Chapman and Hall/CRC
224 pages | 20 B/W Illus.
This book is intended for graduate students, researchers of theoretical physics and applied mathematics, and professionals who want to undertake a course-work in partial di erential equations. It gives all the essentials of the subject with the only prerequisites are an elementary knowledge of introductory calculus, ordinary di erential equations and certain aspects of classical mechanics. We have laid greater stress on the methodologies of partial di erential equations and how they can be implemented as tools for extracting their solutions rather than trying to dwell on the foundational aspects. After covering some basic materials 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 class. For such equations a detailed treatment is given of the derivation of Green's functions, of the role of characteristics and of 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 are worked out and equally a large number of exercises have been appended at the end of each chapter keeping in mind the needs of the students. It is expected that the book would provide a systematic and unitary coverage of the basics of partial di erential equations.
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.