An Introduction to Fourier Analysis

This book is an introductory textbook on Fourier analysis and its applications,written for mathematics,science,and engineering students with a background in calculus and basic linear algebra. It covers Fourier series,orthogonal functions,Fourier and Laplace transforms,and complex variables,with examples and exercises implemented in Maple,MATLAB,and Python.

Format: Paperback / softback
Length: 402 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

This comprehensive textbook serves as an invaluable resource for students seeking to delve into the realm of Fourier analysis and its interconnected subjects. Designed with a primary focus on mathematics, science, and engineering students possessing a foundation in calculus and basic linear algebra, it serves as a textbook for undergraduate courses in Fourier analysis or applied mathematics. Within its pages, these topics are intricately interconnected, facilitated by the application of spectral analysis to both analog and discrete signals. This introductory text provides a solid foundation in Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables.

To enhance comprehension and practical application, numerous examples and exercises are presented, accompanied by implementations of popular computing platforms such as Maple, MATLAB, and Python. These implementations facilitate the computation of series expansions and transforms, enabling students to gain hands-on experience with the subject matter.

Upon completing this book, students will acquire a profound understanding of various key concepts, including:

Convergence and summation of infinite series: This fundamental principle forms the basis for analyzing and computing infinite series, which are essential in Fourier analysis.

Representation of functions by infinite series: Students will learn how to represent functions using infinite series, which allows for a concise and efficient representation of complex functions.

Trigonometric and Generalized Fourier series: This chapter explores the representation of trigonometric functions and other periodic functions using Fourier series, enabling students to understand their behavior and properties.

Legendre, Bessel, gamma, and delta functions: Students will delve into the representation of special functions such as Legendre, Bessel, gamma, and delta functions, which play crucial roles in Fourier analysis and other areas of mathematics.

Complex numbers and functions: This chapter introduces complex numbers and their applications in Fourier analysis, providing students with the tools to work with complex-valued functions and equations.

Analytic functions and integration in the complex plane: Students will study analytic functions, including the exponential, logarithm, and trigonometric functions, and learn how to perform integration in the complex plane.

Fourier and Laplace transforms: This chapter introduces Fourier and Laplace transforms, which are fundamental tools in Fourier analysis and have wide applications in mathematics, physics, and engineering.

The relationship between analog and digital signals: Students will explore the connection between analog and digital signals, recognizing the similarities and differences between these two signal representations.

Dr. Russell L. Herman, a distinguished professor of Mathematics and Physics at the University of North Carolina Wilmington, is the author of this textbook. With an impressive teaching career, Dr. Herman has taught introductory through graduate courses in a diverse range of subjects, including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests span nonlinear wave equations, soliton perturbation theory, fluid dynamics, and other areas of mathematical physics.

By utilizing the insights and practical applications provided in this textbook, students will gain a deep appreciation for Fourier analysis and its profound impact on various fields of mathematics, science, and engineering. Whether they are pursuing careers in mathematics, physics, or any other discipline that relies on Fourier analysis, this resource will serve as a valuable guide and catalyst for their academic journey.

Weight: 1010g
Dimension: 218 x 275 x 26 (mm)
ISBN-13: 9781032477251