This is a very appealing textbook because it offers the instructor a number of choices. As the title says, the text itself mainly focuses on applications, but there is plenty of beautiful theory shown in the exercises. Nice examples of this include the use of orthogonal function series to compute infinite sums, such as the sum of the squares of the reciprocals of all positive integers. In the preface, the author himself explains three different ways to teach using this book, depending on how deeply one wants to go into theory.
The book is on the shorter side, with only 312 pages. This means that some sections have as few as eight exercises, which is less than what most students are used to see. A little bit less than half of them have their numerical answers included at the end, but usually not their full solutions.
The style of the book is simple and reader-friendly, with no unnecessary complications. The balance of theory and applications is well struck. If I teach this course, this book will be on the top of my list. It remains to be seen if my students will complain about the low number of exercises.
Miklós Bóna is Professor of Mathematics at the University of Florida.