Theoretical Numerical Analysis: A Functional Analysis Framework (Texts in Applied Mathematics) [Hardcover]

Kendall Atkinson (Author), Weimin Han (Author)

Book Description

Publication Date: June 21, 2007 | ISBN-10: 0387258876 | ISBN-13: 978-0387258874 | Edition: 2nd

This textbook covers basic results of functional analysis and also some additional topics which are needed in theoretical numerical analysis. For this second edition, a new chapter on Fourier analysis and wavelets and over 140 new exercises have been added, almost doubling the exercise amount from the last edition. Many sections from the first edition have been revised. Some of the other topics covered in this book are functional analysis and approximation theory, nonlinear analysis, Sobolev spaces, elliptic boundary value problems and variational inequalities.

Editorial Reviews

Review

Overall, 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. - SIAM

From the Back Cover

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, boundary integral equations for planar regions, and multivariable polynomial approximations. 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. In this third edition, a new chapter, Multivariable Polynomial Approximations, is included, numerous changes are made 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 --This text refers to the Paperback edition.

Product Details

• Hardcover: 576 pages
• Publisher: Springer; 2nd edition (June 21, 2007)
• Language: English
• ISBN-10: 0387258876
• ISBN-13: 978-0387258874
• Product Dimensions: 9.1 x 6.2 x 1.4 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,246,206 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 12 people found the following review helpful:

5.0 out of 5 stars About Theoretical Numerical Analysis

by Kendall E. Atkinson, April 17, 2005

By 

Sommariva Alvise "Alvise Sommariva" (Australia) - See all my reviews

This review is from: Theoretical Numerical Analysis (Hardcover)

The book presents an abstract point of view of Numerical Analysis (as one can immediatly see by the title!). It is written by a master in the topic, author of more than 70 publications at the higher levels, well known for his contributions in Integral and Partial Differential Equations.

If one is interested on the basic aspects of numerical analysis, I also suggest to consider his well known manual "Elementary Numerical Analysis".

The present book presents several aspects that are not covered by most of the manuals in Numerical Analysis and highly contributes to have a wider idea of convergence and stability of some well known methods.