Texts in Applied Mathematics

Theoretical Numerical Analysis

A Functional Analysis Framework

Authors: Atkinson, Kendall, Han, Weimin

  • Covers basic results of functional analysis and also some additional topics needed in theoretical numerical analysis
  • Includes more than 400 exercises, which are featured at the end of most sections
  • Provides short discussions of the literature, including recommendations for additional reading
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eBook $59.99
price for USA (gross)
  • ISBN 978-1-4419-0458-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-1-4419-0457-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4419-3199-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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, 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

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)


Table of contents (14 chapters)

  • Linear Spaces

    Atkinson, Kendall (et al.)

    Pages 1-50

  • Linear Operators on Normed Spaces

    Atkinson, Kendall (et al.)

    Pages 51-113

  • Approximation Theory

    Atkinson, Kendall (et al.)

    Pages 115-166

  • Fourier Analysis and Wavelets

    Atkinson, Kendall (et al.)

    Pages 167-206

  • Nonlinear Equations and Their Solution by Iteration

    Atkinson, Kendall (et al.)

    Pages 207-252

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4419-0458-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-1-4419-0457-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4419-3199-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4419-0458-4
DOI
10.1007/978-1-4419-0458-4
Hardcover ISBN
978-1-4419-0457-7
Softcover ISBN
978-1-4419-3199-3
Series ISSN
0939-2475
Edition Number
3
Number of Pages
XVI, 625
Topics