This popular text presents some of the most important and widely used methods for solving PDEs. Along with a new chapter on complex variable methods, this edition includes new sections on Cauchy–Euler equations, Bessel functions, Legendre polynomials, spherical harmonics, applications of Fourier transformations, and general hyperbolic equations. It lists additional mathematical models based on PDEs and shows how the methods of separation of variables and eigenfunction expansion work for equations other than heat, wave, and Laplace. The author also added many new worked examples and exercises. Ancillary materials are available upon qualifying course adoption.