Theoretical Numerical Analysis

1. Front Matter

   Pages i-xviii

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2. Linear Spaces

   Pages 1-49

3. Linear Operators on Normed Spaces

   Pages 51-111

4. Approximation Theory

   Pages 113-160

5. Fourier Analysis and Wavelets

   Pages 161-199

6. Nonlinear Equations and Their Solution by Iteration

   Pages 201-247

7. Finite Difference Method

   Pages 249-271

8. Sobolev Spaces

   Pages 273-322

9. Variational Formulations of Elliptic Boundary Value Problems

   Pages 323-359

10. The Galerkin Method and Its Variants

    Pages 361-376

11. Finite Element Analysis

    Pages 377-411

12. Elliptic Variational Inequalities and Their Numerical Approximations

    Pages 413-445

13. Numerical Solution of Fredholm Integral Equations of the Second Kind

    Pages 447-522

14. Boundary Integral Equations

    Pages 523-553

15. Back Matter

    Pages 555-577

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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.

• Finite
• Finite Element Methods
• approximation theory
• calculus
• equation
• finite element method
• function
• functional analysis
• numerical analysis

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

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

  Kendall Atkinson

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

  Weimin Han

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