Theoretical Numerical Analysis: A Functional Analysis Framework: v. 39 (Texts in Applied Mathematics) - Hardcover

Atkinson, Kendall; Han, Weimin

Hardcover

ISBN 10: 0387951423 ISBN 13: 9780387951423

Publisher: Springer-Verlag New York Inc., 2001

Synopsis

This book gives an introduction to functional analysis for graduate students pursuing research involving numerical analysis. The text covers basic results of functional analysis as well as additional topics needed in theoretical numerical analysis. Applications of this functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. Extensive exercises are included at the end of each section along with recommendations for additional reading. This book is especially suited to students interested in the numerical solution of differential and/or integral equations, but it will appeal to numerical analysts and mathematically-oriented students and researchers in engineering, physics, and related areas.

About this title

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

Edition details

• Publisher: Springer-Verlag New York Inc.
• Publication date: 2001
• Language: English
• ISBN 10: 0387951423
• ISBN 13: 9780387951423
• Binding: Hardcover
• Number of pages: 466