In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable t {\displaystyle t} (often time) to a function of a complex variable s {\displaystyle s} (complex frequency). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms linear differential equations into algebraic equations and convolution into multiplication.
For suitable functions f, the Laplace transform is the integral
