This book arose from the development of a course on Fourier and Laplace transforms for the Open University of the Netherlands. Originally it was the intention to get a suitable course by revising part of the book Analysis and numerical analysis, part 3 in the series Mathematics for higher education by R. van Asselt et al. (in Dutch). However, the revision turned out to be so thorough that in fact a completely new book was created. We are grateful that Educaboek was willing to publish the original Dutch edition of the book besides the existing series.

In writing this book, the authors were led by a twofold objective:

1. - the ‘didactical structure’ should be such that the book is suitable for those who want to learn this material through self-study or distance teaching, without damaging its usefulness for classroom use;

2. - the material should be of interest to those who want to apply the Fourier and Laplace transforms as well as to those who appreciate a mathematically sound treatment of the theory.

We assume that the reader has a mathematical background comparable to an undergraduate student in one of the technical sciences. In particular we assume a basic understanding and skill in differential and integral calculus. Some familiarity with complex numbers and series is also presumed, although chapter 2 provides an opportunity to refresh this subject.

The material in this book is subdivided into parts. Each part consists of a number of coherent chapters covering a specific part of the field of Fourier and Laplace transforms.