Theoretical Numerical Analysis A Functional Analysis Framework

ISBN-10: 1441904573
ISBN-13: 9781441904577
Edition: 3rd 2009
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Description: This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move  More...

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Book details

Edition: 3rd
Copyright year: 2009
Publisher: Springer
Publication date: 6/2/2009
Binding: Hardcover
Pages: 625
Size: 6.50" wide x 9.50" long x 1.50" tall
Weight: 2.288
Language: English

This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study. Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added.Review of earlier edition:"...the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references."R. Glowinski, SIAM Review, 2003

Kendall E. Atkinson, PhD, is Professor Emeritus in the Departments of Mathematics and Computer Science at the University of Iowa. He has authored books and journal articles in his areas of research interest, which include the numerical solution of integral equations and boundary integral equation methods. Weimin Han, PhD, is Professor in the Department of Mathematics at the University of Iowa, where he is also Director of the interdisciplinary PhD Program in Applied Mathematical and Computational Science. Dr. Han currently focuses his research on the numerical solution of partial differential equations. David E. Stewart, PhD, is Professor and Associate Chair in the Department of Mathematics at the University of Iowa, where he is also the departmental Director of Undergraduate Studies. Dr. Stewart's research interests include numerical analysis, computational models of mechanics, scientific computing, and optimization.

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