{"id":182,"date":"2018-01-16T15:45:13","date_gmt":"2018-01-16T14:45:13","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=182"},"modified":"2018-01-18T08:57:33","modified_gmt":"2018-01-18T07:57:33","slug":"efm-propiedades-de-la-transformada-de-laplace","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=182","title":{"rendered":"EFM: Propiedades de la Transformada de Laplace"},"content":{"rendered":"<ul>\n<li><strong>Linealidad <\/strong>:$\\mathcal{L}\\left\\{a f(t) + b g(t) \\right\\}= a \\mathcal{L}\\left\\{ f(t) \\right\\} +<br \/>\n    b \\mathcal{L}\\left\\{ g(t) \\right\\}$<\/li>\n<li><strong>Derivaci\u00f3n<\/strong>:\n<ul>\n<li>$\\mathcal{L}\\{f'(t)\\} = s \\mathcal{L}\\{f(t)\\} &#8211; f(0)$<\/li>\n<li>$\\mathcal{L}\\{f\u00bb(t)\\}= s^2 \\mathcal{L}\\{f(t)\\} &#8211; s f(0) &#8211; f'(0)$<\/li>\n<li>$\\mathcal{L}\\left\\{ f^{(n)}(t) \\right\\} = s^n \\mathcal{L}\\{f(t)\\} &#8211; s^{n &#8211; 1} f(0) &#8211; \\dots &#8211; f^{(n &#8211; 1)}(0) = s^n \\mathcal{L}\\{f(t)\\} &#8211; \\sum_{i=1}^{n} s^{n &#8211; i} f^{(i &#8211; 1)}(0)$<\/li>\n<\/ul>\n<li><strong>Integraci\u00f3n<\/strong>: $\\mathcal{L}\\left\\{ \\int_{0^{-}}^{t}f(\\tau )d\\tau \\right\\} = {1 \\over s} \\mathcal{L}\\{f\\}$<\/li>\n<li><strong>Dualidad<\/strong>: $\\mathcal{L}\\{ t f(t)\\} = -F'(s)$<\/li>\n<li><strong>Desplazamiento de la frecuencia<\/strong>: $\\mathcal{L}\\left\\{ e^{at} f(t) \\right\\} = F(s-a)$<\/li>\n<li><strong>Desplazamiento temporal<\/strong>:\n<ul>\n<li> $\\mathcal{L}\\left\\{ f(t &#8211; a) u(t &#8211; a) \\right\\}= e^{-as} F(s)$<\/li>\n<li>$\\mathcal{L}^{-1} \\left\\{ e^{-as} F(s) \\right\\}<br \/>\n= f(t &#8211; a) u(t &#8211; a)$<\/li>\n<\/ul>\n<p>Nota: $u(t)$ es la [[funci\u00f3n escal\u00f3n unitario]].<\/li>\n<li><strong>Desplazamiento potencia $n$-\u00e9sima<\/strong>:<br \/>\n$\\mathcal{L}\\{\\,t^nf(t)\\} = (-1)^nD_s^n[F(s)]$<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Linealidad :$\\mathcal{L}\\left\\{a f(t) + b g(t) \\right\\}= a \\mathcal{L}\\left\\{ f(t) \\right\\} + b \\mathcal{L}\\left\\{ g(t) \\right\\}$ Derivaci\u00f3n: $\\mathcal{L}\\{f'(t)\\} = s \\mathcal{L}\\{f(t)\\} &#8211; f(0)$ $\\mathcal{L}\\{f\u00bb(t)\\}= s^2 \\mathcal{L}\\{f(t)\\} &#8211; s f(0) &#8211; f'(0)$ $\\mathcal{L}\\left\\{ f^{(n)}(t) \\right\\} = s^n \\mathcal{L}\\{f(t)\\} &#8211; s^{n &#8211; 1} f(0) &#8211; \\dots &#8211; f^{(n &#8211; 1)}(0) = s^n \\mathcal{L}\\{f(t)\\} &#8211; \\sum_{i=1}^{n} s^{n &#8211;&hellip; <a class=\"more-link\" href=\"https:\/\/curso17.jesussoto.es\/?p=182\">Seguir leyendo <span class=\"screen-reader-text\">EFM: Propiedades de la Transformada de Laplace<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/182"}],"collection":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=182"}],"version-history":[{"count":4,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/182\/revisions"}],"predecessor-version":[{"id":186,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/182\/revisions\/186"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=182"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}