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Lecture Notes for Laplace Transform

Lecture Notes for Laplace Transform

www.personal.psu.edu

|Laplace Transform is used to handle piecewise continuous or impulsive force. 6.1: Deflnition of the Laplace transform (1) Topics: † Deflnition of Laplace transform, † Compute Laplace transform by deflnition, including piecewise continuous functions. Deflnition: Given a function f(t), t ‚ 0, its Laplace transform F(s) = Lff(t)g is ...

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ELEMENTARY DIFFERENTIAL EQUATIONS WITH BOUNDARY …

ELEMENTARY DIFFERENTIAL EQUATIONS WITH BOUNDARY …

ramanujan.math.trinity.edu

8.1 Introduction to the Laplace Transform 393 8.2 The Inverse Laplace Transform 405 8.3 Solution ofInitial Value Problems 413 8.4 The Unit Step Function 419 8.5 Constant Coefficient Equationswith Piecewise Continuous Forcing Functions 430 8.6 Convolution 440 8.7 Constant Cofficient Equationswith Impulses 452 8.8 A Brief Table of Laplace ...

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Table 1: Properties of Laplace Transforms

Table 1: Properties of Laplace Transforms

web.mit.edu

Table 1: Table of Laplace Transforms Number f(t) F(s) 1 δ(t)1 2 us(t) 1 s 3 t 1 s2 4 tn n! sn+1 5 e−at 1 (s+a)6 te−at 1 (s+a)27 1 (n−1)!tn−1e−at 1 (s+a)n81−e−at a s(s+a) 9 e−at −e−bt b−a (s+a)(s+b)10 be−bt −ae−at (b−a)s (s+a)(s+b)11 sinat a s2+a2 12 cosat s s2+a2 13 e−at cosbt s+a (s+a)2+b214 e−at sinbt b (s+a)2+b215 1−e−at(cosbt+ a b sinbt) a2+b2 s[(s+a ...

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