Engineering Mathematics, Volume II, Second Edition

9

Laplace Transform

The study of Laplace transform is essential for engineers and scientists because these transforms provide easy and powerful means of solving differential and integral equations. The Laplace transforms directly provides the solution of differential equations with given boundary values without finding the general solution first. A Laplace transform is an extension of the continuous-time Fourier transform motivated by the fact that this transform can be used to a wider class of signals than the Fourier transform can. In fact, Fourier transform does not converge for many signals whereas the Laplace transform does. Fourier transform is not applicable to initial-value problems whereas Laplace transform is applicable. Also some ...