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What (who) is Laplace transform - definition
Laplace transform
THE INTEGRAL TRANSFORM ∫₀^∞ D𝑠 𝑓(𝑡)EXP(−𝑠𝑡)
Laplace Transform; Laplace Transformation; S-plane; Laplace domain; Laplace transforms; S-domain; S domain; Laplace transformations; ℒ; Complex frequency; Complex frequency space; Fourier–Laplace transform; Fourier-Laplace transform; Partial fractions in Laplace transforms; Inverse Laplace transform of derivatives; S plane; Laplace transformation
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 t, in the time domain) to a function of a complex variable s (in the complex frequency domain, also known as s-domain, or s-plane). The transform has many applications in science and engineering because it is a tool for solving differential equations.
Two-sided Laplace transform
INTEGRAL TRANSFORM
Bilateral Laplace transform; Double-sided Laplace transform Filter
In mathematics, the two-sided Laplace transform or bilateral Laplace transform is an integral transform equivalent to probability's moment generating function. Two-sided Laplace transforms are closely related to the Fourier transform, the Mellin transform, the Z-transform and the ordinary or one-sided Laplace transform.
Laplace–Stieltjes transform
The Laplace–Stieltjes transform, named for Pierre-Simon Laplace and Thomas Joannes Stieltjes, is an integral transform similar to the Laplace transform. For real-valued functions, it is the Laplace transform of a Stieltjes measure, however it is often defined for functions with values in a Banach space.
