An introductory treatment of Fourier series and their applications to boundary value problems in partial equations that arise in engineering and physics. This revision incorporates up-to-date mathematics. Many sections have been rewritten to improve the motivation of the theory, and numerous illustrations and exercises have been added throughout the book. The new emphasis on solving boundary value problems with non-homogenous differential equations should benefit students who are faced with a wider range of physics and engineering problems than in the past. The introduction to the Sturm-Louisvill problems is motivated by several applications to boundary value problems.