AMS/IP Studies in Advanced Mathematics 1997; 706 pp; hardcover Volume: 6 Reprint/Revision History: reprinted 1998 ISBN10: 0821807757 ISBN13: 9780821807750 List Price: US$84 Member Price: US$67.20 Order Code: AMSIP/6
 The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters. Titles in this series are copublished with International Press, Cambridge, MA. Readership Graduate students and research mathematicians interested in partial differential equations. Reviews "A large variety of examples and problems for solutions is given ... The book will be certainly of great value with respect to applications."  Monatshefte für Mathematik "Although the scope is largethere are 706 pagesthe chapters tend to be short and to the point, with the detailed work developed in the problems set at the end of each chapter. These problem sets should ideally provide instructors delivering an advanced mathematical methods course with plenty of ideas for tutorial material for their students. The book is comprehensive in its background coverage, including, for example, an introductory chapter on partial differentiation, which at the same time brings in and manipulates a couple of wellknown canonical forms, by way of illustration. In all, this text is a useful addition to the extensive literature on PDEs."  Mathematical Reviews "Naturally the book will be helpful for a very wide audience which would benefit from reading itfrom students and Ph.D. candidates (not only of mathematical direction) to specialists. This book can be recommended as a well written handbook containing an original approach to the description of basic and advanced methods of the theory of PDE."  Zentralblatt MATH Table of Contents  Introduction
 Partial differentiation
 Solutions of PDE's and their specification
 PDE's and related arbitrary functions
 Particular solutions of PDE's
 Similarity solutions
 Correctly set problems
 Some preliminary aspects of linear first order PDE's
 First order PDE's, linear
 First order nonlinear PDE's
 Some technical problems and related PDE's
 First order PDE's, general theory
 First order PDE's with multiple independent variables
 Original detaials of the Fourier approach to boundary value problems
 Eigenfunctions and eigenvalues
 Eigenfunctions and eigenvalues, continued
 Nonorthogonal eigenfunctions
 Further example of Fourier style analysis
 Inhomogeneous problems
 Local heat sources
 An inhomogeneous configuration
 Other eigenfunction/eigenvalue problems
 Uniqueness of solutions
 Alternative representations of solutions
 Other differential equations and inferences therefrom
 Second order ODE's
 Boundary value problems and SturmLiouville theory
 Green's functions and boundary value problems
 Green's functions and generalizations
 PDE's, Green's functions, and integral equations
 Singular and infinite range problems
 Orthogonality and its ramifications
 Fourier expansions: Generalities
 Fourier expansions: Varied examples
 Fourier integrals and transforms
 Applications of Fourier transforms
 Legendre polynomials and related expansions
 Bessel functions and related expansions
 Hyperbolic equations
 Afterwords
 Bibliography
 Index
