Partial Differential Equations of Applied Mathematics

This new edition features the latest tools for modeling,characterizing, and solving partial differential equations The Third Edition of this classic text offers a comprehensive guideto modeling, characterizing, and solving partial differentialequations (PDEs). The author provides all the theory and toolsnecessary to solve problems via exact, approximate, and numericalmethods. The Third Edition retains all the hallmarks of itsprevious editions, including an emphasis on practical applications,clear writing style and logical organization, and extensive use ofreal-world examples. Among the new and revised material, the book features: * A new section at the end of each original chapter, exhibiting theuse of specially constructed Maple procedures that solve PDEs viamany of the methods presented in the chapters. The results can beevaluated numerically or displayed graphically. * Two new chapters that present finite difference and finiteelement methods for the solution of PDEs. Newly constructed Mapleprocedures are provided and used to carry out each of thesemethods. All the numerical results can be displayedgraphically. * A related FTP site that includes all the Maple code used in thetext. * New exercises in each chapter, and answers to many of theexercises are provided via the FTP site. A supplementaryInstructor's Solutions Manual is available. The book begins with a demonstration of how the three basic typesof equations-parabolic, hyperbolic, and elliptic-can be derivedfrom random walk models. It then covers an exceptionally broadrange of topics, including questions of stability, analysis ofsingularities, transform methods, Green's functions, andperturbation and asymptotic treatments. Approximation methods forsimplifying complicated problems and solutions are described, andlinear and nonlinear problems not easily solved by standard methodsare examined in depth. Examples from the fields of engineering andphysical sciences are used liberally throughout the text to helpillustrate how theory and techniques are applied to actualproblems. With its extensive use of examples and exercises, this text isrecommended for advanced undergraduates and graduate students inengineering, science, and applied mathematics, as well asprofessionals in any of these fields. It is possible to use thetext, as in the past, without use of the new Maple material. An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.