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 `

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`. Longer answer: https://www.quora.com/What-is-the-purpose-of-Laplace-transforms-in-controls-theory https://www.quora.com/What-is-the-purpose-of-Laplace-transfo...