Laplace transform

Laplace transform
Etymology: Pierre Simon, Marquis de Laplace Date: 1942 a transformation of a function f(x) into the function g(t) = ∫0 e-xt f(x) dx that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation

New Collegiate Dictionary. 2001.

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  • Laplace transform — In mathematics, the Laplace transform is one of the best known and most widely used integral transforms. It is commonly used to produce an easily soluble algebraic equation from an ordinary differential equation. It has many important… …   Wikipedia

  • Laplace transform — Math. a map of a function, as a signal, defined esp. for positive real values, as time greater than zero, into another domain where the function is represented as a sum of exponentials. Cf. Fourier transform. [1940 45; after P. S. LAPLACE] * * *… …   Universalium

  • Laplace transform — Laplaso pertvarkis statusas T sritis fizika atitikmenys: angl. Laplace transform vok. Bildfunktion, f; Laplace Transformierte, f rus. изображение по Лапласу, n; образ Лапласа, m; трансформанта Лапласа, f pranc. fonction image, f; transformée de… …   Fizikos terminų žodynas

  • laplace transform — ləˈpläs , las noun Usage: usually capitalized L Etymology: after Pierre Simon de Laplace died 1827 French astronomer and mathematician : a transformation of a function f(x) into the function g(t) = ∫0∞ e xt f(x) dx that is useful especially in… …   Useful english dictionary

  • Laplace transform — noun a function on positive real numbers such that differentiation and integration are reduced to multiplication and division See Also: ℒ …   Wiktionary

  • Laplace transform applied to differential equations — The use of Laplace transform makes it much easier to solve linear differential equations with given initial conditions.First consider the following relations:: mathcal{L}{f } = s mathcal{L}{f} f(0): mathcal{L}{f } = s^2 mathcal{L}{f} s f(0) f (0) …   Wikipedia

  • Two-sided Laplace transform — In mathematics, the two sided Laplace transform or bilateral Laplace transform is an integral transform closely related to the Fourier transform, the Mellin transform, and the ordinary or one sided Laplace transform. If f ( t ) is a real or… …   Wikipedia

  • Inverse Laplace transform — Contents 1 Mellin s inverse formula 2 Post s inversion formula 3 See also 4 References 5 Ext …   Wikipedia

  • Laplace–Stieltjes transform — The Laplace–Stieltjes transform, named for Pierre Simon Laplace and Thomas Joannes Stieltjes, is a transform similar to the Laplace transform. It is useful in a number of areas of mathematics, including functional analysis, and certain areas of… …   Wikipedia

  • Laplace, Pierre-Simon, marquis de — born March 23, 1749, Beaumount en Auge, France died March 5, 1827, Paris French mathematician, astronomer, and physicist. He is best known for his investigations into the stability of the solar system and the theory of magnetic, electrical, and… …   Universalium

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