First Course in Fourier Analysis, A

Rating:
Summary: Elegant, Sophisticated Math, Great Examples & Problems
Review: I am taking this class as an undergraduate course with Dr. Healy at University of Maryland at College Park. This is an elegant, thoughtful book that provides a rich math course that is a welcome alternative to run-of-the mill engineering math classes lacking in intangible qualities. Many of the problems are tough and require some rigorous math at an advanced, math-major level (real analysis would be helpful) but are overall accessible to engineering seniors with strong math skills and office hours support from the professor, and the problems are well-geared to illustrating and exploring the topics in the text. As another benefit to the student, the examples definitely help one warm up for the problem solving at the end of the chapters. In addition to the richness and elegance of the subject as presented, this is a thoughtfully constructed and presented text.

The first several chapters introduce fourier transforms and related math such as convolutions as a set of operations in a variety of spaces, including continuous, discrete and periodic spaces. Then the text goes into the theory of distributions/generalized functions and solutions of differential equations. Several additional chapters take the subject into wavelets. The presentation of the Fourier transforms having a variety of manifestations in different kinds of spaces unifies in a fundamentally harmonious (no pun intended!) and beautiful way the disjoint and arbitrary Fourier processing taught to engineering undergraduates.

Rating:
Summary: Moder Approach, Good Balance between Theory & Applications
Review: I have been interested in the Mathematics of Fourier Series/Fourier Transform methods for well over 15 years. I own already well over 10 books on this subject. The book by David Kammler strikes me as having a particularly good balance between theory and applications as well as taking a modern computer approach to this ever relevant subject. Important topics such as sampling theory and the Fast Fourier Transform (FFT) are well covered and explained in detail. Also, chapters that apply Fourier Analysis to important physical areas (heat conduction, light diffraction, wave propagation, musical sound, etc.) illustrate and higlight the relevance of Fourier Methods in the real worls. There is also a nice summary at the end of the book that explains the histoy and most important application of Fourier Analyis (very nice). Ample computer excerices and the traditional proof/derivation homework problems are included. The book also seems to prepare the reader well for the increasingly subject of Wavelets and applying them musical sound. Also, what makes the book stand out from more traditional ones is the emphasis on Numerical Method and using the computer to solve or illustrate some of the powers of Fourier Analysis. Readers considering using this text should best have a background in calcus, differential equations and Matrix methods. This probably puts it at the junior/senior undergradudate level. 1st year graduate students might also benefit from the text.

In a nutshell this is an excellent textbook for anyone serious about Fourier Analysis and applying those methods via computer (or pencil) to real world situation. This is probably one of the best books yet on this very important subject. Highly Recommended!