PARTIAL DIFFERENTIAL EQUATIONS FOR MATHEMATICAL PHYSICISTS (HB 2020) Hardcover

Partial Differential Equations for Mathematical Physicists is designed for graduate students, researchers in theoretical physics and applied mathematics, and professionals seeking a course in partial differential equations. The book covers the core aspects of the subject, requiring only a basic understanding of introductory calculus, ordinary differential equations, and certain areas of classical mechanics. Emphasis is placed on the methods of partial differential equations and their application in obtaining solutions, rather than on foundational theory. After introducing basic concepts, the focus shifts to the three primary types of second-order linear equations: elliptic, hyperbolic, and parabolic. Detailed treatments are provided on deriving Green's functions, understanding characteristics, and applying techniques to solve these equations rigorously. The book includes extensive discussions on separation of variables, Green's function methods, and Fourier and Laplace transforms. Appendices offer supplementary materials on the Dirac delta function, Fourier transforms, and Laplace transforms. A variety of worked-out problems and exercises at the end of each chapter are included to support students' learning. This text aims to provide a comprehensive and unified approach to the fundamentals of partial differential equations.