Theoretical numerical analysis : a functional analysis framework
著者
書誌事項
Theoretical numerical analysis : a functional analysis framework
（Texts in applied mathematics, 39）
Springer, c2001
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注記
Includes bibliographical references (p. [436]-444) and index
内容説明・目次
内容説明
This book gives an introduction to functional analysis for graduate students pursuing research involving numerical analysis. The text covers basic results of functional analysis as well as additional topics needed in theoretical numerical analysis. Applications of this functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. Extensive exercises are included at the end of each section along with recommendations for additional reading. This book is especially suited to students interested in the numerical solution of differential and/or integral equations, but it will appeal to numerical analysts and mathematically-oriented students and researchers in engineering, physics, and related areas.
目次
- Preface
- 1 Linear Spaces
- 2 Linear Operators on Normed Spaces
- 3 Approximation Theory
- 4 Nonlinear Equations and Their Solution by Iteration
- 5 Finite Difference Method
- 6 Sobolev Spaces
- 7 Variational Formulations of Elliptic Boundary Value Problems
- 8 The Galerkin Method and Its Variants
- 9 Finite Element Analysis
- 10 Elliptic Variational Inequalities and Their Numerical Approximations
- 11 Numerical Solution of Fredholm Integral Equations of the Second Kind
- 12 Boundary Integral Equations
- References
- Index.
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