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Praise for the Second Edition
"This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics
"No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews
A new edition of the highly-acclaimed 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 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, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving 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.
- Sales Rank: #590355 in Books
- Published on: 2011-02-08
- Original language: English
- Number of items: 1
- Dimensions: 9.50" h x 2.05" w x 6.50" l, 2.99 pounds
- Binding: Hardcover
- 888 pages
Review
From the Publisher
A Systematic analysis of boundary value problems and the principal methods used for their solution, including those based on Green's functions and eigenfunction expansions. Provides necessary background in functional analysis through the study of distributions, Hilbert spaces, integral equations, and spectral theory. Reviews of metric spaces and contraction mappings, spectral theory, transforms, and partial differential equations progress to a treatment of nonlinear problems, including bifurcation and monotone methods. Special sections provide careful derivations of equations in chemical reaction engineering; emphasis on dependence on the data overview of Green's function; a unified treatment of delta sequences; Riesz Schauder theory; and continuous spectrum. Also discusses modeling and approximation techniques such as perturbation theory and variational methods. Examples are chosen from a wide range of applications in engineering and physical sciences.
From the Back Cover
Praise for the Second Edition
"This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics
"No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews
A new edition of the highly-acclaimed 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 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, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving 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.
Most helpful customer reviews
24 of 27 people found the following review helpful.
Systematic, not a 'cookbook'
By Professor Joseph L. McCauley
Actually, I preferred the first (2 volume) edition of this work and used the first volume along with Whittaker and Watson to teach first semester math methods to physics and engineering students. This book provides the most readable, systematic approach to boundary-value problems, based on Weyl's lemma. Not to be compared with the usual cookbooks on math methods because it shows you how to construct nonstandard orthogonal expansions, not merely the usual Fourier, Bessel and Legendre variety. Also very good on Dirac's delta funaction. For second semester, for years I also used Bender and Orszag.
G is called 'the Green function' and not 'the Green's function' (one does not say 'the Bessel's function').
12 of 16 people found the following review helpful.
This is one of the best books on applicable PDE's
By A Customer
This is a classic text. The authors not only knows much more than is in the book but also has a clear idea about the applied side of math.
A close competitor is Sobolev's book on PDE's.
0 of 0 people found the following review helpful.
Five Stars
By S. Thirugnanasampanthan
Excellent Book and in Excellent condition as new !
See all 4 customer reviews...
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