Laplace transform

Integral transform useful in probability theory, physics, and engineering

In mathematics, the Laplace transform, named after Pierre-Simon Laplace, is an integral transform that converts a function of a real variable (usually ⁠ t {\displaystyle t} ⁠, in the time domain) to a function of a complex variable s {\displaystyle s} (in the complex-valued frequency domain, also known as s-domain or s-plane). The functions are often denoted using a lowercase symbol for the time-domain function and the corresponding uppercase symbol for the frequency-domain function, e.g. x ( t) {\displaystyle x(t)} and ⁠ X ( s) {\displaystyle X(s)} ⁠.

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