Includes numerous worked examples and applications in science and engineering.

Includes bibliographical references and index.

Heat equation -- Method of separation of variables -- Fourier series -- Wave equation: vibrating strings and membranes -- Sturm-Liouville eigenvalue problems -- Finite difference numerical methods for partial differential equations -- Higher-dimensional partial differential equations -- Nonhomogeneous problems -- Green's functions for time-independent problems -- Fourier transform solutions of partial differential equations -- Green's functions for wave and heat equations -- Method of characteristics for linear and quasilinear wave equations -- Laplace transform solution of partial differential equations -- Dispersive waves, stability, nonlinearity, and perturbation methods.

The book Applied Partial Differential Equations with Fourier Series and Boundary Value Problems provides a thorough introduction to analytical and numerical methods for solving partial differential equations. It covers the heat, wave, and Laplace equations, Fourier series, Sturm–Liouville theory, Green's functions, transform methods, finite difference methods, and perturbation techniques. Rich with worked examples and engineering applications, it is widely used by students of mathematics, physics, and engineering for understanding mathematical models of physical phenomena.