Some Exercises in Laplace Transform Integrals

Extract

If 𝜙(t) is a given function of the real variable t then the integral (in which p is constant)

if convergent, is defined to be the Laplace transform of 𝜙(t). The use of the integral in determining the solutions of certain types of differential equations is now well known; see, for example, Carslaw and Jaeger, Operational methods in applied mathematics (Oxford University Press).