Since its introduction in 1828, using Green's functions has become a fundamental mathematical technique for solving boundary value problems. Most treatments of the technique, however, focus on its theory and classical application, in physics, rather than the practical means of finding Green's functions for applications in engineering and the sciences. Green's Functions with Applications systematically presents the various methods of deriving these useful functions. It leads readers step by step through the process of developing Green's functions for ordinary and partial differential equations. Exploring beyond the classical problems involving the wave, heat, and Helmholtz equations, the book includes special sections on leaky modes, water waves, and absolute/convective instability. With its wealth of examples and problems drawn from the literature, this book provides a treasure trove of methods to construct and compute Green's functions. It is the most exhaustive source book of Green's functions yet available and the only one designed specifically for engineering and scientific applications.