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Definition of LAPLACE TRANSFORM
: a transformation of a function f(x) into the function g(t) that is found by multiplying f(x) by the transcendental number e raised to the exponent -xt and integrating this product with respect to x from 0 to positive infinity and that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation
Origin of LAPLACE TRANSFORM
Pierre Simon, Marquis de Laplace
First Known Use: 1942
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 functionept 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.