Definition of Integral Transforms and Distributions

Abstract

This first chapter describes a brief definition of integral transforms, such as Laplace and Fourier transforms, a rough definition of delta and step functions which are frequently used as the source function, and a concise introduction of the branch cut for a multi-valued square root function. The multiple integral transforms and their notations are also explained. The newly added Sect. 1.3 explains closely how to introduce the branch cut for the multi-valued square root function. The branch cut and the argument of the square root function along the branch cut are employed throughout the book. The discussion on the argument of the root function along the branch cut is unique and instructive for the reader, when he/she starts to apply the complex integral to the inverse transform. The last short comment lists some important formula books which are crucial for the inverse transform, i.e. the evaluation of the inversion integral.