The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms, and Laplace transforms. Fourier series (and power series) are important examples of useful series of functions. Applications of Fourier series may be found in many diverse theoretical and applied areas. The same holds for integral transforms. The Fourier and Laplace transforms are the best known of these transforms and are prototypes of the general integral transforms.

Fourier series and integral transforms are theoretically based on a natural amalgamation of concepts from both linear algebra and integral and differential calculus. In other words, they are a mix of algebra and analysis. We assume that the reader is well versed in the basics of these two areas. Nevertheless, in Chapter 1 is found a somewhat concise review of some of the relevant concepts and facts from linear algebra.

The best, most efficient, and perhaps only way to learn mathematics is to study and review the material and to solve exercises. At the end of almost every section of this book may be found a collection of exercises. A set of review exercises is to be found at the end of each chapter. To truly and properly understand the subject matter, it is essential to solve exercises.