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© 2009

Theoretical Numerical Analysis

A Functional Analysis Framework

  • Authors
Textbook

Part of the Texts in Applied Mathematics book series (TAM, volume 39)

Table of contents

  1. Front Matter
    Pages 1-13
  2. Kendall Atkinson, Weimin Han
    Pages 1-50
  3. Kendall Atkinson, Weimin Han
    Pages 51-113
  4. Kendall Atkinson, Weimin Han
    Pages 115-166
  5. Kendall Atkinson, Weimin Han
    Pages 167-206
  6. Kendall Atkinson, Weimin Han
    Pages 207-252
  7. Kendall Atkinson, Weimin Han
    Pages 253-275
  8. Kendall Atkinson, Weimin Han
    Pages 277-326
  9. Kendall Atkinson, Weimin Han
    Pages 327-365
  10. Kendall Atkinson, Weimin Han
    Pages 367-382
  11. Kendall Atkinson, Weimin Han
    Pages 383-422
  12. Kendall Atkinson, Weimin Han
    Pages 551-581
  13. Kendall Atkinson, Weimin Han
    Pages 583-599
  14. Back Matter
    Pages 1-24

About this book

Introduction

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

Keywords

Approximation Finite Element Methods approximation theory calculus finite element method functional analysis numerical analysis numerical methods

Bibliographic information

  • Book Title Theoretical Numerical Analysis
  • Book Subtitle A Functional Analysis Framework
  • Authors Kendall Atkinson
    Weimin Han
  • Series Title Texts in Applied Mathematics
  • DOI https://doi.org/10.1007/978-1-4419-0458-4
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4419-0457-7
  • Softcover ISBN 978-1-4419-3199-3
  • eBook ISBN 978-1-4419-0458-4
  • Series ISSN 0939-2475
  • Edition Number 3
  • Number of Pages XVI, 625
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
    Numerical Analysis
  • Buy this book on publisher's site
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Reviews

From the reviews of the third edition:

“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)

“This is the third edition, based on a graduate course taught by the authors at the University of Iowa for many years. … There are tons and tons of well chosen explicit examples. … it can be used for reading courses in functional analysis for strong senior undergraduates that aren’t quite ready for a graduate analysis course, and it can be used as a reference for analysts of all stripes. I got a lot from reading it and so will you.” (Andrew Locascio, The Mathematical Association of America, October, 2010)