Theoretical Numerical Analysis

1. Front Matter

   Pages i-xvi

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2. Linear Spaces

   • Kendall Atkinson, Weimin Han

   Pages 1-37

3. Linear Operators on Normed Spaces

   • Kendall Atkinson, Weimin Han

   Pages 38-91

4. Approximation Theory

   • Kendall Atkinson, Weimin Han

   Pages 92-130

5. Nonlinear Equations and Their Solution by Iteration

   • Kendall Atkinson, Weimin Han

   Pages 131-170

6. Finite Difference Method

   • Kendall Atkinson, Weimin Han

   Pages 171-192

7. Sobolev Spaces

   • Kendall Atkinson, Weimin Han

   Pages 193-237

8. Variational Formulations of Elliptic Boundary Value Problems

   • Kendall Atkinson, Weimin Han

   Pages 238-269

9. The Galerkin Method and Its Variants

   • Kendall Atkinson, Weimin Han

   Pages 270-280

10. Finite Element Analysis

    • Kendall Atkinson, Weimin Han

    Pages 281-312

11. Elliptic Variational Inequalities and Their Numerical Approximations

    • Kendall Atkinson, Weimin Han

    Pages 313-341

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

    • Kendall Atkinson, Weimin Han

    Pages 342-404

13. Boundary Integral Equations

    • Kendall Atkinson, Weimin Han

    Pages 405-435

14. Back Matter

    Pages 436-451

    PDF

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas­ 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). The development of new courses is a natural consequence of a high level of 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 text book series is to meet the current and future needs of these advances and 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 Math­ ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs.

• Banach fixed-point theorem
• Derivative
• Finite Element Methods
• calculus
• differential equation
• finite element method
• fixed-point theorem
• functional analysis
• numerical analysis
• numerical methods
• orthogonal polynomials

From the reviews:

MATHEMATICAL REVIEWS

"The book starts with two chapters that introduce the reader to functional analysis. In these 89 pages the functional-analytic framework for dealing with theoretical numerical analysis problems is developed from scratch, starting with the definition of a linear space. The authors achieve this remarkable feat by avoiding a formalized framework Lebesgue measure, integration, and distribution theory. Instead they use more standard results on the completion of normal spaces and the unique extension of densely defined bounded linear operators. This is a very interesting approach. Actually these two chapters might form the basis for a functional analysis course in its own right. The rest of the book covers a wealth of topics and might serve as the basis for several graduate courses…The book is well written and accessible to students who have had the usual mathematics undergraduate courses in analysis, linear algebra and numerical analysis. It can be recommended as a textbook for several graduate mathematical courses and also as a reference work for numerical analysts who are interested in the general mathematical aspects of their work."

K.l. Atkinson and W. Han

Theoretical Numerical Analysis A Functional Analysis Framework

"The book is well written and accessible to students who have had the usual mathematics undergraduate courses in analysis, linear algebra and numerical analysis. It can be recommended as a textbook for several graduate mathematical courses and as a reference work for numerical analysts interested in the general mathematical aspects of their work." —AMERICAN MATHEMATICAL SOCIETY

From the reviews of the second edition:

"This is the second, expanded edition of the book published originally in 2001. … The book can be recommended as an introduction to the so-called theoretical numerical analysis … . The text presupposes onlythe basic undergraduate knowledge of linear algebra, analysis and numerical methods and is thus suitable as a basis for advanced undergraduate and beginning graduate courses. All sections end with exercises, and at the end of each chapter the reader will find useful suggestions for further reading." (Aleksandar Perovic, Zentralblatt MATH, Vol. 1068, 2005)

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

  Kendall Atkinson

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

  Weimin Han

• Department of Mathematics, Zhejiang University, Hangzhou, People’s Republic of China

  Weimin Han

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