<story><title>Breakthrough in inverse Laplace transform procedures</title><url>http://inverselaplace.org/</url></story><parent_chain><item><author>rollulus</author><text>A little ELI5 for those who haven&amp;#x27;t had Laplace transforms at school, from someone who only had a Laplace 101 course, so for what&amp;#x27;s it worth: Laplace transforms allow you to convert differential equations into easier equations, and back: the differentials and integrals become multiplications and divisions. So you can take a differential equation, transform it into the Laplace domain, manipulate it, and convert it back. And that&amp;#x27;s cool because differential equations tend to appear everywhere, for instance to model springs, electrical circuits with caps and coils, the surface of a soap bubble in a metal rod, etc. A sibling is the z-transform, which is like the digital version. This one is used for instance to design digital audio filters. I&amp;#x27;m sure some math wizards here can elaborate and correct me.</text></item></parent_chain><comment><author>GolDDranks</author><text>I don&amp;#x27;t have any real understanding over the Laplace transform, but I understand Fourier transform well enough that it makes sense to me. Back then, I saw an claim that Laplace transform is a generalization of Fourer transform in the sense that it transforms a function not only to a space of frequencies and phases of sine waves, but to a larger space of parameters of exponentials. Note that the parameter space of the sine waves is subset of the (complex) parameter space of exponentials.&lt;p&gt;Is this claim correct?</text></comment>
<story><title>Breakthrough in inverse Laplace transform procedures</title><url>http://inverselaplace.org/</url></story><parent_chain><item><author>rollulus</author><text>A little ELI5 for those who haven&amp;#x27;t had Laplace transforms at school, from someone who only had a Laplace 101 course, so for what&amp;#x27;s it worth: Laplace transforms allow you to convert differential equations into easier equations, and back: the differentials and integrals become multiplications and divisions. So you can take a differential equation, transform it into the Laplace domain, manipulate it, and convert it back. And that&amp;#x27;s cool because differential equations tend to appear everywhere, for instance to model springs, electrical circuits with caps and coils, the surface of a soap bubble in a metal rod, etc. A sibling is the z-transform, which is like the digital version. This one is used for instance to design digital audio filters. I&amp;#x27;m sure some math wizards here can elaborate and correct me.</text></item></parent_chain><comment><author>taneq</author><text>Sounds right to my (very very rusty) recollection. Laplace transforms are a magic trick that let you easily solve some kinds of differential equations.</text></comment>