# Category:Definitions/Laplace Transforms

This category contains definitions related to Laplace Transforms.
Related results can be found in Category:Laplace Transforms.

Let $f: \hointr 0 \to \to \mathbb F$ be a function of a real variable $t$, where $\mathbb F \in \set {\R, \C}$.

The Laplace transform of $f$, denoted $\laptrans f$ or $F$, is defined as:

$\laptrans {\map f t} = \map F s = \displaystyle \int_0^{\to +\infty} e^{-s t} \map f t \rd t$

whenever this improper integral converges.

If this improper integral does not converge, then $\laptrans {\map f t}$ does not exist.

## Pages in category "Definitions/Laplace Transforms"

The following 11 pages are in this category, out of 11 total.