Partial Differential Equations for Mathematical Physicists

Partial Differential Equations for Mathematical Physicists is intended for graduate students, researchers of theoretical physics and applied mathematics, and professionals who want to take a course in partial differential equations. This book offers the essentials of the subject with the prerequisite being only an elementary knowledge of introductory calculus, ordinary differential equations, and certain aspects of classical mechanics. We have stressed more the methodologies of partial differential equations and how they can be implemented as tools for extracting their solutions rather than dwelling on the foundational aspects. After covering some basic material, the book proceeds to focus mostly on the three main types of second order linear equations, namely those belonging to the elliptic, hyperbolic, and parabolic classes. For such equations a detailed treatment is given of the derivation of Green's functions, and of the roles of characteristics and techniques required in handling the solutions with the expected amount of rigor. In this regard we have discussed at length the method of separation variables, application of Green's function technique, and employment of Fourier and Laplace's transforms. Also collected in the appendices are some useful results from the Dirac delta function, Fourier transform, and Laplace transform meant to be used as supplementary materials to the text. A good number of problems is worked out and an equally large number of exercises has been appended at the end of each chapter keeping in mind the needs of the students. It is expected that this book will provide a systematic and unitary coverage of the basics of partial differential equations. Key Features An adequate and substantive exposition of the subject. Covers a wide range of important topics. Maintains mathematical rigor throughout. Organizes materials in a self-contained way with each chapter ending with a summary. Contains a large number of worked out problems.

Author Biography: Bijan Bagchi received his B.Sc., M.Sc., and Ph.D. degrees from the University of Calcutta. He has a variety of research interests and involvements ranging from spectral problems in quantum mechanics to exactly solvable models, supersymmetric quantum mechanics, parity-time- symmetry and related non-Hermitian phenomenology, nonlinear dynamics, integrable models and high energy phenomenology. He has published more than 150 research articles in refereed journals and held a number of international visiting positions. He is the author of the books entitled Advanced Classical Mechanics and Supersymmetry in Quantum and Classical Mechanics both published by CRC respectively in the years 2017 and 2000. He was formerly a Professor in Applied Mathematics at the University of Calcutta and currently a Professor in the Department of Physics at Shiv Nadar University.

Preface. Author Bio. Preliminary concepts and background material. Basic properties of a second order linear PDE. PDE: The elliptic form. PDE: The hyperbolic form. PDE: The parabolic form. Solving PDEs by the integral transform method. A Dirac delta function. B Fourier transform. C Laplace transform. Bibliography. Index.