{"id":155278,"date":"2022-03-26T00:28:06","date_gmt":"2022-03-25T18:58:06","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/inverse-laplace-transform-theorem-and-solved-examples\/"},"modified":"2024-05-06T14:36:18","modified_gmt":"2024-05-06T09:06:18","slug":"inverse-laplace-transform-theorem-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/inverse-laplace-transform\/","title":{"rendered":"Inverse Laplace Transform"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/inverse-laplace-transform\/#Laplace_Transform_and_Inverse_Laplace_Transform\" title=\"Laplace Transform and Inverse Laplace Transform\">Laplace Transform and Inverse Laplace Transform<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/inverse-laplace-transform\/#What_is_Laplace_Transform\" title=\"What is Laplace Transform\">What is Laplace Transform<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/inverse-laplace-transform\/#What_is_Inverse_Laplace_Transform\" title=\"What is Inverse Laplace Transform:\">What is Inverse Laplace Transform:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/inverse-laplace-transform\/#Laplace_Transform_and_Inverse_Laplace_Transform-2\" title=\"Laplace Transform and Inverse Laplace Transform\">Laplace Transform and Inverse Laplace Transform<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/inverse-laplace-transform\/#Inverse_Laplace_Transform_Table\" title=\"Inverse Laplace Transform Table\">Inverse Laplace Transform Table<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/inverse-laplace-transform\/#Inverse_Laplace_Transform_Theorems\" title=\"Inverse Laplace Transform Theorems\">Inverse Laplace Transform Theorems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/inverse-laplace-transform\/#Inverse_Laplace_Transform_Examples\" title=\"Inverse Laplace Transform Examples\">Inverse Laplace Transform Examples<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Laplace_Transform_and_Inverse_Laplace_Transform\"><\/span>Laplace Transform and Inverse Laplace Transform<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Laplace transform is a mathematical operation that takes a function of a real variable and transforms it into a function of a complex variable. The Laplace transform is used in many branches of mathematics, engineering, and physics.<\/p>\n<p>Inverse Laplace Transform<\/p>\n<p>The inverse Laplace transform is the operation that transforms a function of a complex variable back into a function of a real variable. The inverse Laplace transform is used to solve problems in many branches of mathematics, engineering, and physics.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Laplace_Transform\"><\/span>What is Laplace Transform<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Laplace transform is a mathematical operation that allows us to calculate the derivative of a function using its integral. It is a function of a complex variable, and it is used to solve problems in physics and engineering.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Inverse_Laplace_Transform\"><\/span>What is Inverse Laplace Transform:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The inverse Laplace transform is a mathematical function that takes a Laplace transform (s) of a function and returns the original function. It is usually denoted by the symbol L-1.<\/p>\n<p>The inverse Laplace transform can be used to solve problems in physics and engineering. It is also used in the field of signal processing.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Laplace_Transform_and_Inverse_Laplace_Transform-2\"><\/span>Laplace Transform and Inverse Laplace Transform<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Inverse Laplace Transform<\/p>\n<p>If is a function of time, then the inverse Laplace transform is a function of .<\/p>\n<p>The inverse Laplace transform is usually denoted by .<\/p>\n<p>It is defined as:<\/p>\n<p>where is the Laplace transform of .<\/p>\n<p>Example<\/p>\n<p>Find the inverse Laplace transform of<\/p>\n<p>The inverse Laplace transform of is:<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Inverse_Laplace_Transform_Table\"><\/span>Inverse Laplace Transform Table<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Inverse Laplace Transform<\/p>\n<p>This table is a collection of inverse Laplace transforms for common functions.<\/p>\n<p>To use the table, find the function in the left column and then read across to the right to find the corresponding inverse Laplace transform.<\/p>\n<p>If the function is not listed, then the inverse Laplace transform does not exist.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Inverse_Laplace_Transform_Theorems\"><\/span>Inverse Laplace Transform Theorems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Inverse Laplace Transform Theorem 1<\/p>\n<p>If is a function and is its Laplace transform, then the inverse Laplace transform of is .<\/p>\n<p>Inverse Laplace Transform Theorem 2<\/p>\n<p>If is a function and is its Laplace transform, then the inverse Laplace transform of is .<\/p>\n<p>Inverse Laplace Transform Theorem 3<\/p>\n<p>If is a function and is its Laplace transform, then the inverse Laplace transform of is .<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Inverse_Laplace_Transform_Examples\"><\/span>Inverse Laplace Transform Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. Find the inverse Laplace transform of<\/p>\n<p>We will use the Laplace transform calculator to find the inverse Laplace transform of the given function.<\/p>\n<p>The inverse Laplace transform of is .<\/p>\n<p>2. Find the inverse Laplace transform of<\/p>\n<p>We will use the Laplace transform calculator to find the inverse Laplace transform of the given function.<\/p>\n<p>The inverse Laplace transform of is .<\/p>\n<p>1. Locate the DHCP server in the network.<\/p>\n<p>2. Verify that the DHCP server is functioning.<\/p>\n<p>3. Verify that the DHCP server is configured to lease addresses to clients.<\/p>\n<p>4. Verify that the DHCP server is configured to lease addresses in the correct range.<\/p>\n<p>5. Verify that the DHCP server is configured to lease addresses to the correct clients.<\/p>\n<p>6. Verify that the DHCP server is configured to lease addresses for the correct amount of time.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Laplace Transform and Inverse Laplace Transform The Laplace transform is a mathematical operation that takes a function of a real [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Inverse Laplace Transform","_yoast_wpseo_title":"Inverse Laplace Transform \u2013 Theorem and Solved Examples","_yoast_wpseo_metadesc":"Learn about Inverse Laplace Transform topic of Maths in details explained by subject experts on infinitylearn.com","custom_permalink":"maths\/inverse-laplace-transform\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Inverse Laplace Transform \u2013 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