Fourier Series and Orthogonal Functions (Dover Books on Mathematics)

Book Details:

• Author: Harry F. Davis

• Publisher: Dover

• Edition: New

• Binding: Paperback

• Number of Pages: 416

• ISBN: 9780486659732

• Release Date: 01-05-1989

• Languages: English

• Package Dimensions: 8.4 x 5.5 x 0.9 inches

About the Book:

"Fourier Series and Orthogonal Functions" by Harry F. Davis is a comprehensive and insightful textbook that combines both theory and practical examples to introduce Fourier series and orthogonal functions. The book's focus on the Fourier method and its application to solving boundary-value problems makes it an essential resource for advanced undergraduate and graduate students in mathematics, physics, and engineering.

The text does not require prior knowledge of partial differential equations or advanced vector analysis, making it accessible to students who are familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations. The book begins by laying the foundation with topics such as linear spaces, orthogonal functions, and the Fourier series, followed by an introduction to Legendre polynomials and Bessel functions. In Chapter 5, the author explores heat and temperature, and in the final chapter, the book delves into waves, vibrations, and harmonic analysis.

Davis introduces several topics not often found in typical undergraduate texts, including summability theory, generalized functions, and spherical harmonics. The book also includes 570 exercises that encourage students to review and apply the theory to practical problems, making it ideal for those preparing for advanced studies in functional analysis, quantum mechanics, or abstract harmonic analysis. With its depth of content and accessibility, this book serves as both a textbook and a valuable reference for professionals seeking to expand their mathematical expertise.