 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.[194045; after P. S. LAPLACE]
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In mathematics, an integral transform useful in solving differential equations.The Laplace transform of a function is found by integrating the product of that function and the exponential function e^{pt} over the interval from zero to infinity. The Laplace transform's applications include solving linear differential equations with constant coefficients and solving boundary value problems, which arise in calculations relating to physical systems.* * *
in mathematics, a particular integral transform invented by the French mathematician PierreSimon Laplace (Laplace, PierreSimon, marquis de) (1749–1827), and systematically developed by the British physicist Oliver Heaviside (Heaviside, Oliver) (1850–1925), to simplify the solution of many differential equations (differential equation) that describe physical processes. Today it is used most frequently by electrical engineers in the solution of various electronic circuit problems.The Laplace transform f(p), also denoted by L{F(t)} or Lap F(t), is defined by the integralinvolving the exponential (exponential function) parameter p in the kernel K = e^{−pt}. The linear Laplace operator L thus transforms each function F(t) of a certain set of functions into some function f(p). The inverse transform F(t) is written L^{−1}{f(p)} or Lap^{−1}f(p).* * *
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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 — 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 — 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… … New Collegiate 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
Twosided 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, PierreSimon, 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