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Inverse Laplace Transform-Signals And Systems-Lecture Slides

Slides, Signals And Systems Theory

Post: July 17th, 2012
Description
Prof. Sahendra Agneya delivered this lecture at Fakir Mohan University, Balasore for Signals and Systems course. Inverse, Laplace, Transform, Function, Defined, Linear, Operator, Initial, Value, Problem
Prof. Sahendra Agneya delivered this lecture at Fakir Mohan University, Balasore for Signals and Systems course. Inverse, Laplace, Transform, Function, Defined, Linear, Operator, Initial, Value, Problem
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Inverse Laplace Transform • Consider a given function F(s), is it possible to find a function f(t) defined on [0,  ), such that L{f (t)} F(s) ? • If this is possible, we say f(t) is the inverse Laplace transform of F(s), and we write 1 docsity.com Some Examples. • First we note that the Inverse Laplace Transform is a “ Linear Operator”. s-a , 1. F(s)  2 2 (s-a)  b b , 2 . F(s)  2 2 (s-a)  b 3s  2 , 3 . F(s)  2 s  2 s  10 2 docsity.com Applications • Consider the Initial Value Problem: y "  2 y ' 5 y   8 e  t ; y ( 0 )  2 , y ' ( 0 )  12 . • We shall use Laplace Transform and Inverse Laplace Transform to solve this I.V.P. 3 docsity.com Next let us consider a D.E. with variable coefficents • Given the following I.V.P: (#36, P. 406) ty "  ty '  y  2 y (0 )  2 y ' (0 )   1 . 4 docsity.com Laplace Transform of Discontinuous and Periodic Functions • Discontinuous functions play a very imp..

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