The Laplace transform is named after mathematician and astronomer Pierre-Simon, Marquis de Laplace, who used a similar transform in … See more

The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), which is a unilateral transform defined by
where s is a complex frequency domain parameter
An alternate … See more

The Laplace transform's key property is that it is converts differentiation and integration in the time domain into multiplication and division s in the Laplace domain. Thus, the … See more

The Laplace transform is often used in circuit analysis, and simple conversions to the s-domain of circuit elements can be made. Circuit elements can be transformed into See more

If f is a locally integrable function (or more generally a Borel measure locally of bounded variation), then the Laplace transform F(s) of f … See more

Laplace–Stieltjes transform
The (unilateral) Laplace–Stieltjes transform of a function g : ℝ → ℝ is defined by the See more

The following table provides Laplace transforms for many common functions of a single variable. For definitions and explanations, see the Explanatory Notes at the end of the table. See more