## Textbook for Math 480B, Spring 2018

The textbook for this course is Fourier Analysis and Its Applications, by Gerald B. Folland. We will cover most of Chapters 1 through 4 (Fourier Series and their use, via separation of variables, in solving boundary value problems [BVPs]), substantial parts of Chapter 5 (Bessel Functions and their use in BVPs), and a bit of Chapter 6 (Legendre polynomials and their use in BVPs).

The text has been published by the American Mathematical Society in recent years and in the 1990's by Wadsworth & Brooks/Cole. The two versions are essentially identical, so either will work. Errata (corrections) are available at Professor Folland's homepage. Be sure to check the errata. Some are minor (e.g., mispellings) but many are important. If you have a first, second or third printing by Brooks/Cole, check BOTH lists of errata.

Suggestions for using the text.

1. This book is designed to be read (unlike some math books, which are best used by scanning for important formulas and example problems to mimic). It is written at a fairly sophisticated level, discussing not just how to do the calculations but how to think about them for greatest understanding. In a couple of spots in chapter 3, the book is perhaps a touch too advanced for this course: cf. remarks on p. vi in the Preface. In class we will discuss this material, indicating which ideas you need to grasp fully and which are included more for background.
2. Many of the examples and solutions in the book are computed or presented in an extremely efficient way. When you, as a beginner in the subject, tackle similar problems, you should not expect to achieve the same degree of efficiency. In particular frequently some steps are skipped, especially if they are "elementary" (e.g., compute a derivative or do some algebra) or have appeared in a previous example. Don't be shy about writing out more steps for the book's examples and going through the steps again in each problem (until they become as obvious to you as they are to the author). In fact, every time the author says something like "using formulas a and b, equation c can be rewritten ... ", it's a good idea for you to write out the (possibly several lines of) computation neatly and completely, and add them to your course notes.
3. Ignore the book's answers (pp. 413 ff.) until you have computed your own! Your goal is to learn to solve problems, not to reverse engineer the solution from the answer. Also, I've seen students give up on perfectly correct work because they couldn't see how it would lead to the book's answer. (A simplification or re-indexing a summation at the end of the computation can change appearances substantially.)
4. Note the Index of Symbols on p. 429.