# Laplace transform

From AMS Glossary

## Laplace transform

(Also called Laplace transformation.) An integral transform of a function obtained by multiplying the given function

*f*(*t*) by*e*^{-pt}, where*p*is a new variable, and integrating with respect to*t*from*t*= 0 to*t*= ∞.Thus, the Laplace transform of and may be denoted by the symbol

*f*(*t*) is*F*(*p*). The Laplace transform is especially useful in solving initial-value problems associated with inhomogeneous linear differential equations with constant coefficients.*See*Fourier transform.