This book shows the power of the separation of variables technique by solving a variety of problems, many of which go well beyond the usual textbook problems. With a focus on the potential, heat, and wave equations throughout the book, the authors take a spectral expansion view of the technique and explore it in detail. Written at the advanced undergraduate level, the presentation requires a background in engineering mathematics, but no prior exposure to the method. The abundant worked examples provide guidelines for deciding whether and how to apply the method to any given problem, will help in interpreting computed solutions, and give insight into cases in which formal answers may be useless