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Laplace Transform - Math

Chapter 7 Laplace TransformThe Laplace Transform can be used to solve differential equations. Be-sides being a different and efficient alternative to variation of parame-ters and undetermined coefficients, theLaplace methodis particularlyadvantageous for input terms that are piecewise-defined, periodic or Laplace transformor theLaplace integralof a functionf(t) defined for 0 t < is the ordinary calculus integration problem 0f(t)e stdt,succinctly denotedL(f(t)) in science and engineering literature. TheL notation recognizes that integration always proceeds overt= 0 tot= and that the integral involves anintegratore stdtinstead of theusualdt.

The direct Laplace transform or the Laplace integral of a function f(t) defined for 0 • t < 1 is the ordinary calculus integration problem Z 1 0 f(t)e¡stdt; succinctly denoted L(f(t)) in science and engineering literature. The L–notation recognizes that integration always proceeds over t = 0 to

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Laplace Transform - Home - Math

www.math.utah.edu

Laplace Transform The Laplace transform can be used to solve di erential equations. Be-sides being a di erent and e cient alternative to variation of parame-ters and undetermined coe cients, the Laplace method is particularly advantageous for input terms that are piecewise-de ned, periodic or im-

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