{"id":100278,"date":"2018-03-11T10:21:41","date_gmt":"2018-03-11T10:21:41","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/nuevos-metodos-de-laplace-y-saddle-point-mas-sencillos-y-sistematicos\/"},"modified":"2018-03-11T10:21:41","modified_gmt":"2018-03-11T10:21:41","slug":"nuevos-metodos-de-laplace-y-saddle-point-mas-sencillos-y-sistematicos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/funciones-especiales\/nuevos-metodos-de-laplace-y-saddle-point-mas-sencillos-y-sistematicos\/","title":{"rendered":"Nuevos metodos de laplace y saddle point mas sencillos y sistem\u00e1ticos"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Pedro Jes\u00fas Pagola Martinez <\/strong><\/h2>\n<p>En este trabajo nos hemos centrado en el estudio del c\u00e1lculo de desarrollos asint\u00f3ticos de integrales. Los m\u00e9todos de laplace y saddle point son los mas utilizados para calcular desarrollos asint\u00f3ticos. Sin embargo, estos m\u00e9todos tienen sus dificultades t\u00e9cnicas a la hora de ponerlos en pr\u00e1ctica. Por un lado, ambos m\u00e9todos necesitan de un cambio de variable que posteriormente hace que los coeficientes del desarrollo asint\u00f3tico sean los coeficientes de taylor de una funci\u00f3n definida impl\u00edcitamente y por tanto, no son f\u00e1cilmente calculables. Por otro lado, y previamente a este cambio de variable, en el m\u00e9todo saddle point se necesita la validaci\u00f3n de un cambio de camino de integraci\u00f3n: el camino original por el camino steepest descent de la funci\u00f3n fase f(t). En general, esta tarea suele ser complicada y sobretodo, no es sistem\u00e1tica. a la vista de estas dificultades t\u00e9cnicas, en esta tesis hemos propuesto dos nuevos m\u00e9todos derivados de los m\u00e9todos laplace y saddle point originales que los hacen mas sencillos y sistem\u00e1ticos:  1.- Un primer m\u00e9todo que consiste en desarrolla la funci\u00f3n g(t) que multiplica a la exponencial en el integrando , entorno a los puntos asint\u00f3ticamente relevantes de la funci\u00f3n fase f(t).   2.- Un segundo m\u00e9todo consistente en , no solo desarrollar la funci\u00f3n g(t) si no tambi\u00e9n la funci\u00f3n fase f(t) entorno a sus puntos asint\u00f3ticamente relevantes.  en ambos casos conseguimos omitir el cambio de variable que dificulta los c\u00e1lculos en los m\u00e9todos cl\u00e1sicos y sistematiza los c\u00e1lculos tanto de la sucesi\u00f3n asint\u00f3tica como de los coeficientes, dando formulas explicitas para ambos. Adem\u00e1s, en la segunda modificaci\u00f3n, sistematizamos el calculo del camino steepest descent de manera que su calculo sea universal, valido para cualquier problema planteado.  finalmente, y como consecuencia de la segunda modificaci\u00f3n, hemos obtenido formulas parcialmente explicitas para los coeficientes del m\u00e9todo saddle point cl\u00e1sico.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Nuevos metodos de laplace y saddle point mas sencillos y sistem\u00e1ticos<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Nuevos metodos de laplace y saddle point mas sencillos y sistem\u00e1ticos <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Pedro Jes\u00fas Pagola Martinez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 P\u00fablica de navarra<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 15\/04\/2010<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Jos\u00e9 Luis L\u00f3pez Garc\u00eda<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jes\u00fas Francisco Palacian subiela <\/li>\n<li>alejandro Zarzo altarejos (vocal)<\/li>\n<li>  (vocal)<\/li>\n<li>  (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Pedro Jes\u00fas Pagola Martinez En este trabajo nos hemos centrado en el estudio del c\u00e1lculo de desarrollos [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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