{"version":"1.0","provider_name":"SOUL OF MATHEMATICS","provider_url":"https:\/\/soulofmathematics.com","author_name":"Rajarshi Dey","author_url":"https:\/\/soulofmathematics.com\/index.php\/author\/rajarshidey1729gmail-com\/","title":"INTEGRAL TRANSFORMS - SOUL OF MATHEMATICS","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"fPMKShQeSm\"><a href=\"https:\/\/soulofmathematics.com\/index.php\/integral-transforms\/\">INTEGRAL TRANSFORMS<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/soulofmathematics.com\/index.php\/integral-transforms\/embed\/#?secret=fPMKShQeSm\" width=\"600\" height=\"338\" title=\"&#8220;INTEGRAL TRANSFORMS&#8221; &#8212; SOUL OF MATHEMATICS\" data-secret=\"fPMKShQeSm\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/* ]]> *\/\n<\/script>\n","thumbnail_url":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/AffectionateDirectAmazontreeboa-size_restricted.gif?fit=640%2C320&ssl=1","thumbnail_width":640,"thumbnail_height":320,"description":"In&nbsp;mathematics, an&nbsp;integral transform&nbsp;maps a&nbsp;function&nbsp;from its original&nbsp;function space&nbsp;into another function space via&nbsp;integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space. The transformed function can generally be mapped back to the original function space using the&nbsp;inverse transform. An integral transform is any&nbsp;transform&nbsp;T&nbsp;of the following form: Mathematical notation aside, the motivation behind integral transforms is easy to understand. There are many classes of problems that are difficult to solve\u2014or at least quite unwieldy algebraically\u2014in their original representations. An integral transform &#8220;maps&#8221; an equation from its original &#8220;domain&#8221; into another domain. Manipulating and solving the equation in the target domain can be much easier than manipulation and solution in the original domain. The solution is then mapped back to the original domain with the inverse of the integral transform. Table of Transforms Transform Symbol K t1 t2 Abel transform u Fourier transform Fourier sine transform Fourier cosine transform 0 Hankel transform 0 Hartley transform Hermite transform Hilbert transform Jacobi transform Laguerre transform Laplace transform e\u2212ut 0 Legendre transform Mellin transform tu\u22121 0 Two-sided Laplacetransform e\u2212ut Poisson kernel 0 2\u03c0 Radon Transform R\u0192 Weierstrass transform We will get into details of few of the most popular transforms like Laplace Transform, Fourier Transform an many more."}