Texts in Applied Mathematics

Theoretical Numerical Analysis

A Functional Analysis Framework

Authors: Atkinson, Kendall, Han, Weimin

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  • ISBN 978-0-387-28769-0
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About this Textbook

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. In this new edition many sections from the first edition have been revised to varying degrees as well as over 140 new exercises added. A new chapter on Fourier Analysis and wavelets has been included.

 

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

Reviews

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

Table of contents (13 chapters)

Table of contents (13 chapters)
  • Linear Spaces

    Pages 1-49

  • Linear Operators on Normed Spaces

    Pages 51-111

  • Approximation Theory

    Pages 113-160

  • Fourier Analysis and Wavelets

    Pages 161-199

  • Nonlinear Equations and Their Solution by Iteration

    Pages 201-247

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-0-387-28769-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Theoretical Numerical Analysis
Book Subtitle
A Functional Analysis Framework
Authors
Series Title
Texts in Applied Mathematics
Series Volume
39
Copyright
2005
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-28769-0
DOI
10.1007/978-0-387-28769-0
Series ISSN
0939-2475
Edition Number
2
Number of Pages
XVIII, 576
Number of Illustrations
33 b/w illustrations
Topics