amp;\\vdots &amp; \\ddots  &amp; \\vdots  \\\\\n\n\\displaystyle \\dfrac{\\partial F(x_1, \\cdots, x_n)}{\\partial x_1} &amp; \\dfrac{\\partial F(x_1, \\cdots, x_n)}{\\partial x_2} &amp; \\cdots  &amp; \\dfrac{\\partial F(x_1, \\cdots, x_n)}{\\partial x_n}\n\n\\end{array}\\right), <\/span>\n<p>\u0443\u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u0435\u0451 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043e\u0442\u043b\u0438\u0447\u0435\u043d \u043e\u0442 \u043d\u0443\u043b\u044f \u0432 \u0442\u043e\u0447\u043a\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1,\\cdots, a_n)<\/span><\/span>, \u0438\u043c\u0435\u043d\u043d\u043e \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e, \u043a\u0430\u043a \u0431\u044b\u043b\u043e \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043b\u0435\u043d\u043e \u0432 \u043d\u0430\u0447\u0430\u043b\u0435, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\partial F(a_1,\\cdots, a_n)\/\\partial x_n \\neq 0.<\/span><\/span> \u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e \u0443 <span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span> \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043e\u0431\u0440\u0430\u0442\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0430 \u043e\u0442\u043a\u0440\u044b\u0442\u043e\u043c \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">W<\/span>, \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0449\u0435\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1,\\cdots, a_n).<\/span><\/span><\/p>\n<h5>\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f<\/h5>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tilde{V}=\\psi(W)\\ni \\psi(a_1,\\cdots,a_{n}) = (a_1,\\cdots,a_{n-1},F(a_1,\\cdots,a_{n}))=(a_1,\\cdots,a_{n-1},0).<\/span>\n<p>\u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0434\u0440\u0443\u0433\u043e\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V=\\{(x_1,\\cdots,x_{n-1}) \\;|\\; (x_1,\\cdots,x_{n-1},0)\\in \\tilde{V}\\}\\ni (a_1,\\cdots,a_{n-1})<\/span>\n<p>\u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span>, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u043c \u0438 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0442\u043e\u0447\u043a\u0443 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a_1,\\cdots,a_{n-1})\\in\\mathbb{R}^{n-1}.<\/span><\/span><\/p>\n<p>\u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span> \u043e\u0431\u0440\u0430\u0442\u0438\u043c\u0430 (\u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">W<\/span>), \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(y_1,\\cdots,y_n)\\in W<\/span><\/span>, \u0442\u0430\u043a\u0430\u044f \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi(y_1,\\cdots,y_n) = (x_1,\\cdots,x_{n-1},0).<\/span><\/span> \u042d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl} y_1 &amp;= x_1 \\\\ \\\\ \\vdots &amp; \\vdots \\\\ \\\\ y_{n-1} &amp;= x_{n-1} \\\\ \\\\ F(x_1,\\cdots,x_{n-1},y_n) &amp;= 0 \\end{array}<\/span>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi(x_1,\\cdots,x_{n-1}) = y_n<\/span><\/span>, \u0442\u0430\u043a \u0447\u0442\u043e:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi^{-1}(x_1,\\cdots,x_{n-1},0) = (x_1,\\cdots,x_{n-1},\\varphi(x_1,\\cdots,x_{n-1}))<\/span>\n<p>\u0438<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x_1,\\cdots,x_{n-1},\\varphi(x_1,\\cdots,x_{n-1})) = 0<\/span>\n<p>\u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi(V)\\ni a_n,<\/span><\/span> \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V\\times\\varphi(V) \\subset U,<\/span><\/span> \u0438 \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x_1,\\cdots,x_{n-1},x_n) = 0 \\leftrightarrow x_n = \\varphi(x_1,\\cdots,x_{n-1})<\/span>\n<h5>\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u044c<\/h5>\n<p>\u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u044c <span class=\"katex-eq\" data-katex-display=\"false\">\\psi<\/span> \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u0442 \u043a \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi^{-1}<\/span><\/span>, \u0447\u0442\u043e \u0432 \u0441\u0432\u043e\u044e \u043e\u0447\u0435\u0440\u0435\u0434\u044c \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u0442 \u043a \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\varphi<\/span> \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span>. \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u044d\u0442\u043e, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044e <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u0447\u0435\u0440\u0435\u0437 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(x_1, \\cdots,x_{n-1}) = F(x_1,\\cdots,x_{n-1},\\varphi(x_1,\\cdots,x_{n-1})) = 0<\/span>\n<p>\u0417\u0430\u0442\u0435\u043c, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u043e\u0447\u043a\u0438, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{\\partial g}{\\partial x_i} = \\frac{\\partial F}{\\partial x_i} + \\frac{\\partial F}{\\partial x_n}\\frac{\\partial \\varphi }{\\partial x_i} = 0,<\/span>\n<p>\u0433\u0434\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">i=1,\\cdots, n-1.<\/span><\/span> \u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u0435\u0442:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{\\partial \\varphi(a_1,\\cdots,a_{n-1})}{\\partial x_i} = - \\dfrac{\\dfrac{\\partial F(a_1,\\cdots,a_{n})}{\\partial x_i}}{\\dfrac{\\partial F(a_1,\\cdots,a_{n})}{\\partial x_n}}<\/span>\n<p>\u041d\u0430 \u044d\u0442\u043e\u043c \u0437\u0430\u0432\u0435\u0440\u0448\u0430\u0435\u0442\u0441\u044f \u0432\u0441\u0451, \u0447\u0442\u043e \u0442\u0440\u0435\u0431\u043e\u0432\u0430\u043b\u043e\u0441\u044c \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c \u25a0<\/p>\n<p><a name=\"LaSolucionDeUnaEcuacionDiferencialOrdinaria\"><\/a><\/p>\n<h3>\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=2249s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u041e\u0414\u0423, \u0437\u0430\u043f\u0438\u0441\u0430\u043d\u043d\u043e\u0435 \u0432 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u0435<\/span><\/strong><\/a><\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(n)} = f(x,y(x),y^\\prime(x),\\cdots,y^{(n-1)(x)})<\/span>\n<p>\u0422\u043e\u0433\u0434\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\varphi : I_\\phi \\longmapsto \\mathbb{R}^n,<\/span><\/span> \u0433\u0434\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_\\phi<\/span><\/span> \u2014 \u044d\u0442\u043e \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b \u0432 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R},<\/span><\/span> \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u041e\u0414\u0423<\/strong>, \u0435\u0441\u043b\u0438:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall x \\in I_\\phi \\right) \\left(\\varphi^{(n)}(x) = f(x,\\varphi(x),\\varphi^\\prime(x),\\cdots,\\varphi^{(n-1)(x)}\\right)<\/span>\n<p><a name=\"CuidadoConElDominioDeDefinicionDeLasSoluciones\"><\/a><\/p>\n<h4>\u041e\u0441\u0442\u043e\u0440\u043e\u0436\u043d\u043e \u0441 \u043e\u0431\u043b\u0430\u0441\u0442\u044c\u044e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0439<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=2387s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u041d\u0430 \u044d\u0442\u043e\u043c \u044d\u0442\u0430\u043f\u0435 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u043e\u0434\u0447\u0435\u0440\u043a\u043d\u0443\u0442\u044c<\/span><\/strong><\/a> \u0432\u0430\u0436\u043d\u043e\u0441\u0442\u044c \u044f\u0432\u043d\u043e\u0433\u043e \u0443\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi<\/span><\/span>, \u043e \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043c\u044b \u0433\u043e\u0432\u043e\u0440\u0438\u043b\u0438 \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0430\u0431\u0437\u0430\u0446\u0435, \u2014 \u044d\u0442\u043e \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_\\phi.<\/span><\/span> \u042d\u0442\u043e \u0432\u0430\u0436\u043d\u043e, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0451\u043d\u043d\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430 \u043f\u0440\u0438 \u0440\u0430\u0431\u043e\u0442\u0435 \u0441 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u2014 \u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0434\u0432\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_1<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_2<\/span><\/span> \u0440\u0430\u0432\u043d\u044b\u043c\u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u043e\u0442\u043e\u043c\u0443, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall x \\in I_{\\phi_1}\\cap I_{\\phi_2}\\right)\\left(\\phi_1(x) = \\phi_2(x)\\right),<\/span><\/span> \u043d\u0435\u0441\u043c\u043e\u0442\u0440\u044f \u043d\u0430 \u0442\u043e \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{\\phi_1}\\neq I_{\\phi_2}.<\/span><\/span> \u0427\u0442\u043e\u0431\u044b \u043f\u043e\u044f\u0441\u043d\u0438\u0442\u044c \u044d\u0442\u043e, \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^\\prime = -y^2.<\/span>\n<p>\u041e\u0434\u043d\u043e \u0438\u0437 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u0440\u0435\u0448\u0435\u043d\u0438\u0439 \u044d\u0442\u043e\u0433\u043e \u041e\u0414\u0423 \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1 : ]0,+\\infty[ \\longrightarrow \\mathbb{R}^+\\setminus\\{0\\}<\/span><\/span>, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u0430\u044f \u043a\u0430\u043a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1(x)=1\/x,<\/span><\/span> \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1^{\\prime} = -1\/x^2 = -\\psi_1^2<\/span><\/span> \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]0,+\\infty[.<\/span><\/span> \u041e\u0434\u043d\u0430\u043a\u043e, \u0441 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u043c\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0434\u0440\u0443\u0433\u043e\u0435, \u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u043d\u043e \u043e\u0442\u043b\u0438\u0447\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435, \u0435\u0441\u043b\u0438 \u043d\u0435 \u0443\u0434\u0435\u043b\u044f\u0442\u044c \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u0434\u0435\u0442\u0430\u043b\u044f\u043c. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{1}{x} = \\frac{1}{1 - (1-x)},<\/span>\n<p>\u0430 \u043f\u0440\u0430\u0432\u0430\u044f \u0447\u0430\u0441\u0442\u044c \u044d\u0442\u043e\u0433\u043e \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u2014 \u044d\u0442\u043e \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0440\u044f\u0434\u0430:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle \\sum_{n=0}^{+\\infty} (1-x)^n = \\frac{1}{1 - (1-x)}<\/span>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043d\u0435\u0438\u0441\u043a\u0443\u0448\u0451\u043d\u043d\u044b\u0439 \u0432\u0437\u0433\u043b\u044f\u0434 \u043c\u043e\u0436\u0435\u0442 \u043e\u0448\u0438\u0431\u043e\u0447\u043d\u043e \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u044c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1<\/span><\/span><br \/>\n \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_2 = \\sum_{n=0}^{+\\infty} (1-x)^n <\/span><\/span> \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0434\u0430\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f; \u043e\u0434\u043d\u0430\u043a\u043e \u043e\u043d \u0443\u043f\u0443\u0441\u0442\u0438\u0442 \u0438\u0437 \u0432\u0438\u0434\u0443, \u0447\u0442\u043e \u044d\u0442\u043e\u0442 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0440\u044f\u0434 \u0441\u043f\u0440\u0430\u0432\u0435\u0434\u043b\u0438\u0432 \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|1-x| \\lt 1<\/span><\/span>, \u0442\u043e \u0435\u0441\u0442\u044c \u043a\u043e\u0433\u0434\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in]0,2[)<\/span><\/span>. \u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]0,2[\\subset]0,+\\infty[<\/span><\/span>, \u0442\u0430\u043a\u0436\u0435 \u0441\u043f\u0440\u0430\u0432\u0435\u0434\u043b\u0438\u0432\u043e, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1<\/span><\/span> \u043f\u0440\u043e\u0434\u043e\u043b\u0436\u0430\u0435\u0442\u0441\u044f \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_2<\/span><\/span>, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438, \u0433\u0434\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_2<\/span><\/span> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\psi_1<\/span><\/span> \u0442\u0430\u043a\u0436\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u0438 \u0432\u044b\u0445\u043e\u0434\u0438\u0442 \u0437\u0430 \u0435\u0451 \u043f\u0440\u0435\u0434\u0435\u043b\u044b.<\/P><\/p>\n<p><a name=\"SolucionExtendidaYSolucionMaximal\"><\/a><\/p>\n<h4>\u0420\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/h4>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0434\u0432\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_1<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_2<\/span><\/span>, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0430\u0445 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{\\phi_1}<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{\\phi_2},<\/span><\/span> \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{\\phi_1}\\subset I_{\\phi_2},<\/span><\/span> \u0442\u043e \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_2<\/span><\/span> \u0440\u0430\u0441\u0448\u0438\u0440\u044f\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_1,<\/span><\/span> \u0438\u043b\u0438 \u0447\u0442\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_2<\/span><\/span> \u0431\u043e\u043b\u0435\u0435 \u043e\u0431\u0449\u0435\u0435, \u0447\u0435\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_1.<\/span><\/span> \u0420\u0435\u0448\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">\\phi<\/span> \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u00ab\u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u043c\u00bb, \u0435\u0441\u043b\u0438 \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0434\u0440\u0443\u0433\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0431\u044b \u0435\u0433\u043e \u043d\u0435\u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u043e \u0440\u0430\u0441\u0448\u0438\u0440\u044f\u043b\u043e.<\/p>\n<p><a name=\"SolucionExplicitaYSolucionImplicita\"><\/a><\/p>\n<h4>\u042f\u0432\u043d\u043e\u0435 \u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=zE29azRIKng&#038;t=2649s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">\\phi<\/span> \u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u041e\u0414\u0423 \u043f\u043e\u0440\u044f\u0434\u043a\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> (\u0437\u0430\u043f\u0438\u0441\u0430\u043d\u043d\u043e\u0433\u043e \u0432 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u0435)<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^{(n)}(x)=f(x,y(x),y^\\prime(x),\\cdots,y^{(n-1)}(x)),<\/span>\n<p>\u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span>, \u0435\u0441\u043b\u0438<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall x\\in I)\\left(\\phi^{n}(x) = f(x,\\phi(x),\\phi^\\prime(x),\\cdots,\\phi^{(n-1)}(x))\\right)<\/span>\n<p>\u0422\u043e, \u0447\u0442\u043e \u043c\u044b \u0443\u0436\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u043b\u0438 \u0440\u0430\u043d\u0435\u0435, \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e \u043a\u0430\u043a <strong>\u044f\u0432\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">I.<\/span><\/strong> \u041a\u0430\u043a \u0441\u043b\u0435\u0434\u0443\u0435\u0442 \u0438\u0437 \u043d\u0430\u0437\u0432\u0430\u043d\u0438\u044f, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0438 \u043d\u0435\u044f\u0432\u043d\u0430\u044f \u0444\u043e\u0440\u043c\u0430 \u0437\u0430\u0434\u0430\u043d\u0438\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0439. \u0413\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi(x,y)=0<\/span><\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u043d\u0435\u044f\u0432\u043d\u044b\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/strong>, \u0435\u0441\u043b\u0438 \u043e\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442 \u0434\u0432\u0430 \u0438\u043b\u0438 \u0431\u043e\u043b\u0435\u0435 \u043d\u0435\u044f\u0432\u043d\u044b\u0445 \u0440\u0435\u0448\u0435\u043d\u0438\u0439 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I.<\/span>\n<h3>\u0417\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435<\/h3>\n<p>\u041d\u0430 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u043c\u044b \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441 \u043f\u043e\u0437\u0438\u0446\u0438\u0438 \u0441\u0442\u0440\u043e\u0433\u043e\u0433\u043e, \u043d\u043e \u0434\u043e\u0441\u0442\u0443\u043f\u043d\u043e\u0433\u043e \u043f\u043e\u0434\u0445\u043e\u0434\u0430, \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0432 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0435 \u043e\u0441\u043d\u043e\u0432\u044b, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0438\u0435 \u043d\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u0440\u0430\u0441\u043f\u043e\u0437\u043d\u0430\u0432\u0430\u0442\u044c \u041e\u0414\u0423, \u043d\u043e \u0438 \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c \u043b\u043e\u0433\u0438\u043a\u0443, \u043b\u0435\u0436\u0430\u0449\u0443\u044e \u0432 \u043e\u0441\u043d\u043e\u0432\u0435 \u0438\u0445 \u0440\u0435\u0448\u0435\u043d\u0438\u0439. \u0411\u043b\u0430\u0433\u043e\u0434\u0430\u0440\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u043d\u0435\u044f\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0443\u0434\u0430\u043b\u043e\u0441\u044c \u0447\u0451\u0442\u043a\u043e \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u0442\u044c \u043f\u0435\u0440\u0435\u0445\u043e\u0434 \u043e\u0442 \u043e\u0431\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043a \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439, \u0447\u0442\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043a\u043b\u044e\u0447\u0435\u0432\u0443\u044e \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u043e\u0441\u0442\u044c \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447.<\/p>\n<p>\u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u0442\u043e\u0447\u043d\u043e \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u043b\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u0441\u043f\u043e\u0441\u043e\u0431\u044b \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f: \u043a\u0430\u043a \u044f\u0432\u043d\u043e\u0433\u043e \u0438\u043b\u0438 \u043d\u0435\u044f\u0432\u043d\u043e\u0433\u043e, \u0440\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u043d\u043e\u0433\u043e \u0438\u043b\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e, \u0438 \u043f\u043e\u0434\u0447\u0435\u0440\u043a\u043d\u0443\u043b\u0438 \u0432\u0430\u0436\u043d\u043e\u0441\u0442\u044c \u2014 \u0447\u0430\u0441\u0442\u043e \u043d\u0435\u0434\u043e\u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c\u0443\u044e \u2014 \u043a\u043e\u0440\u0440\u0435\u043a\u0442\u043d\u043e\u0433\u043e \u0443\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f. \u042d\u0442\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u044f \u2014 \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u044c: \u043e\u043d\u0438 \u0438\u043c\u0435\u044e\u0442 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435. \u0418\u0445 \u0438\u0433\u043d\u043e\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u043c\u043e\u0436\u0435\u0442, \u043a\u0430\u043a \u043c\u044b \u0443\u0432\u0438\u0434\u0435\u043b\u0438, \u043f\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u043a \u0441\u0435\u0440\u044c\u0451\u0437\u043d\u044b\u043c \u043a\u043e\u043d\u0446\u0435\u043f\u0442\u0443\u0430\u043b\u044c\u043d\u044b\u043c \u043e\u0448\u0438\u0431\u043a\u0430\u043c \u043f\u0440\u0438 \u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0430\u0446\u0438\u0438 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0445 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)? \u0420\u0435\u0437\u044e\u043c\u0435:\u0412 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u044b\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f (\u041e\u0414\u0423) \u043f\u043e\u0440\u044f\u0434\u043a\u0430 k, \u043d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 \u0438\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0432 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u0438 \u043e\u0431\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0435. \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0442\u0430\u043a\u0438\u0445 \u043f\u043e\u043d\u044f\u0442\u0438\u0439, \u043a\u0430\u043a \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438 \u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0435\u044f\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0437\u0430\u043a\u043b\u0430\u0434\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0441\u043d\u043e\u0432\u044b \u0434\u043b\u044f \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0439 \u044d\u0442\u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0438 \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u044b\u0445 \u0441 \u043d\u0438\u043c\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432, \u0442\u0430\u043a\u0438\u0445 \u043a\u0430\u043a \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":32838,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":4,"footnotes":""},"categories":[19,573,1160],"tags":[],"class_list":["post-32866","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sin-categoria-ru","category-573","category-1160"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)? - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0423\u0437\u043d\u0430\u0439, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043e\u0432\u043b\u0430\u0434\u0435\u0439 \u0435\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043c\u0438 \u0441 \u044f\u0441\u043d\u043e\u0441\u0442\u044c\u044e, \u0441\u0442\u0440\u043e\u0433\u043e\u0441\u0442\u044c\u044e \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/ru\/\u0447\u0442\u043e-\u0442\u0430\u043a\u043e\u0435-\u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435-\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?\" \/>\n<meta property=\"og:description\" content=\"\u0423\u0437\u043d\u0430\u0439, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043e\u0432\u043b\u0430\u0434\u0435\u0439 \u0435\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043c\u0438 \u0441 \u044f\u0441\u043d\u043e\u0441\u0442\u044c\u044e, \u0441\u0442\u0440\u043e\u0433\u043e\u0441\u0442\u044c\u044e \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/ru\/\u0447\u0442\u043e-\u0442\u0430\u043a\u043e\u0435-\u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435-\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2022-04-28T13:00:43+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-04-03T23:15:02+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo-1024x381.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?\" \/>\n<meta name=\"twitter:description\" content=\"\u0423\u0437\u043d\u0430\u0439, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043e\u0432\u043b\u0430\u0434\u0435\u0439 \u0435\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043c\u0438 \u0441 \u044f\u0441\u043d\u043e\u0441\u0442\u044c\u044e, \u0441\u0442\u0440\u043e\u0433\u043e\u0441\u0442\u044c\u044e \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?\",\"datePublished\":\"2022-04-28T13:00:43+00:00\",\"dateModified\":\"2025-04-03T23:15:02+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/\"},\"wordCount\":1789,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg\",\"articleSection\":{\"1\":\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\",\"2\":\"\u041e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u044b\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/\",\"url\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/\",\"name\":\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)? - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg\",\"datePublished\":\"2022-04-28T13:00:43+00:00\",\"dateModified\":\"2025-04-03T23:15:02+00:00\",\"description\":\"\u0423\u0437\u043d\u0430\u0439, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043e\u0432\u043b\u0430\u0434\u0435\u0439 \u0435\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043c\u0438 \u0441 \u044f\u0441\u043d\u043e\u0441\u0442\u044c\u044e, \u0441\u0442\u0440\u043e\u0433\u043e\u0441\u0442\u044c\u044e \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438.\",\"breadcrumb\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#primaryimage\",\"url\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg\",\"contentUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg\",\"width\":1792,\"height\":666,\"caption\":\"toposuranos.com\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/toposuranos.com\/material\/#website\",\"url\":\"https:\/\/toposuranos.com\/material\/\",\"name\":\"toposuranos.com\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/toposuranos.com\/material\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\",\"name\":\"toposuranos.com\/material\",\"url\":\"https:\/\/toposuranos.com\/material\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\/material\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/groups\/toposuranos\",\"https:\/\/x.com\/topuranos\",\"https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\/\/www.linkedin.com\/company\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\/\/toposuranos.com\/material\"],\"url\":\"https:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)? - toposuranos.com\/material","description":"\u0423\u0437\u043d\u0430\u0439, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043e\u0432\u043b\u0430\u0434\u0435\u0439 \u0435\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043c\u0438 \u0441 \u044f\u0441\u043d\u043e\u0441\u0442\u044c\u044e, \u0441\u0442\u0440\u043e\u0433\u043e\u0441\u0442\u044c\u044e \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/toposuranos.com\/material\/ru\/\u0447\u0442\u043e-\u0442\u0430\u043a\u043e\u0435-\u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435-\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\/","og_locale":"es_ES","og_type":"article","og_title":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?","og_description":"\u0423\u0437\u043d\u0430\u0439, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043e\u0432\u043b\u0430\u0434\u0435\u0439 \u0435\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043c\u0438 \u0441 \u044f\u0441\u043d\u043e\u0441\u0442\u044c\u044e, \u0441\u0442\u0440\u043e\u0433\u043e\u0441\u0442\u044c\u044e \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438.","og_url":"https:\/\/toposuranos.com\/material\/ru\/\u0447\u0442\u043e-\u0442\u0430\u043a\u043e\u0435-\u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435-\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2022-04-28T13:00:43+00:00","article_modified_time":"2025-04-03T23:15:02+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo-1024x381.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?","twitter_description":"\u0423\u0437\u043d\u0430\u0439, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043e\u0432\u043b\u0430\u0434\u0435\u0439 \u0435\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043c\u0438 \u0441 \u044f\u0441\u043d\u043e\u0441\u0442\u044c\u044e, \u0441\u0442\u0440\u043e\u0433\u043e\u0441\u0442\u044c\u044e \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438.","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?","datePublished":"2022-04-28T13:00:43+00:00","dateModified":"2025-04-03T23:15:02+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/"},"wordCount":1789,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg","articleSection":{"1":"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430","2":"\u041e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u044b\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f"},"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/","url":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/","name":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)? - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg","datePublished":"2022-04-28T13:00:43+00:00","dateModified":"2025-04-03T23:15:02+00:00","description":"\u0423\u0437\u043d\u0430\u0439, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0438 \u043e\u0432\u043b\u0430\u0434\u0435\u0439 \u0435\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043c\u0438 \u0441 \u044f\u0441\u043d\u043e\u0441\u0442\u044c\u044e, \u0441\u0442\u0440\u043e\u0433\u043e\u0441\u0442\u044c\u044e \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438.","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2022\/04\/edo.jpg","width":1792,"height":666,"caption":"toposuranos.com"},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/ru\/%d1%87%d1%82%d0%be-%d1%82%d0%b0%d0%ba%d0%be%d0%b5-%d0%be%d0%b1%d1%8b%d0%ba%d0%bd%d0%be%d0%b2%d0%b5%d0%bd%d0%bd%d0%be%d0%b5-%d0%b4%d0%b8%d1%84%d1%84%d0%b5%d1%80%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u041e\u0414\u0423)?"}]},{"@type":"WebSite","@id":"https:\/\/toposuranos.com\/material\/#website","url":"https:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"https:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"https:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"https:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/32866","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=32866"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/32866\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/32838"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=32866"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=32866"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=32866"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}