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Theoretical Numerical Analysis: A Functional Analysis Framework

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This textbook covers basic results of functional analysis and also some additional topics which are needed in theoretical numerical analysis. For this second edition, a new chapter on Fourier analysis and wavelets and over 140 new exercises have been added, almost doubling the exercise amount from the last edition. Many sections from the first edition have been revised. Some of the other topics covered in this book are functional analysis and approximation theory, nonlinear analysis, Sobolev spaces, elliptic boundary value problems and variational inequalities.

Author(s): Kendall Atkinson, Weimin Han (auth.)
Series: Texts in Applied Mathematics 39
Edition: 1
Publisher: Springer New York
Year: 2005

Language: English
Pages: 463
City: New York
Tags: Analysis; Numerical Analysis

Front Matter....Pages i-xviii
Linear Spaces....Pages 1-49
Linear Operators on Normed Spaces....Pages 51-111
Approximation Theory....Pages 113-160
Fourier Analysis and Wavelets....Pages 161-199
Nonlinear Equations and Their Solution by Iteration....Pages 201-247
Finite Difference Method....Pages 249-271
Sobolev Spaces....Pages 273-322
Variational Formulations of Elliptic Boundary Value Problems....Pages 323-359
The Galerkin Method and Its Variants....Pages 361-376
Finite Element Analysis....Pages 377-411
Elliptic Variational Inequalities and Their Numerical Approximations....Pages 413-445
Numerical Solution of Fredholm Integral Equations of the Second Kind....Pages 447-522
Boundary Integral Equations....Pages 523-553
Back Matter....Pages 555-577