# Theoretical Numerical Analysis

## A Functional Analysis Framework

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

Book

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

This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, boundary integral equations for planar regions, and multivariable polynomial approximations. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study. In this third edition, a new chapter, Multivariable Polynomial Approximations, is included, numerous changes are made throughout the entire text, and new exercises are added.

Review of earlier edition:

"...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."

R. Glowinski, SIAM Review, 2003

Approximation Finite Element Methods approximation theory calculus finite element method functional analysis numerical analysis numerical methods

- DOI https://doi.org/10.1007/978-1-4419-0458-4
- Copyright Information Springer-Verlag New York 2009
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-4419-0457-7
- Online ISBN 978-1-4419-0458-4
- Series Print ISSN 0939-2475
- About this book