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Principles of Fourier Analysis (Studies in Advanced Mathematics): Kenneth B. Howell (Repost)

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.

Review:

I really Like this Book

This book is wonderful. It is quite clear and is written at a level for seniors and beginning graduate students.

It presentation is not as intense and terse as Lighthill's and Zemanian's on this subject. There is a good balance between the rigor and pedagogy that is quite appealing to me, along with examples and exercise with some answers/hints in the back for the end of chapter exercises.

Hopefully, Dr. Howell will update this book soon if needed. Also, it would be nice if the book were available in the size, shape and price of the books published by Dover. The book is quite big, thick and costs a hundred bucks.

Overall, I think many like/would like this book - it seems to get much use in the Library.

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Rating:
2.5 out of 5 by Book123