DOI link for Laplace Transforms
Laplace Transforms book
The Laplace transform has been introduced into the mathematical literature by a variety of procedures. Among these are: (a) in its relation to the Heaviside operational calculus, (b) as an extension of the Fourier integral, (c) by the selection of a particular form for the kernel in the general Integral transform, (d) by a direct deﬁnition of the Laplace transform, and (e) as a mathematical procedure that involves multiplying the function f(t) by est dt and integrating over the limits 0 to 1. We will adopt this latter procedure.