This text is designed to be an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It will primarily be used by mathematics students with a background in ordinary differential equations and advanced calculus. There are two main objectives of this text. The first is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. The second is a clear presentation of the classical method of separation of variables used in solving boundary value problems with the aid of those representations. This book has been published by McGraw-Hill since 1941.

1 Partial Differential Equations of Physics 2 The Fourier Method 3 Orthonormal Sets and Fourier Series 4 Convergence of Fourier Series 5 Boundary Value Problems 6 Sturm-Liouville Problems and Applications 7 Fourier Integrals and Applications 8 Bessel Functions and Applications 9 Legendre Polynomials and Applications 10 Verification of Solutions and Uniqueness Appendixes

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