{"id":2382,"date":"2021-12-22T21:42:20","date_gmt":"2021-12-22T21:42:20","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=2382"},"modified":"2022-02-08T19:17:17","modified_gmt":"2022-02-08T19:17:17","slug":"clase-digital-2-fundamentos-matematicos","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-2-fundamentos-matematicos\/","title":{"rendered":"Clase digital 2. Fundamentos matem\u00e1ticos"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"has-background-dim-40 wp-block-cover__gradient-background has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-2481\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/pexels-lumn-167682-scaled.jpg\" style=\"object-position:57% 49%\" data-object-fit=\"cover\" data-object-position=\"57% 49%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1707\" class=\"wp-block-cover__image-background wp-image-2481\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/pexels-lumn-167682-scaled.jpg\" style=\"object-position:57% 49%\" data-object-fit=\"cover\" data-object-position=\"57% 49%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/pexels-lumn-167682-scaled.jpg 2560w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/pexels-lumn-167682-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/pexels-lumn-167682-1024x683.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/pexels-lumn-167682-768x512.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/pexels-lumn-167682-1536x1024.jpg 1536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/pexels-lumn-167682-2048x1365.jpg 2048w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/pexels-lumn-167682-272x182.jpg 272w\" sizes=\"auto, (max-width: 2560px) 100vw, 2560px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\">Fundamentos matem\u00e1ticos<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Hola!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Siento una gran emoci\u00f3n por compartir contigo esta segunda clase, espero contar con tu disposici\u00f3n y entrega por aprender algo nuevo e interesante.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Te deseo el mayor de los \u00e9xitos!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema <\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"conceptos-de-variable-compleja\">Conceptos de variable compleja<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Una variable compleja <em><strong>s<\/strong><\/em> tiene dos componentes: una parte real <strong><em>\u03c3<\/em><\/strong> y una parte imaginaria <strong><em>\u03c9<\/em><\/strong>. En forma gr\u00e1fica, la parte real de <strong><em>s<\/em><\/strong> est\u00e1 representada por el eje de los reales en la direcci\u00f3n horizontal mientras que la componente imaginaria se representa a lo largo del eje imaginario en la direcci\u00f3n vertical.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P1.png\" alt=\"\" class=\"wp-image-2434\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"543\" height=\"495\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P1.png\" alt=\"\" class=\"wp-image-2434\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P1.png 543w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P1-300x273.png 300w\" sizes=\"auto, (max-width: 543px) 100vw, 543px\" \/><\/noscript><figcaption>Figura 1. Plano complejo.<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P2-1.png\" alt=\"\" class=\"wp-image-2436\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1001\" height=\"78\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P2-1.png\" alt=\"\" class=\"wp-image-2436\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P2-1.png 1001w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P2-1-300x23.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P2-1-768x60.png 768w\" sizes=\"auto, (max-width: 1001px) 100vw, 1001px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"funciones-de-variable-compleja\">Funciones de variable compleja<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Se dice que una funci\u00f3n <strong><em>G(s)<\/em><\/strong> es una funci\u00f3n de la variable compleja <strong><em>s<\/em><\/strong>, si para cada valor de <strong><em>s<\/em><\/strong> existe uno y s\u00f3lo un valor correspondiente de <strong><em>G(s)<\/em><\/strong>, es decir, <strong><em>G(s)<\/em><\/strong> es un mapeo <strong><em>G(s) : C \u2192 C<\/em><\/strong>. Debido a que <strong><em>s<\/em><\/strong> se define con parte real e imaginaria, la funci\u00f3n <strong>G(s)<\/strong> tambi\u00e9n est\u00e1 representada por sus partes real e imaginaria esto es:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P3.png\" alt=\"\" class=\"wp-image-2437\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"488\" height=\"119\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P3.png\" alt=\"\" class=\"wp-image-2437\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P3.png 488w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P3-300x73.png 300w\" sizes=\"auto, (max-width: 488px) 100vw, 488px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"funcion-analitica\">Funci\u00f3n anal\u00edtica<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Definici\u00f3n: Una funci\u00f3n <strong><em>G(s)<\/em><\/strong> de una variable compleja <strong><em>s<\/em><\/strong> se denomina funci\u00f3n anal\u00edtica en una regi\u00f3n del plano <strong><em>s<\/em><\/strong> si la funci\u00f3n y todas sus derivadas existen en dicha regi\u00f3n. Por ejemplo sea la funci\u00f3n:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P4.png\" alt=\"\" class=\"wp-image-2438\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"115\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P4.png\" alt=\"\" class=\"wp-image-2438\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Es anal\u00edtica en cada punto del plano <strong><em>s<\/em><\/strong>, excepto en los puntos <strong><em>s = 0 y s = \u22121<\/em><\/strong>. En estos puntos <strong><em>G(s)<\/em><\/strong> est\u00e1 indeterminada.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P5.png\" alt=\"\" class=\"wp-image-2439\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"539\" height=\"427\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P5.png\" alt=\"\" class=\"wp-image-2439\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P5.png 539w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P5-300x238.png 300w\" sizes=\"auto, (max-width: 539px) 100vw, 539px\" \/><\/noscript><figcaption>Figura 2. <strong>G(s)<\/strong> es una funci\u00f3n anal\u00edtica en todo el plano complejo <strong><em>s<\/em><\/strong>, excepto en <strong><em>R<sub>0<\/sub><\/em><\/strong> cuando <strong><em>s = 0<\/em><\/strong> y <strong><em>R<sub>1<\/sub><\/em><\/strong> donde <strong><em>s = \u22121<\/em><\/strong>.<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Se puede definir el dominio <strong><em>D = s \u2208 C<\/em><\/strong> siempre y cuando <strong><em>Re(s) 6= 0<\/em><\/strong> y <strong><em>Re(s) 6= \u22121<\/em><\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"ceros-de-una-funcion\">Ceros de una funci\u00f3n<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Definici\u00f3n: Si la funci\u00f3n es anal\u00edtica en <strong><em>s = s<sub>i<\/sub><\/em><\/strong>, se dice que tiene un cero de orden <strong><em>r<\/em><\/strong> en <strong><em>s = s<sub>i<\/sub><\/em><\/strong> si el l\u00edmite:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P6.png\" alt=\"\" class=\"wp-image-2440\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"308\" height=\"82\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P6.png\" alt=\"\" class=\"wp-image-2440\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P6.png 308w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P6-300x80.png 300w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">tiene un valor finito diferente de cero. Por ejemplo, la funci\u00f3n:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P7.png\" alt=\"\" class=\"wp-image-2441\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"394\" height=\"108\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P7.png\" alt=\"\" class=\"wp-image-2441\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P7.png 394w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P7-300x82.png 300w\" sizes=\"auto, (max-width: 394px) 100vw, 394px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Para <strong><em>s1 = \u22122<\/em><\/strong>, desarrollando el l\u00edmite (3) se tiene:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P8.png\" alt=\"\" class=\"wp-image-2442\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"296\" height=\"74\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P8.png\" alt=\"\" class=\"wp-image-2442\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">y al sustituir se obtiene:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P9-1-1024x76.png\" alt=\"\" class=\"wp-image-2444\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"76\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P9-1-1024x76.png\" alt=\"\" class=\"wp-image-2444\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P9-1-1024x76.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P9-1-300x22.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P9-1-768x57.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P9-1.png 1078w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">As\u00ed <strong>G(s)<\/strong> tiene un cero sencillo en <strong><em>s = \u22122<\/em><\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"singularidades-y-polos-de-una-funcion\">Singularidades y polos de una funci\u00f3n<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Las singularidades de una funci\u00f3n son los puntos en el plano <strong><em>s<\/em><\/strong> en donde la funci\u00f3n y sus derivadas no existen. Un polo es el tipo m\u00e1s com\u00fan de singularidad y juega un papel muy importante en la teor\u00eda de control.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Definici\u00f3n: Si una funci\u00f3n <strong>G(s)<\/strong> es anal\u00edtica y univaluada en la vecindad de <strong><em>s<sub>i<\/sub><\/em><\/strong>, se dice que tiene un polo de orden <strong><em>r<\/em><\/strong> en <strong><em>s = s<sub>i<\/sub><\/em><\/strong> si el l\u00edmite:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P10.png\" alt=\"\" class=\"wp-image-2447\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"293\" height=\"81\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P10.png\" alt=\"\" class=\"wp-image-2447\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">tiene un valor finito diferente de cero. Por ejemplo sea la funci\u00f3n:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P11.png\" alt=\"\" class=\"wp-image-2448\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"388\" height=\"113\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P11.png\" alt=\"\" class=\"wp-image-2448\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P11.png 388w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P11-300x87.png 300w\" sizes=\"auto, (max-width: 388px) 100vw, 388px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Sea <strong><em>s<sub>1<\/sub> = 0<\/em><\/strong>, desarrollando el l\u00edmite (4) para el primer polo<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P12.png\" alt=\"\" class=\"wp-image-2449\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"261\" height=\"69\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P12.png\" alt=\"\" class=\"wp-image-2449\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">y al sustituir se obtiene:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P13.png\" alt=\"\" class=\"wp-image-2451\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"969\" height=\"95\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P13.png\" alt=\"\" class=\"wp-image-2451\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P13.png 969w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P13-300x29.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P13-768x75.png 768w\" sizes=\"auto, (max-width: 969px) 100vw, 969px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Sea <strong><em>s<sub>2<\/sub> = \u22121<\/em><\/strong>, desarrollando el l\u00edmite (4) para el segundo polo<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P14.png\" alt=\"\" class=\"wp-image-2453\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"66\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P14.png\" alt=\"\" class=\"wp-image-2453\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">y al sustituir se obtiene:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P15-1024x96.png\" alt=\"\" class=\"wp-image-2455\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"96\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P15-1024x96.png\" alt=\"\" class=\"wp-image-2455\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P15-1024x96.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P15-300x28.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P15-768x72.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P15.png 1079w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Sea <strong><em>s<sub>3<\/sub> = \u22123<\/em><\/strong>, desarrollando el l\u00edmite (4) para el tercer polo<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P16.png\" alt=\"\" class=\"wp-image-2456\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"279\" height=\"68\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P16.png\" alt=\"\" class=\"wp-image-2456\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">y al sustituir se obtiene<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P17-1024x91.png\" alt=\"\" class=\"wp-image-2458\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"91\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P17-1024x91.png\" alt=\"\" class=\"wp-image-2458\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P17-1024x91.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P17-300x27.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P17-768x68.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P17.png 1145w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Sea <strong><em>s<sub>4<\/sub> = 10<\/em><\/strong>, desarrollando el l\u00edmite (4) para el cuarto polo<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P18.png\" alt=\"\" class=\"wp-image-2462\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"254\" height=\"66\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P18.png\" alt=\"\" class=\"wp-image-2462\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">y al sustituir se obtiene<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P19.png\" alt=\"\" class=\"wp-image-2463\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"963\" height=\"100\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P19.png\" alt=\"\" class=\"wp-image-2463\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P19.png 963w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P19-300x31.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P19-768x80.png 768w\" sizes=\"auto, (max-width: 963px) 100vw, 963px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">As\u00ed, la funci\u00f3n tiene un polo, de orden 2, en <strong><em>s = \u22123<\/em><\/strong> y polos sencillos en <strong><em>s = 0<\/em><\/strong> y <strong><em>s = \u22121<\/em><\/strong>. Otro ejemplo, sea la funci\u00f3n:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P20.png\" alt=\"\" class=\"wp-image-2464\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"295\" height=\"94\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P20.png\" alt=\"\" class=\"wp-image-2464\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Resolviendo la ecuaci\u00f3n cuadr\u00e1tica<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P21.png\" alt=\"\" class=\"wp-image-2467\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"272\" height=\"62\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P21.png\" alt=\"\" class=\"wp-image-2467\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">el primer polo se obtiene como:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P22.png\" alt=\"\" class=\"wp-image-2468\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"492\" height=\"112\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P22.png\" alt=\"\" class=\"wp-image-2468\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P22.png 492w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P22-300x68.png 300w\" sizes=\"auto, (max-width: 492px) 100vw, 492px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">El segundo t\u00e9rmino se obtiene como:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P23.png\" alt=\"\" class=\"wp-image-2469\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"461\" height=\"111\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P23.png\" alt=\"\" class=\"wp-image-2469\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P23.png 461w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P23-300x72.png 300w\" sizes=\"auto, (max-width: 461px) 100vw, 461px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P24.png\" alt=\"\" class=\"wp-image-2470\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"545\" height=\"455\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P24.png\" alt=\"\" class=\"wp-image-2470\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P24.png 545w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P24-300x250.png 300w\" sizes=\"auto, (max-width: 545px) 100vw, 545px\" \/><\/noscript><figcaption>Figura 3. Los polos complejos conjugados son sim\u00e9tricos.<\/figcaption><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"ecuaciones-diferenciales\">Ecuaciones diferenciales<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Una gran variedad de sistemas en ingenier\u00eda se modelan matem\u00e1ticamente mediante ecuaciones diferenciales. Por ejemplo, la red RLC de la figura 4 se puede representar por la ecuaci\u00f3n diferencial:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P25.png\" alt=\"\" class=\"wp-image-2471\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"571\" height=\"111\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P25.png\" alt=\"\" class=\"wp-image-2471\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P25.png 571w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P25-300x58.png 300w\" sizes=\"auto, (max-width: 571px) 100vw, 571px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Donde:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><em>i<\/em><\/strong>: Es la corriente de la red<\/li><li><strong><em>V<\/em><\/strong>: Es el voltaje aplicado<\/li><li><strong><em>R<\/em><\/strong>: Es la resistencia<\/li><li><strong><em>C<\/em><\/strong>: Es la capacitancia<\/li><li><strong><em>L<\/em><\/strong>: Es la inductancia<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">En este caso <strong><em>V(t)<\/em><\/strong> es la funci\u00f3n de excitaci\u00f3n, <strong><em>t<\/em><\/strong> es la variable independiente e <strong><em>i(t)<\/em><\/strong> es la variable dependiente. La ecuaci\u00f3n anterior se puede transformar en una ecuaci\u00f3n diferencial como:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P26.png\" alt=\"\" class=\"wp-image-2474\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"462\" height=\"113\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P26.png\" alt=\"\" class=\"wp-image-2474\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P26.png 462w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P26-300x73.png 300w\" sizes=\"auto, (max-width: 462px) 100vw, 462px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">donde <strong><em>q(t)<\/em><\/strong> representa la carga del circuito. Esta ecuaci\u00f3n es una ecuaci\u00f3n diferencial de segundo orden (pues est\u00e1 representada por derivadas de orden menor o igual a dos) y hacen referencia a un sistema de segundo orden.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P27.png\" alt=\"\" class=\"wp-image-2475\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"747\" height=\"301\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P27.png\" alt=\"\" class=\"wp-image-2475\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P27.png 747w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P27-300x121.png 300w\" sizes=\"auto, (max-width: 747px) 100vw, 747px\" \/><\/noscript><figcaption>Figura 4: Circuito RLC.<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">En general, una gran variedad de sistemas en ingenier\u00eda son modelados matem\u00e1ticamente mediante ecuaciones diferenciales. La ecuaci\u00f3n diferencial de un sistema de orden n se escribe:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P28.png\" alt=\"\" class=\"wp-image-2477\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"742\" height=\"91\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P28.png\" alt=\"\" class=\"wp-image-2477\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P28.png 742w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C2P28-300x37.png 300w\" sizes=\"auto, (max-width: 742px) 100vw, 742px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Si los coeficientes <strong><em>a<sub>0<\/sub>, a<sub>1<\/sub>, a<sub>2<\/sub>, . . . , a<sub>n\u22121<\/sub><\/em><\/strong> no son funciones de <strong><em>y(t)<\/em><\/strong> la ecuaci\u00f3n (5) es conocida como Ecuaci\u00f3n diferencial ordinaria lineal.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Para recordar:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Una variable compleja <strong><em>s<\/em><\/strong> tiene una parte real y una parte imaginaria.<\/li><li>Una funci\u00f3n anal\u00edtica <strong><em>G(s)<\/em><\/strong> es aquella que est\u00e1 bien definida y sus derivadas existen en un dominio bien definido.<\/li><li>Los ceros de una funci\u00f3n anal\u00edtica son los valores de <strong><em>s<\/em><\/strong> que hacen que la funci\u00f3n tome el valor cero.<\/li><li>Los polos de una funci\u00f3n anal\u00edtica son los valores de <strong><em>s<\/em><\/strong> que hacen que la funci\u00f3n se indetermine.<\/li><li>Los sistemas din\u00e1micos se modelan matem\u00e1ticamente por ecuaciones diferenciales.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Hasta aqu\u00ed concluimos nuestra sesi\u00f3n. \u00a1Te felicito por tu desempe\u00f1o! Ahora toca el turno de realizar la tarea, te encuentro en tu pr\u00f3xima clase.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Siento una gran emoci\u00f3n por compartir contigo esta segunda clase, espero contar con tu disposici\u00f3n y entrega por aprender algo nuevo e interesante. \u00a1Te deseo el mayor de los \u00e9xitos! Desarrollo del tema Conceptos de variable compleja Una variable compleja s tiene dos componentes: una parte real \u03c3 y una parte imaginaria \u03c9. &#8230; <a title=\"Clase digital 2. Fundamentos matem\u00e1ticos\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-2-fundamentos-matematicos\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 2. Fundamentos matem\u00e1ticos\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[17,30],"tags":[41,100,106],"class_list":["post-2382","post","type-post","status-publish","format-standard","hentry","category-ingenieria-en-comunicaciones-y-electronica","category-uda-control-continuo","tag-clase-digital","tag-iili04029","tag-jesus-ixbalank-torres-zuniga-2"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/2382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=2382"}],"version-history":[{"count":6,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/2382\/revisions"}],"predecessor-version":[{"id":7025,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/2382\/revisions\/7025"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=2382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=2382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=2382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}