Re:Breakthrough in inverse Laplace transform procedures
by mgraczyk on Friday June 19, 2020 @12:18PM
(#23575926)
Remember in linear algebra how you spent most of the time learning about eigenvalues and eigenvectors, and particularly how to "diagonalize" a matrix `A` into `A=PDP^-1`? Doing this makes `A` easier to work with, so problems that include `A` are often easier to solve if you replace `A` with `PDP^-1`.
The laplace transform is the same thing, but instead of matrices, it works on derivatives. Equations involving `d/dt` are often made easier to work with by instead using `s`.
Re:Breakthrough in inverse Laplace transform procedures
by dls2016 on Friday June 19, 2020 @03:42PM
(#23578165)
This is true of the Fourier transform, too. The duality properties of the FT make it a nice theoretical tool. And the existence of the FFT make it a nice practical tool, too.
The laplace transform is the same thing, but instead of matrices, it works on derivatives. Equations involving `d/dt` are often made easier to work with by instead using `s`.
Longer answer: https://www.quora.com/What-is-the-purpose-of-Laplace-transfo...