{"id":32814,"date":"2022-03-15T13:00:49","date_gmt":"2022-03-15T13:00:49","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=32814"},"modified":"2025-04-03T12:22:35","modified_gmt":"2025-04-03T12:22:35","slug":"%e0%a4%b8%e0%a4%be%e0%a4%a7%e0%a4%be%e0%a4%b0%e0%a4%a3-%e0%a4%85%e0%a4%b5%e0%a4%95%e0%a4%b2-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%be%e0%a4%a7%e0%a4%be%e0%a4%b0%e0%a4%a3-%e0%a4%85%e0%a4%b5%e0%a4%95%e0%a4%b2-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa\/","title":{"rendered":"\u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f"},"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>\u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f<\/h1>\n<p style=\"text-align:center;\"><em>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0907\u0928 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0914\u0930 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u094b\u0902 \u092e\u0947\u0902 \u0909\u0928\u0915\u0947 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u0915\u094b \u0928\u093f\u092f\u0902\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u092e\u094c\u0932\u093f\u0915 \u0935\u093f\u091a\u093e\u0930\u094b\u0902 \u0915\u0940 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0916\u094b\u091c \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0939\u092e\u093e\u0930\u0947 \u091a\u093e\u0930\u094b\u0902 \u0913\u0930 \u0915\u0940 \u0926\u0941\u0928\u093f\u092f\u093e \u092e\u0947\u0902 \u0928\u093f\u0930\u0902\u0924\u0930 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0940 \u092a\u094d\u0930\u0915\u0943\u0924\u093f \u0915\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0915\u0930, \u0915\u093e\u0930\u094d\u092f, \u0905\u0935\u0915\u0932\u091c \u0914\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0924\u0925\u093e \u0935\u093f\u0935\u093f\u0915\u094d\u0924 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u0938\u093e\u0925 \u0909\u0928\u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u091c\u0948\u0938\u0947 \u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0906\u0902\u0936\u093f\u0915 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 (\u0908\u0921\u0940\u092a\u0940) \u0914\u0930 \u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 (\u0908\u0921\u0940\u0913) \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0905\u0902\u0924\u0930 \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u0908\u0921\u0940\u0913 \u0915\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u091c\u0948\u0938\u0947 \u090f\u0915 \u0915\u092a \u0915\u0949\u092b\u0940 \u0915\u093e \u0920\u0902\u0921\u093e \u0939\u094b\u0928\u093e, \u0928\u094d\u092f\u0942\u091f\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e \u0914\u0930 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0949\u0921\u0932 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0938\u094d\u092a\u0937\u094d\u091f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0914\u0930 \u092d\u094c\u0924\u093f\u0915 \u0918\u091f\u0928\u093e\u0913\u0902 \u0915\u094b \u0928\u093f\u092f\u0902\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0938\u0947 \u092a\u0930\u093f\u091a\u093f\u0924 \u0939\u094b\u0928\u0947, \u0909\u0928\u094d\u0939\u0947\u0902 \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0915\u0948\u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u092f\u0939 \u091c\u093e\u0928\u0928\u0947 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0915\u0941\u091b \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u093e \u0905\u0935\u0938\u0930 \u092e\u093f\u0932\u0947\u0917\u093e\u0964 \u092f\u0939 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u091c\u094d\u091e\u093e\u0928 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0914\u0930 \u0935\u093f\u091c\u094d\u091e\u093e\u0928 \u090f\u0935\u0902 \u0905\u092d\u093f\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915\u0940 \u092e\u0947\u0902 \u0909\u0928\u0915\u0947 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u0915\u0947 \u0909\u0928\u094d\u0928\u0924 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0932\u093f\u090f \u0906\u0927\u093e\u0930 \u0924\u0948\u092f\u093e\u0930 \u0915\u0930\u0947\u0917\u093e\u0964<\/em><\/p>\n<p style=\"text-align:center;\"><strong><u>\u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/u>:<\/strong><br \/>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902 \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0917\u093e:<\/p>\n<ol>\n<li><strong>\u0938\u092e\u091d\u0928\u093e<\/strong> \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b, \u091c\u0948\u0938\u0947 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0940 \u092a\u094d\u0930\u0915\u0943\u0924\u093f, \u0915\u093e\u0930\u094d\u092f, \u0905\u0935\u0915\u0932\u091c \u0914\u0930 \u0906\u0902\u0936\u093f\u0915 (\u0908\u0921\u0940\u092a\u0940) \u0914\u0930 \u0938\u093e\u0927\u093e\u0930\u0923 (\u0908\u0921\u0940\u0913) \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0905\u0902\u0924\u0930<\/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>\u0938\u0942\u091a\u0915\u093e\u0902\u0915<\/strong><br \/>\n<a href=\"#LasEcuacionesDiferencialesYLaNaturalezaDeLasCosas\"><strong>\u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0935\u0938\u094d\u0924\u0941\u0913\u0902 \u0915\u0940 \u092a\u094d\u0930\u0915\u0943\u0924\u093f<\/strong><\/a><br \/>\n<a href=\"#ElCambioIncesante\">\u0928\u093f\u0930\u0902\u0924\u0930 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928<\/a><br \/>\n<a href=\"#FuncionesDerivadasYSusCambios\">\u0915\u093e\u0930\u094d\u092f, \u0905\u0935\u0915\u0932\u091c \u0914\u0930 \u0909\u0928\u0915\u0947 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928<\/a><br \/>\n<a href=\"#EDOyEDP\">\u0908\u0921\u0940\u0913 \u0914\u0930 \u0908\u0921\u0940\u092a\u0940<\/a><br \/>\n<a href=\"#EjemplosDeEcuacionesDiferencialesOrdinarias\"><strong>\u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923<\/strong><\/a><br \/>\n<a href=\"#ElEnfriamientoDeUnaTazaDeCafe\">\u090f\u0915 \u0915\u092a \u0915\u0949\u092b\u0940 \u0915\u093e \u0920\u0902\u0921\u093e \u0939\u094b\u0928\u093e<\/a><br \/>\n<a href=\"#LasLeyesDeNewton\">\u0928\u094d\u092f\u0942\u091f\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e<\/a><br \/>\n<a href=\"#ModeloDePoblaciones\">\u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0949\u0921\u0932<\/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>\u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0935\u0938\u094d\u0924\u0941\u0913\u0902 \u0915\u0940 \u092a\u094d\u0930\u0915\u0943\u0924\u093f<\/h2>\n<p><a name=\"ElCambioIncesante\"><\/a><\/p>\n<h3>\u0928\u093f\u0930\u0902\u0924\u0930 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=133s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u092a\u094d\u0930\u0915\u0943\u0924\u093f \u092e\u0947\u0902, \u0938\u092c \u0915\u0941\u091b \u0928\u093f\u0930\u0902\u0924\u0930 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u092e\u0947\u0902 \u0939\u0948\u0964<\/span><\/strong><\/a> \u092f\u0939\u093e\u0901 \u0924\u0915 \u0915\u093f \u091c\u094b \u0915\u0941\u091b \u0915\u092d\u0940 \u0928\u0939\u0940\u0902 \u092c\u0926\u0932\u0924\u093e \u092a\u094d\u0930\u0924\u0940\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u0948\u0938\u0947 \u0938\u0942\u0930\u094d\u092f \u0915\u0940 \u091a\u092e\u0915, \u0935\u0939 \u092d\u0940 \u0938\u092e\u092f \u0915\u0947 \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u092a\u0948\u092e\u093e\u0928\u0947 \u092a\u0930 \u0926\u0947\u0916\u0928\u0947 \u092a\u0930 \u092c\u0926\u0932\u0924\u0940 \u0939\u0948\u0964 \u0938\u092c \u0915\u0941\u091b \u092c\u0926\u0932\u0924\u093e \u0939\u0948: \u0924\u093e\u0930\u094b\u0902 \u0915\u0940 \u091a\u092e\u0915, \u090f\u0915 \u0915\u092a \u092e\u0947\u0902 \u0915\u0949\u092b\u0940 \u0915\u093e \u0924\u093e\u092a\u092e\u093e\u0928, \u0915\u093f\u0938\u0940 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f, \u0914\u0930 \u0915\u093f\u0938\u0940 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0906\u0915\u093e\u0930 \u0915\u0941\u091b \u0909\u0926\u093e\u0939\u0930\u0923 \u0939\u0948\u0902, \u0914\u0930 \u0907\u0928 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928\u094b\u0902 \u0915\u0940 \u0926\u0930\u0947\u0902 \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u0909\u0938 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0905\u0935\u0938\u094d\u0925\u093e \u0938\u0947 \u091c\u0941\u0921\u093c\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902 \u091c\u094b \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u0926\u094c\u0930\u093e\u0928 \u092c\u0926\u0932 \u0930\u0939\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p>\u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u093e \u090f\u0915 \u0938\u0939\u091c \u0924\u0930\u0940\u0915\u093e \u0939\u0948 \u092f\u0939 \u0926\u0947\u0916\u0928\u093e \u0915\u093f \u0938\u092e\u092f \u092c\u0940\u0924\u0928\u0947 \u0915\u0947 \u0938\u093e\u0925 \u091a\u0940\u091c\u0947\u0902 \u0915\u0948\u0938\u0947 \u092c\u0926\u0932\u0924\u0940 \u0939\u0948\u0902\u0964 \u091c\u094b \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0939\u094b\u0924\u093e \u0939\u0948, \u0909\u0938\u0947 \u0939\u092e \u0935\u093f\u0915\u093e\u0938 (evolution) \u0915\u0939\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u091c\u094b \u0915\u0941\u091b \u092d\u0940 \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0935\u0939 \u0928\u093f\u0930\u0902\u0924\u0930 \u0935\u093f\u0915\u093e\u0938\u0936\u0940\u0932 \u0939\u0948\u0964 \u0932\u0947\u0915\u093f\u0928 \u0935\u093f\u0915\u093e\u0938 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u090f\u0915\u092e\u093e\u0924\u094d\u0930 \u0930\u0942\u092a \u0928\u0939\u0940\u0902 \u0939\u0948; \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u094d\u092f\u092a\u093f \u0938\u092e\u0941\u0926\u094d\u0930 \u0924\u0932 \u0938\u0947 \u0939\u092e\u093e\u0930\u0940 \u090a\u0901\u091a\u093e\u0908 \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u092c\u0926\u0932 \u0938\u0915\u0924\u0940 \u0939\u0948, \u092f\u0939 \u0905\u0927\u093f\u0915 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0939\u0948 \u0915\u093f \u092f\u0939 \u0939\u092e\u093e\u0930\u0940 \u0938\u094d\u0925\u093f\u0924\u093f (\u092f\u093e \u092d\u094c\u0917\u094b\u0932\u093f\u0915 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915\u094b\u0902) \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u092c\u0926\u0932\u0947\u0964<\/p>\n<p><a name=\"FuncionesDerivadasYSusCambios\"><\/a><\/p>\n<h3>\u0915\u093e\u0930\u094d\u092f, \u0905\u0935\u0915\u0932\u091c \u0914\u0930 \u0909\u0928\u0915\u0947 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=301s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u0914\u0930 \u0905\u0927\u093f\u0915 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902,<\/span><\/strong><\/a> \u0915\u0908 \u091a\u0930\u094b\u0902 \u0935\u093e\u0932\u093e \u090f\u0915 \u092b\u0932\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_1,x_2, \\cdots, x_n)<\/span><\/span> \u0924\u092c \u092c\u0926\u0932 \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u092c \u0907\u0938\u0915\u0940 \u0915\u094b\u0908 \u092d\u0940 \u091a\u0930 \u092c\u0926\u0932\u0947, \u0914\u0930 \u092f\u0939 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0938\u0924\u0924 \u092f\u093e \u0935\u093f\u0935\u093f\u0915\u094d\u0924 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0915\u0908 \u091a\u0930\u094b\u0902 \u0935\u093e\u0932\u0947 \u092b\u0932\u0928 \u0915\u0947 \u0932\u093f\u090f, \u0938\u0924\u0924 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 <strong>\u0906\u0902\u0936\u093f\u0915 \u0905\u0935\u0915\u0932\u091c<\/strong> \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/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>\u092f\u0926\u093f \u092b\u0932\u0928 \u090f\u0915 \u0939\u0940 \u091a\u0930 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948, \u0924\u094b <strong>\u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932\u091c<\/strong> \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/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>\u092f\u0926\u093f \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0938\u0924\u0924 \u0915\u0947 \u092c\u091c\u093e\u092f \u0935\u093f\u0935\u093f\u0915\u094d\u0924 \u0939\u094b, \u0924\u094b \u0905\u0935\u0915\u0932\u091c \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0928\u0947 \u0935\u093e\u0932\u0940 \u0938\u0940\u092e\u093e (limit) \u0915\u0940 \u0917\u0923\u0928\u093e \u0928\u0939\u0940\u0902 \u0915\u0940 \u091c\u093e\u0924\u0940\u0964<\/p>\n<p><a name=\"EDOyEDP\"><\/a><\/p>\n<h3>\u0908\u0921\u0940\u0913 \u0914\u0930 \u0908\u0921\u0940\u092a\u0940<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=624s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u090f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u091c\u093f\u0938\u092e\u0947\u0902 \u0915\u093f\u0938\u0940 \u092b\u0932\u0928 \u0914\u0930 \u0909\u0938\u0915\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0905\u0935\u0915\u0932\u091c \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0902<\/span><\/strong><\/a> \u0909\u0938\u0947 <strong>\u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u092f\u0947 \u0905\u0935\u0915\u0932\u091c \u0906\u0902\u0936\u093f\u0915 \u092f\u093e \u0938\u093e\u0927\u093e\u0930\u0923 \u0939\u094b\u0902, \u0924\u094b \u0907\u0928\u094d\u0939\u0947\u0902 \u0915\u094d\u0930\u092e\u0936\u0903 <strong>\u0906\u0902\u0936\u093f\u0915 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923 (\u0908\u0921\u0940\u092a\u0940)<\/strong> \u092f\u093e <strong>\u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923 (\u0908\u0921\u0940\u0913)<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0938\u092e\u092f, \u0939\u092e \u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u0915\u0941\u091b \u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947 \u091c\u0939\u093e\u0901 \u092f\u0947 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"EjemplosDeEcuacionesDiferencialesOrdinarias\"><\/a><\/p>\n<h2>\u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923<\/h2>\n<p><a name=\"ElEnfriamientoDeUnaTazaDeCafe\"><\/a><\/p>\n<h3>\u090f\u0915 \u0915\u092a \u0915\u0949\u092b\u0940 \u0915\u093e \u0920\u0902\u0921\u093e \u0939\u094b\u0928\u093e<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=680s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u090f\u0915 \u0915\u092a \u0915\u0949\u092b\u0940 \u0915\u0947 \u0920\u0902\u0921\u093e \u0939\u094b\u0928\u0947 \u0915\u0940 \u0926\u0930<\/span><\/strong><\/a> \u0935\u093e\u0924\u093e\u0935\u0930\u0923 \u0914\u0930 \u0915\u0949\u092b\u0940 \u0915\u0947 \u0924\u093e\u092a\u092e\u093e\u0928 \u0915\u0947 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u092f\u0926\u093f \u0939\u0935\u093e \u0915\u093e \u0924\u093e\u092a\u092e\u093e\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_a<\/span><\/span> \u0938\u094d\u0925\u093f\u0930 \u0939\u0948 \u0914\u0930 \u0915\u0949\u092b\u0940 \u0915\u093e \u0924\u093e\u092a\u092e\u093e\u0928 \u0938\u092e\u092f \u0915\u093e \u092b\u0932\u0928 \u0939\u0948 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_c=T_c(t),<\/span><\/span> \u0924\u094b \u0939\u092e \u090f\u0915 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u094d\u0937\u0923 \u092e\u0947\u0902 \u0915\u0949\u092b\u0940 \u0915\u093e \u0924\u093e\u092a\u092e\u093e\u0928 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0917\u093e\u0964 \u092a\u094d\u0930\u093e\u0930\u0902\u092d \u092e\u0947\u0902 \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u094b\u0924\u093e \u0939\u0948:<\/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>\u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u090f\u0915 \u0905\u0928\u0941\u092a\u093e\u0924\u093e\u0902\u0915 (proportionality constant) \u0939\u0948, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_a \\lt T_c(t)<\/span><\/span> \u0914\u0930 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u091a\u093f\u0928\u094d\u0939 \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u0949\u092b\u0940 \u0915\u093e \u0924\u093e\u092a\u092e\u093e\u0928 \u0918\u091f \u0930\u0939\u093e \u0939\u0948\u0964 \u092c\u093e\u0926 \u092e\u0947\u0902, \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0939\u0932 \u0907\u0938 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u094b\u0924\u093e \u0939\u0948:<\/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>\u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u090f\u0915 \u0928\u093f\u092f\u0924\u093e\u0902\u0915 (constant) \u0939\u0948 \u091c\u093f\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0928\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"LasLeyesDeNewton\"><\/a><\/p>\n<h3>\u0928\u094d\u092f\u0942\u091f\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=885s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u0928\u094d\u092f\u0942\u091f\u0928 \u0915\u093e \u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0928\u093f\u092f\u092e \u092e\u0942\u0932 \u0930\u0942\u092a \u0938\u0947 \u090f\u0915 \u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u0948,<\/span><\/strong><\/a> \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F=ma<\/span><\/span> (\u092c\u0932 = \u0926\u094d\u0930\u0935\u094d\u092f\u092e\u093e\u0928 \u00d7 \u0924\u094d\u0935\u0930\u0923) \u092e\u0947\u0902, \u0924\u094d\u0935\u0930\u0923 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a=d^2x(t)\/dt^2,<\/span><\/span> \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u092a\u0947\u0915\u094d\u0937 \u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0905\u0935\u0915\u0932\u091c \u0939\u0948\u0964 \u0907\u0938 \u0928\u093f\u092f\u092e \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947, \u0939\u092e \u0910\u0938\u0947 \u0938\u0902\u092c\u0902\u0927 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u092a\u093f\u0902\u0921\u094b\u0902 \u0915\u0940 \u0917\u0924\u093f \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u090f\u0915 \u0938\u0930\u0932 \u0909\u0926\u093e\u0939\u0930\u0923 \u0939\u0948 \u0938\u094d\u092a\u094d\u0930\u093f\u0902\u0917 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928: \u092f\u0926\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u0938\u094d\u092a\u094d\u0930\u093f\u0902\u0917 \u0939\u0948 \u091c\u094b \u090f\u0915 \u0913\u0930 \u090f\u0915 \u0926\u0940\u0935\u093e\u0930 \u0938\u0947 \u0914\u0930 \u0926\u0942\u0938\u0930\u0940 \u0913\u0930 \u090f\u0915 \u0926\u094d\u0930\u0935\u094d\u092f\u092e\u093e\u0928 \u0938\u0947 \u091c\u0941\u0921\u093c\u093e \u0939\u0941\u0906 \u0939\u0948, \u0914\u0930 \u0939\u092e \u0909\u0938 \u0926\u094d\u0930\u0935\u094d\u092f\u092e\u093e\u0928 \u0915\u094b \u0938\u0902\u0924\u0941\u0932\u0928 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u0926\u0942\u0930\u0940 \u0924\u0915 \u0935\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u0941\u0915 \u0915\u0947 \u0928\u093f\u092f\u092e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0909\u0938 \u0926\u094d\u0930\u0935\u094d\u092f\u092e\u093e\u0928 \u092a\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u093e\u0938\u094d\u0925 \u092c\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F=-kx<\/span><\/span> \u0915\u093e\u0930\u094d\u092f \u0915\u0930\u0947\u0917\u093e\u0964 \u092b\u093f\u0930 \u0928\u094d\u092f\u0942\u091f\u0928 \u0915\u0947 \u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0928\u093f\u092f\u092e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930, \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/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>\u0906\u0917\u0947 \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0907\u0938\u0915\u093e \u0938\u092e\u093e\u0927\u093e\u0928 \u0907\u0938 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u094b\u0924\u093e \u0939\u0948:<\/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>\u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\phi<\/span> \u0928\u093f\u092f\u0924\u093e\u0902\u0915 \u0939\u0948\u0902 \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0940 <strong>\u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902<\/strong> \u0926\u094d\u0935\u093e\u0930\u093e \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0917\u093e\u0964<\/p>\n<p><a name=\"ModeloDePoblaciones\"><\/a><\/p>\n<h3>\u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0949\u0921\u0932<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KgUDA2Q1qaA&#038;t=1184s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u092a\u094d\u0930\u0924\u093f \u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0935\u0943\u0926\u094d\u0927\u093f \u0926\u0930<\/span><\/strong><\/a> \u0915\u093f\u0938\u0940 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0940 \u091c\u0928\u094d\u092e \u0914\u0930 \u092e\u0943\u0924\u094d\u092f\u0941 \u0926\u0930 \u0915\u0947 \u092c\u0940\u091a \u0905\u0902\u0924\u0930 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924\u094d:<\/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>\u092f\u0926\u093f \u091c\u0928\u094d\u092e \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u0938\u094d\u0925\u093f\u0930 \u0930\u0939\u0924\u0940 \u0939\u0948 \u0914\u0930 \u092e\u0943\u0924\u094d\u092f\u0941 \u0926\u0930 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0938\u092e\u093e\u0928\u0941\u092a\u093e\u0924\u0940 \u0939\u094b, \u0905\u0930\u094d\u0925\u093e\u0924\u094d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M=\\alpha^2 x(t),<\/span><\/span> \u0924\u092c \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0907\u0938 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948:<\/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>\u0907\u0938\u0947 <strong>\u00ab\u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0940 \u0932\u0949\u091c\u093f\u0938\u094d\u091f\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923\u00bb<\/strong> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947, \u0939\u092e \u0915\u0908 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1(t), x_2(t), \\cdots, x_n(t)<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u0947 \u0932\u093f\u090f \u0906\u092a\u0938 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u092a\u0930\u094d\u0927\u093e \u0915\u0930\u0924\u0940 \u0939\u0948\u0902:<\/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>\u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">i\\in\\{1,\\cdots, n\\}<\/span><\/span>\u0964 \u0907\u0938\u0947 <strong>\u0932\u0949\u091f\u0915\u093e-\u0935\u094b\u0932\u094d\u091f\u0947\u0930\u093e \u0938\u092e\u0940\u0915\u0930\u0923<\/strong> \u0915\u0947 \u0928\u093e\u092e \u0938\u0947 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<h2>\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h2>\n<p>\u0938\u093e\u0927\u093e\u0930\u0923 \u0905\u0935\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u0907\u0938 \u092a\u0930\u093f\u091a\u092f \u0915\u0947 \u0926\u094c\u0930\u093e\u0928, \u0939\u092e\u0928\u0947 \u0926\u0947\u0916\u093e \u0915\u093f \u0915\u0948\u0938\u0947 \u0917\u0923\u093f\u0924 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u091c\u0917\u0924 \u092e\u0947\u0902 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928\u094b\u0902 \u0915\u094b \u0938\u091f\u0940\u0915 \u0914\u0930 \u0938\u0941\u0930\u0941\u091a\u093f\u092a\u0942\u0930\u094d\u0923 \u0922\u0902\u0917 \u0938\u0947 \u0926\u0930\u094d\u0936\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u091a\u093e\u0939\u0947 \u0935\u0939 \u090f\u0915 \u0915\u092a \u0915\u0949\u092b\u0940 \u0915\u093e \u0920\u0902\u0921\u093e \u0939\u094b\u0928\u093e \u0939\u094b, \u090f\u0915 \u0938\u094d\u092a\u094d\u0930\u093f\u0902\u0917 \u0915\u0940 \u0917\u0924\u093f \u092f\u093e \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0940 \u0935\u0943\u0926\u094d\u0927\u093f \u2014 \u0908\u0921\u0940\u0913 \u0939\u092e\u0947\u0902 \u091c\u091f\u093f\u0932 \u0917\u0924\u093f\u0936\u0940\u0932\u0924\u093e\u0913\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u092f\u094b\u0917\u094d\u092f \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u092e\u0947\u0902 \u0905\u0928\u0941\u0935\u093e\u0926 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p>\u0907\u0928 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0940 \u0938\u0902\u0930\u091a\u0928\u093e \u0914\u0930 \u0905\u0930\u094d\u0925 \u0915\u094b \u0938\u092e\u091d\u0928\u093e \u092d\u094c\u0924\u093f\u0915\u0940, \u091c\u0940\u0935\u0935\u093f\u091c\u094d\u091e\u093e\u0928, \u0905\u0930\u094d\u0925\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u0914\u0930 \u0905\u092d\u093f\u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915\u0940 \u091c\u0948\u0938\u0940 \u0915\u0908 \u0935\u093f\u0927\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u092e\u093e\u0930\u094d\u0917 \u0916\u094b\u0932\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u0915\u0915\u094d\u0937\u093e \u0909\u0928 \u0935\u0948\u091a\u093e\u0930\u093f\u0915 \u0928\u0940\u0902\u0935\u094b\u0902 \u0915\u0940 \u0938\u094d\u0925\u093e\u092a\u0928\u093e \u0915\u0930\u0924\u0940 \u0939\u0948 \u091c\u094b \u0906\u0917\u0947 \u0915\u0947 \u0909\u0928\u094d\u0928\u0924 \u0905\u0927\u094d\u092f\u092f\u0928 \u2014 \u091c\u0948\u0938\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u0924\u0915\u0928\u0940\u0915\u0947\u0902, \u0917\u0941\u0923\u093e\u0924\u094d\u092e\u0915 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0935\u093f\u0927\u093f\u092f\u093e\u0901 \u2014 \u0915\u0947 \u0932\u093f\u090f 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