Praise for the Second Edition
"This book is an excellent introduction to the wide field ofboundary value problems."--Journal of EngineeringMathematics
"No doubt this textbook will be useful for both students andresearch workers."--Mathematical Reviews
A new edition of the highly-acclaimed guide to boundary valueproblems, now featuring modern computational methods andapproximation theory
Green's Functions and Boundary Value Problems, Third Editioncontinues the tradition of the two prior editions by providingmathematical techniques for the use of differential and integralequations to tackle important problems in applied mathematics, thephysical sciences, and engineering. This new edition presentsmathematical concepts and quantitative tools that are essential foreffective use of modern computational methods that play a key rolein the practical solution of boundary value problems. With acareful blend of theory and applications, the authors successfullybridge the gap between real analysis, functional analysis,nonlinear analysis, nonlinear partial differential equations,integral equations, approximation theory, and numerical analysis toprovide a comprehensive foundation for understanding and analyzingcore mathematical and computational modeling problems.
Thoroughly updated and revised to reflect recent developments,the book includes an extensive new chapter on the modern tools ofcomputational mathematics for boundary value problems. The ThirdEdition features numerous new topics, including:
* Nonlinear analysis tools for Banach spaces
* Finite element and related discretizations
* Best and near-best approximation in Banach spaces
* Iterative methods for discretized equations
* Overview of Sobolev and Besov space linear
* Methods for nonlinear equations
* Applications to nonlinear elliptic equations
In addition, various topics have been substantially expanded,and new material on weak derivatives and Sobolev spaces, theHahn-Banach theorem, reflexive Banach spaces, the Banach Schauderand Banach-Steinhaus theorems, and the Lax-Milgram theorem has beenincorporated into the book. New and revised exercises foundthroughout allow readers to develop their own problem-solvingskills, and the updated bibliographies in each chapter provide anextensive resource for new and emerging research andapplications.
With its careful balance of mathematics and meaningfulapplications, Green's Functions and Boundary Value Problems, ThirdEdition is an excellent book for courses on applied analysis andboundary value problems in partial differential equations at thegraduate level. It is also a valuable reference for mathematicians,physicists, engineers, and scientists who use applied mathematicsin their everyday work.