Partial Differential Equations (AMS Chelsea Publishing) Hardcover – 30 Aug. 1998

This book is a gem. It fills the gap between the standard introductory material on PDEs that an undergraduate is likely to encounter after a good ODE course (separation of variables, the basics of the second-order equations from mathematical physics) and the advanced methods (such as Sobolev spaces and fixed point theorems) that one finds in modern books.Although this is not designed as a textbook for applied mathematics, the approach is strongly informed by applications. For instance, there are many existence and uniqueness results, but they are usually approached via very concrete techniques. The text contains the standard topics that one expects in an intermediate PDE course: the Dirichlet and Neumann problems, Cauchy's problem, characteristics, the fundamental solution, PDEs in the complex domain, plus a chapter on finite differences, on nonlinear fluid mechanics, and another on integral equations. It is an excellent text for advanced undergraduates or beginning graduate students in mathematics or neighboring fields, such as engineering and physics, where PDEs play a central role. Contents: The method of power series Equations of the first order Classification of partial differential equations Cauchy's problem for equations with two independent variables The fundamental solution Cauchy's problem in space of higher dimension The Dirichlet and Neumann problems Dirichlet's principle Existence theorems of potential theory Integral equations Eigenvalue problems Tricomi's problem; formulation of well posed problems Finite differences Fluid dynamics Free boundary problems Partial differential equations in the complex domain Bibliography Index.