Laplace Transform Theory

Description

In this book I have tried to present a rigorous account of the elementary theory of the Laplace transform, besides giving a description of some of its more useful applications. The book is primarily intended for mathe- matics students, though it is hoped that it will also be of value to students of physics or engineering who wish to understand more of the mathe- matical tools they use. I have taken as my standard the level of a course comparable with those required in Methods of Mathematical Physics for the Special Mathematics Degree, or the Postgraduate Diploma in Mathematics of the University of London. I have been associated with both courses at my present college. I have therefore assumed a knowledge of mathematics which a student taking such a course could ordinarily be expected to possess. In particular I have assumed that the reader is familiar with Cauchy's theorem and its immediate consequences and of the simple properties of the factorial function z! (used in preference to the Gamma function r(z)=(z-l)!), the Legendre function Pv(z) and the Bessel function of the first kind lv(z). Other functions are referred to, but then I hope the passages are self-contained, and need no previous knowledge.