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Theoretical Numerical Analysis

A Functional Analysis Framework

  • Textbook
  • © 2005
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Overview

Authors:
  1. Kendall Atkinson

    1. Department of Computer Science, University of Iowa, Iowa City, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Weimin Han

    1. Department of Mathematics, University of Iowa, Iowa City, USA

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    You can also search for this author in PubMed   Google Scholar

  • Covers basic results of functional analysis and also some additional topics which are needed in theoretical numerical analysis
  • New chapter on Fourier Analysis and Wavelets
  • Exercises at the end of most sections are included (419)
  • Short discussion of the literature, including recommendations for additional reading is provided at the end of each chapter
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Linear Spaces

    Pages 1-49
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  3. Linear Operators on Normed Spaces

    Pages 51-111
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  4. Approximation Theory

    Pages 113-160
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  5. Fourier Analysis and Wavelets

    Pages 161-199
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  6. Nonlinear Equations and Their Solution by Iteration

    Pages 201-247
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  7. Finite Difference Method

    Pages 249-271
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  8. Sobolev Spaces

    Pages 273-322
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  9. Variational Formulations of Elliptic Boundary Value Problems

    Pages 323-359
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  10. The Galerkin Method and Its Variants

    Pages 361-376
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  11. Finite Element Analysis

    Pages 377-411
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  12. Elliptic Variational Inequalities and Their Numerical Approximations

    Pages 413-445
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  13. Numerical Solution of Fredholm Integral Equations of the Second Kind

    Pages 447-522
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  14. Boundary Integral Equations

    Pages 523-553
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  15. Back Matter

    Pages 555-577
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Keywords

About this book

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

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

Authors and Affiliations

  • Department of Computer Science, University of Iowa, Iowa City, USA

    Kendall Atkinson

  • Department of Mathematics, University of Iowa, Iowa City, USA

    Weimin Han

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/10.1007/978-0-387-28769-0

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag New York 2005

  • eBook ISBN: 978-0-387-28769-0Published: 07 June 2007

  • Series ISSN: 0939-2475

  • Series E-ISSN: 2196-9949

  • Edition Number: 2

  • Number of Pages: XVIII, 576

  • Number of Illustrations: 33 b/w illustrations

  • Topics: Analysis, Numerical Analysis

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