Holst, Michael J.
Green's Functions and Boundary Value Problems
"This book is an excellent introduction to the wide field of boundary value problems."â€”Journal of Engineering Mathematics
"No doubt this textbook will be useful for both students and research workers."â€”Mathematical Reviews
A new edition of the highlyacclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory
Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems.
Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including:

Nonlinear analysis tools for Banach spaces

Finite element and related discretizations

Best and nearbest 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, the HahnBanach theorem, reflexive Banach spaces, the Banach Schauder and BanachSteinhaus theorems, and the LaxMilgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problemsolving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications.
With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.
Keywords: Numerical Methods & Algorithms, Applied Mathematics in Engineering, Numerical Methods & Algorithms, Applied Mathematics in Engineering
 Author(s)
 Holst, Michael J.
 Stakgold, Ivar
 Publisher
 John Wiley and Sons, Inc.
 Publication year
 2011
 Language
 en
 Edition
 3
 Series
 Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
 Page amount
 736 pages
 Format
 Ebook
 eISBN (PDF)
 9780470906521
 Printed ISBN
 9780470609705