Definition of Laplace Transform


       The Laplace transform is defined as below :
        Let f(t) be a real function of a real variable t defined for t˃0, then

       Where F(s) is called Laplace transform of f(t). and the variable 's' which appears F(s) is frequency dependent complex variable. It is given by,

Where    σ = Real part of complex variable 's'.
               ω= Imaginary part of complex variable 's'.
       The time function f(t) is obtained back from the Laplace transform by a process called Inverse Laplace transform and denoted as L-1. Thus,

       The time function f(t) and its Laplace transform F(s) is called transform pair.



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