In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace , is an integral transform that converts a function of a real variable (usually , in the time domain) to a function of a complex variable (in the complex-valued frequency domain, also known as s-domain, or s-plane). The transform is useful for converting differentiation and integration in t… 詳細
The Laplace transform is named after mathematician and astronomer Pierre-Simon, Marquis de Laplace, who u… 詳細
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 … 詳細
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 converges provided that the limit The Laplace tran… 詳細
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 Laplace variable s is also known as operator variabl… 詳細
The (unilateral) Laplace–Stieltjes transform of a function g : ℝ → ℝ is defined by the Lebesgue–Stieltjes integral The function g is assumed to be of bounded variation. If g is the antiderivative of f: then the Laplace… 詳細
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. Because the Lap… 詳細
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 impedances, very similar to phasor impedances. … 詳細