Sumudu transform

Summary

The Sumudu transform of a function $f$ on $[0, \infty)$ is $G(u) = \int_0^\infty f(ut)\, e^{-t}\, dt$. It is the Laplace transform in disguise: $G(u) = \frac{1}{u} F\big(\frac{1}{u}\big)$, where $F$ is the Laplace transform of $f$. Its appeal is that it keeps units and scales: it sends $t^n$ to $n!\, u^n$ and constants to the same constants. It is used, like the Laplace transform, to solve linear differential equations with constant coefficients.