A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley begins with a physical problem and applies the results to different situations. 1966 edition. Reprint of the W. A. Benjamin, Inc., New York, 1966 edition.
Here's a sample of other books in this Dover category
Fourier Series and Orthogonal Polynomials by Dunham Jackson This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Includes Pearson frequency functions, Jacobi, Hermite, and Laguerre polynomials, more.1941 edition.
Fourier Series by Georgi P. Tolstov This reputable translation covers trigonometric Fourier series, orthogonal systems, double Fourier series, Bessel functions, the Eigenfunction method and its applications to mathematical physics, operations on Fourier series, more. Over 100 problems. 1962 edition.
Fourier Series and Orthogonal Functions by Harry F. Davis An incisive text combining theory and practical example to introduce Fourier series, orthogonal functions and applications of the Fourier method to boundary-value problems. Includes 570 exercises. Answers and notes.
Fourier Series, Transforms, and Boundary Value Problems: Second Edition by J. Ray Hanna, John H. Rowland This volume introduces Fourier and transform methods for solutions to boundary value problems associated with natural phenomena. It emphasizes basics and techniques rather than theory and includes exercises with solutions. 1990 edition.