Principles of Fourier Analysis

by Kenneth B. Howell

Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented.Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.

Genres: Mathematics

791 pages, Kindle Edition

First published May 18, 2001

Reviews

[5dd · Rating 5 out of 5]

Great book on a very important topic in applied mathematics. I first read the manuscript in 2000 when I took a class on Fourier Analysis from the author, Prof Howell. I've since returned to the published version of the text on a number of occasions, sometimes as a reference and sometimes just for the pleasure of following along as Dr. Howell constructs a clear, logical and well-ordered foundation for the subject. Aside from its wonderful clarity, it is the only mathematics book I've ever read that is truly 'witty'. Not merely 'clever'; lots of descriptions and asides are downright funny. In that regard, it is most certainly a reflection of the author. I wish there were more math, science and engineering books written in such a personable style.

With more than 700 pages, the book provides an excellent introduction to Fourier before addressing more advanced topics like the generalized theory of Fourier transforms and the discrete Fourier transform. It is almost entirely self-contained in the sense that the only prerequisites are a basic knowledge of calculus and some linear algebra. Anybody seeking a solid foundation in Fourier Analysis (which, in my opinion, ought to include all mathematicians, all scientist and all engineers) is strongly encouraged to take a look at this book.