Applied Partial Differential Equations (4th Edition)
Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations.  Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial differential equations, nonhomogeneous problems, Green's functions for time-independent problems, infinite domain problems, Green's functions for wave and heat equations, the method of characteristics for linear and quasi-linear  wave equations and a brief introduction to Laplace transform solution of  partial differential equations.  For scientists and engineers.