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The Laplace Transform

2008 Zachary S Tseng C 1 1 The Laplace Transform Definition and properties of Laplace Transform , piecewise continuous functions, the Laplace Transform method of solving initial value problems The method of Laplace transforms is a system that relies on algebra (rather than calculus based methods) to solve linear differential equations. While it might seem to be a somewhat cumbersome method at times, it is a very powerful tool that enables us to readily deal with linear differential equations with discontinuous forcing functions. Definition: Let f (t) be defined for t 0. The Laplace Transform of f (t), denoted by F(s) or L{f (t)}, is an integral Transform given by the Laplace integral: L {f (t)} = =0)()(dttfesFst. Provided that this (improper) integral exists, that the integral is convergent.

functions, the Laplace Transform method of solving initial value problems The method of Laplace transforms is a system that relies on algebra (rather than calculus-based methods) to solve linear differential equations.

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www.math.psu.edu

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