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.
- 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.
- 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.
- 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.)
- Note the Index of Symbols on p. 429.
Return to the
Math 480 Homepage.
Most recently updated on March 24, 2018.