Principles of Fourier Analysis

Principles of Fourier Analysis is a practical and mathematically solid introduction to Fourier analysis, providing a comprehensive overview of the mathematical theory, including Fourier series, classical Fourier transforms, generalized Fourier transforms, and discrete theory. It offers a cleaner and more coherent theory, with insightful derivations and thought-provoking examples, and helps readers develop the ability to handle the more sophisticated mathematics required.

Format: Paperback / softback
Length: 804 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

Fourier analysis stands as a remarkable and indispensable toolkit for engineers, scientists, and applied mathematicians alike. Consequently, students and practitioners in these fields require a practical and mathematically robust introduction to its principles. They seek straightforward verifications of its results and formulas, as well as clear indications of the limitations of those results and formulas.

Principles of Fourier Analysis meets these demands in abundance. It offers a comprehensive exposition of the mathematical theory of Fourier analysis, encompassing the development of Fourier series, classical Fourier transforms, generalized Fourier transforms, and analysis, as well as the discrete theory. The author's unique approach to defining the classical Fourier transform yields a much cleaner, more coherent theory that seamlessly leads to a foundational point for the generalized theory. Furthermore, he introduces a novel generalized theory based on the utilization of Gaussian test functions, resulting in a theory that is even more general yet remarkably simpler than commonly presented.

Principles of Fourier Analysis fosters a deep appreciation and comprehension of the fundamental concepts, catering to both novice students who have encountered limited or no Fourier analysis and advanced students seeking a deeper understanding. Insightful, non-rigorous derivations drive much of the material, while thought-provoking examples illustrate the potential pitfalls of misusing formulas. With clear and engaging exposition, readers cultivate the ability to handle the more sophisticated mathematics that Fourier analysis ultimately demands.

Weight: 1490g
Dimension: 254 x 178 (mm)
ISBN-13: 9781032477008
Edition number: 2 ed