{"id":2479,"date":"2021-12-22T21:42:41","date_gmt":"2021-12-22T21:42:41","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=2479"},"modified":"2022-02-08T19:17:23","modified_gmt":"2022-02-08T19:17:23","slug":"clase-digital-3-transformada-de-laplace","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-3-transformada-de-laplace\/","title":{"rendered":"Clase digital 3. Transformada de Laplace"},"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-2551\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/differential-calculus-g03bf2c4bf_1920.jpg\" style=\"object-position:52% 31%\" data-object-fit=\"cover\" data-object-position=\"52% 31%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1920\" height=\"1280\" class=\"wp-block-cover__image-background wp-image-2551\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/differential-calculus-g03bf2c4bf_1920.jpg\" style=\"object-position:52% 31%\" data-object-fit=\"cover\" data-object-position=\"52% 31%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/differential-calculus-g03bf2c4bf_1920.jpg 1920w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/differential-calculus-g03bf2c4bf_1920-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/differential-calculus-g03bf2c4bf_1920-1024x683.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/differential-calculus-g03bf2c4bf_1920-768x512.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/differential-calculus-g03bf2c4bf_1920-1536x1024.jpg 1536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/differential-calculus-g03bf2c4bf_1920-272x182.jpg 272w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/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\">Transformada de Laplace<\/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\">Es un placer contar en este d\u00eda con tu presencia, espero que goces de buena salud y sobre todo, que tu \u00e1nimo siga ayudando a mejorar tu aprendizaje. Por lo tanto, te invito a tu tercera clase, espero que la encuentres fascinante.<\/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=\"transformada-de-laplace\">Transformada de Laplace<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">La transformada de Laplace es una herramienta que es utilizada (entre otras cosas) para resolver ecuaciones diferenciales ordinarias lineales. En comparaci\u00f3n con el m\u00e9todo cl\u00e1sico de resoluci\u00f3n de ecuaciones diferenciales lineales, la transformada de Laplace tiene dos caracter\u00edsticas atractivas:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>La soluci\u00f3n de la ecuaci\u00f3n homog\u00e9nea y la soluci\u00f3n particular se obtienen en una sola operaci\u00f3n.<\/li><li>La transformada de Laplace convierte la ecuaci\u00f3n diferencial en una ecuaci\u00f3n algebraica en la variable <strong><em>s<\/em><\/strong>. La soluci\u00f3n en <strong><em>s<\/em><\/strong> se obtiene al manipular una ecuaci\u00f3n algebraica y finalmente, la soluci\u00f3n en <strong><em>t<\/em><\/strong> se obtiene por medio de la transformada inversa de Laplace de la soluci\u00f3n en <strong><em>s<\/em><\/strong>.<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Definici\u00f3n. Dada una funci\u00f3n, real <strong><em>f(t)<\/em><\/strong> que satisface la condici\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_C3P1.png\" alt=\"\" class=\"wp-image-2490\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"335\" height=\"132\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P1.png\" alt=\"\" class=\"wp-image-2490\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P1.png 335w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P1-300x118.png 300w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Para alguna funci\u00f3n <strong><em>f(t)<\/em><\/strong> real finita, la transformada de Laplace de <strong><em>f(t)<\/em><\/strong> se define 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_C3P2.png\" alt=\"\" class=\"wp-image-2491\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"667\" height=\"130\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P2.png\" alt=\"\" class=\"wp-image-2491\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P2.png 667w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P2-300x58.png 300w\" sizes=\"auto, (max-width: 667px) 100vw, 667px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La variable <strong><em>s<\/em><\/strong> se denomina operador de Laplace, una variable compleja tal que <strong><em>s = \u03c3 + j\u03c9<\/em><\/strong>. Ejemplo. Sea <strong><em>f(t)<\/em><\/strong> una funci\u00f3n escal\u00f3n unitario el cual se define 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_C3P3.png\" alt=\"\" class=\"wp-image-2492\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"388\" height=\"144\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P3.png\" alt=\"\" class=\"wp-image-2492\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P3.png 388w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P3-300x111.png 300w\" sizes=\"auto, (max-width: 388px) 100vw, 388px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La transformada de Laplace de <strong><em>f(t)<\/em><\/strong> est\u00e1 dada por:<\/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_C3P4.png\" alt=\"\" class=\"wp-image-2494\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"571\" height=\"128\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P4.png\" alt=\"\" class=\"wp-image-2494\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P4.png 571w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P4-300x67.png 300w\" sizes=\"auto, (max-width: 571px) 100vw, 571px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Sustituyendo en la integral:<\/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_C3P5-1024x285.png\" alt=\"\" class=\"wp-image-2496\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"285\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P5-1024x285.png\" alt=\"\" class=\"wp-image-2496\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P5-1024x285.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P5-300x84.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P5-768x214.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P5.png 1267w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo. Consid\u00e9rese la ecuaci\u00f3n exponencial<\/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_C3P8.png\" alt=\"\" class=\"wp-image-2502\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"527\" height=\"73\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P8.png\" alt=\"\" class=\"wp-image-2502\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P8.png 527w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P8-300x42.png 300w\" sizes=\"auto, (max-width: 527px) 100vw, 527px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La transformada de Laplace de <strong><em>f(t)<\/em><\/strong> est\u00e1 dada por:<\/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_C3P6.png\" alt=\"\" class=\"wp-image-2499\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"664\" height=\"572\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P6.png\" alt=\"\" class=\"wp-image-2499\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P6.png 664w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P6-300x258.png 300w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo. Consid\u00e9rese la ecuaci\u00f3n exponencial:<\/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_C3P9.png\" alt=\"\" class=\"wp-image-2504\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"70\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P9.png\" alt=\"\" class=\"wp-image-2504\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P9.png 343w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P9-300x61.png 300w\" sizes=\"auto, (max-width: 343px) 100vw, 343px\" \/><\/noscript><\/figure><\/div>\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_C3P7-1024x306.png\" alt=\"\" class=\"wp-image-2500\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"306\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P7-1024x306.png\" alt=\"\" class=\"wp-image-2500\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P7-1024x306.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P7-300x90.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P7-768x230.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P7.png 1250w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Puesto que<\/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_C3P10.png\" alt=\"\" class=\"wp-image-2506\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"578\" height=\"63\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P10.png\" alt=\"\" class=\"wp-image-2506\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P10.png 578w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P10-300x33.png 300w\" sizes=\"auto, (max-width: 578px) 100vw, 578px\" \/><\/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_C3P11.png\" alt=\"\" class=\"wp-image-2507\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"489\" height=\"149\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P11.png\" alt=\"\" class=\"wp-image-2507\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P11.png 489w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P11-300x91.png 300w\" sizes=\"auto, (max-width: 489px) 100vw, 489px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">As\u00ed<\/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_C3P12.png\" alt=\"\" class=\"wp-image-2508\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"692\" height=\"337\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P12.png\" alt=\"\" class=\"wp-image-2508\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P12.png 692w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P12-300x146.png 300w\" sizes=\"auto, (max-width: 692px) 100vw, 692px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Adem\u00e1s,<\/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_C3P13.png\" alt=\"\" class=\"wp-image-2509\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"611\" height=\"479\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P13.png\" alt=\"\" class=\"wp-image-2509\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P13.png 611w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P13-300x235.png 300w\" sizes=\"auto, (max-width: 611px) 100vw, 611px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo. Consid\u00e9rese la ecuaci\u00f3n exponencial<\/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_C3P14.png\" alt=\"\" class=\"wp-image-2510\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"425\" height=\"59\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P14.png\" alt=\"\" class=\"wp-image-2510\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P14.png 425w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P14-300x42.png 300w\" sizes=\"auto, (max-width: 425px) 100vw, 425px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">con transformada de Laplace<\/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_C3P15.png\" alt=\"\" class=\"wp-image-2513\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"255\" height=\"69\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P15.png\" alt=\"\" class=\"wp-image-2513\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Usando la propiedad de linealidad del operador de Laplace (puesto que la integral es un operador lineal), 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_C3P16.png\" alt=\"\" class=\"wp-image-2515\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"715\" height=\"556\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P16.png\" alt=\"\" class=\"wp-image-2515\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P16.png 715w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P16-300x233.png 300w\" sizes=\"auto, (max-width: 715px) 100vw, 715px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">De la misma forma:<\/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_C3P17.png\" alt=\"\" class=\"wp-image-2517\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"594\" height=\"576\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P17.png\" alt=\"\" class=\"wp-image-2517\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P17.png 594w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P17-300x291.png 300w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Propiedad<\/strong>. Una de las m\u00e1s b\u00e1sicas y \u00fatiles propiedades del operador de Laplace <strong><em>L<\/em><\/strong> es la linealidad. Sea<\/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_C3P18.png\" alt=\"\" class=\"wp-image-2518\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"533\" height=\"61\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P18.png\" alt=\"\" class=\"wp-image-2518\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P18.png 533w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P18-300x34.png 300w\" sizes=\"auto, (max-width: 533px) 100vw, 533px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Propiedad de homogeneidad<\/strong><\/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_C3P19-1024x121.png\" alt=\"\" class=\"wp-image-2520\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"121\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P19-1024x121.png\" alt=\"\" class=\"wp-image-2520\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P19-1024x121.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P19-300x36.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P19-768x91.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P19.png 1240w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Propiedad de actividad<\/strong><\/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_C3P20-1024x546.png\" alt=\"\" class=\"wp-image-2527\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"546\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P20-1024x546.png\" alt=\"\" class=\"wp-image-2527\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P20-1024x546.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P20-300x160.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P20-768x410.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P20.png 1040w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicando ambas propiedades se obtiene la <strong>propiedad de superposici\u00f3n<\/strong>:<\/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_C3P21.png\" alt=\"\" class=\"wp-image-2528\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"799\" height=\"81\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P21.png\" alt=\"\" class=\"wp-image-2528\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P21.png 799w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P21-300x30.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P21-768x78.png 768w\" sizes=\"auto, (max-width: 799px) 100vw, 799px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Teorema de la derivada. Suponga que <strong><em>f(t)<\/em><\/strong> es una funci\u00f3n continua en <strong>[0,\u221e)<\/strong> y que <strong><em>f(t)<\/em><\/strong> es continua a trozos en <strong>[0,\u221e)<\/strong>, entonces:<\/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_C3P22.png\" alt=\"\" class=\"wp-image-2530\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"879\" height=\"159\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P22.png\" alt=\"\" class=\"wp-image-2530\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P22.png 879w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P22-300x54.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P22-768x139.png 768w\" sizes=\"auto, (max-width: 879px) 100vw, 879px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Consid\u00e9rese el cambio de variable:<\/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_C3P23.png\" alt=\"\" class=\"wp-image-2532\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"641\" height=\"142\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P23.png\" alt=\"\" class=\"wp-image-2532\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P23.png 641w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P23-300x66.png 300w\" sizes=\"auto, (max-width: 641px) 100vw, 641px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">As\u00ed, integrando por partes 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_C3P24.png\" alt=\"\" class=\"wp-image-2534\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"907\" height=\"392\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P24.png\" alt=\"\" class=\"wp-image-2534\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P24.png 907w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P24-300x130.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P24-768x332.png 768w\" sizes=\"auto, (max-width: 907px) 100vw, 907px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Definici\u00f3n. La convoluci\u00f3n de dos funciones <strong><em>f(t)<\/em><\/strong> y <strong><em>g(t)<\/em><\/strong>, definidas para <strong><em>t &gt; 0<\/em><\/strong>, est\u00e1 dada por la integral:<\/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_C3P25.png\" alt=\"\" class=\"wp-image-2535\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"628\" height=\"251\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P25.png\" alt=\"\" class=\"wp-image-2535\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P25.png 628w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P25-300x120.png 300w\" sizes=\"auto, (max-width: 628px) 100vw, 628px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La integral de convoluci\u00f3n existe siempre que <strong><em>f(t)<\/em><\/strong> y <strong><em>g(t)<\/em><\/strong> sean funciones continuas a trozos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Teorema de Convoluci\u00f3n<\/strong>. Si <strong><em>f(t)<\/em><\/strong> y <strong><em>g(t)<\/em><\/strong> son funciones continuas a trozos en <strong>[0,\u221e)<\/strong>, entonces:<\/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_C3P26.png\" alt=\"\" class=\"wp-image-2537\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"617\" height=\"72\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P26.png\" alt=\"\" class=\"wp-image-2537\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P26.png 617w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P26-300x35.png 300w\" sizes=\"auto, (max-width: 617px) 100vw, 617px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La transformada de Laplace de la integral anterior est\u00e1 dada por:<\/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_C3P27.png\" alt=\"\" class=\"wp-image-2539\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"897\" height=\"410\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P27.png\" alt=\"\" class=\"wp-image-2539\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P27.png 897w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P27-300x137.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P27-768x351.png 768w\" sizes=\"auto, (max-width: 897px) 100vw, 897px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Teorema general de la derivada y la integral<\/strong>. Si <strong><em>f(t), f'(t), \u2026, f <sup>n\u22121<\/sup>(t)<\/em><\/strong> son continuos en <strong>[0,\u221e)<\/strong>, de orden exponencial y adem\u00e1s, <strong><em>f <sup>n<\/sup>(t)<\/em><\/strong> es continua a trozos en <strong>[0,\u221e)<\/strong>, entonces:<\/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_C3P28-1024x68.png\" alt=\"\" class=\"wp-image-2540\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"68\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P28-1024x68.png\" alt=\"\" class=\"wp-image-2540\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P28-1024x68.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P28-300x20.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P28-768x51.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P28.png 1156w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Para la integraci\u00f3n de n-\u00e9simo 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_C3P29.png\" alt=\"\" class=\"wp-image-2541\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"899\" height=\"163\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P29.png\" alt=\"\" class=\"wp-image-2541\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P29.png 899w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P29-300x54.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P29-768x139.png 768w\" sizes=\"auto, (max-width: 899px) 100vw, 899px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La transformada de Laplace tiene dos prioridades que son \u00fatiles para determinar valores l\u00edmite de una funci\u00f3n <strong><em>f(t)<\/em><\/strong>, cuando <strong><em>t = 0<\/em><\/strong> o cuando <strong><em>t \u2192 \u221e<\/em><\/strong>, aun si la funci\u00f3n <strong><em>f(t)<\/em><\/strong> no se conoce expl\u00edcitamente.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Teorema del valor inicial<\/strong>. Sea la funci\u00f3n <strong><em>h(t)<\/em><\/strong> continua en el intervalo <strong>[0, \u221e)<\/strong> y de orden exponencial, adem\u00e1s, <strong><em>f'(t)<\/em><\/strong> es continua a trozos en el mismo intervalo, entonces:<\/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_C3P30.png\" alt=\"\" class=\"wp-image-2542\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"595\" height=\"88\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P30.png\" alt=\"\" class=\"wp-image-2542\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P30.png 595w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P30-300x44.png 300w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Teorema del valor inicial<\/strong>. Sea la funci\u00f3n <strong><em>f(t)<\/em><\/strong> continua en el intervalo <strong>[0,\u221e)<\/strong> y de orden exponencial, adem\u00e1s, <strong><em>f'(t)<\/em><\/strong> es continua a trozos en el mismo intervalo. Sup\u00f3ngase tambi\u00e9n que 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_C3P31.png\" alt=\"\" class=\"wp-image-2543\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"237\" height=\"55\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P31.png\" alt=\"\" class=\"wp-image-2543\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">existe, entonces:<\/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_C3P32.png\" alt=\"\" class=\"wp-image-2544\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"568\" height=\"84\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P32.png\" alt=\"\" class=\"wp-image-2544\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P32.png 568w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P32-300x44.png 300w\" sizes=\"auto, (max-width: 568px) 100vw, 568px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"transformada-inversa-de-laplace\">Transformada Inversa de Laplace<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Dada una funci\u00f3n en el dominio de Laplace <strong><em>F(s)<\/em><\/strong>, la operaci\u00f3n para obtener <strong><em>f(t)<\/em><\/strong> se denomina como la transformada inversa de Laplace y se denota 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_C3P33.png\" alt=\"\" class=\"wp-image-2545\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"368\" height=\"74\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P33.png\" alt=\"\" class=\"wp-image-2545\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P33.png 368w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P33-300x60.png 300w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La integral de la transformada inversa de Laplace se representa 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_C3P34.png\" alt=\"\" class=\"wp-image-2547\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"594\" height=\"165\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P34.png\" alt=\"\" class=\"wp-image-2547\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P34.png 594w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/UDA_ControlContinuo_C3P34-300x83.png 300w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">donde <strong><em>c \u2208 R<\/em><\/strong> y es mayor que las partes reales de todas las singularidades de <strong><em>F(s)<\/em><\/strong>. En la mayor\u00eda de los problemas de control, la evaluaci\u00f3n de la transformada inversa de Laplace no requiere el uso de la integral de inversi\u00f3n definida anteriormente. La operaci\u00f3n de la transformada inversa de Laplace que involucra funciones racionales se puede realizar mediante el empleo de las transformadas de Laplace conocidas y la expansi\u00f3n en fracciones parciales.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">La transformada de Laplace es una herramienta que es utilizada (entre otras cosas) para resolver ecuaciones diferenciales ordinarias lineales. En comparaci\u00f3n con el m\u00e9todo cl\u00e1sico de resoluci\u00f3n de ecuaciones diferenciales lineales, la transformada de Laplace tiene dos caracter\u00edsticas atractivas:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>La soluci\u00f3n de la ecuaci\u00f3n homog\u00e9nea y la soluci\u00f3n particular se obtienen en una sola operaci\u00f3n.<\/li><li>La transformada de Laplace convierte la ecuaci\u00f3n diferencial en una ecuaci\u00f3n algebraica en la variable <strong><em>s<\/em><\/strong>. La soluci\u00f3n en s se obtiene al manipular una ecuaci\u00f3n algebraica y finalmente, la soluci\u00f3n en <strong><em>t<\/em><\/strong> se obtiene por medio de la transformada inversa de Laplace de la soluci\u00f3n en <strong><em>s<\/em><\/strong>.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Hemos llegado al final de la sesi\u00f3n, \u00a1Muchas felicidades por tu logro! no olvides la tarea que es evidencia de tu aprendizaje. Te encuentro en la pr\u00f3xima sesi\u00f3n.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Es un placer contar en este d\u00eda con tu presencia, espero que goces de buena salud y sobre todo, que tu \u00e1nimo siga ayudando a mejorar tu aprendizaje. Por lo tanto, te invito a tu tercera clase, espero que la encuentres fascinante. \u00a1Te deseo el mayor de los \u00e9xitos! Desarrollo del tema Transformada &#8230; <a title=\"Clase digital 3. Transformada de Laplace\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-3-transformada-de-laplace\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 3. Transformada de Laplace\">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-2479","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\/2479","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=2479"}],"version-history":[{"count":5,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/2479\/revisions"}],"predecessor-version":[{"id":7026,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/2479\/revisions\/7026"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=2479"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=2479"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=2479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}