The goal of the book is to obtain a formal solution to a given problem either by the method of separation of variables or by the method of general solutions and to verify that the formal solution possesses all the required properties. To provide the mathematical justification for this approach, the theory of Sturm–Liouville problems, the Fourier series, and the Fourier transform are fully developed. The book assumes a knowledge of advanced calculus and elementary differential equations.

Contents:

• Linear Partial Differential Equations
• The Wave Equation
• Green's Function and Sturm–Liouville Problems
• Fourier Series and Fourier Transforms
• The Heat Equation
• Laplace's Equation and Poisson's Equation
• Problems in Higher Dimensions