Applied Functional Analysis

by J. Tinsley Oden, Leszek Demkowicz

Overview

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science.

This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces.

The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory.

The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.

Product Details

ISBN-13:	9781498761147
Publisher:	Taylor & Francis
Publication date:	01/16/2018
Series:	Textbooks in Mathematics
Edition description:	Revised
Pages:	632
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

J. Tinsley Oden is the Director of the Institute for Computational Engineering and Sciences (ICES) and Associate Vice President for

Research at The University of Texas at Austin. Dr. Oden is also a member of the US National Academy of Engineering and the

recipient of the 2009 SIAM Distinguished Career Award. He holds five honorary doctorates and was knighted Chevalier de l’Ordre

des Palmes Académiques by the French government.

Leszek F. Demkowicz is the Assistant Director of ICES and a professor in the Department of Aerospace Engineering and

Engineering Mechanics at The University of Texas at Austin. Dr. Demkowicz was one of the founding members of the Polish

Association for Computational Mechanics (PACM), serving as its first president from 1991 to 1993. His recent research has been

summarized in the two volumes Computing with hp-ADAPTIVE FINITE ELEMENTS (CRC Press, 2007 and 2008). For his work on

hp methods, he was awarded the 2009 Zienkiewicz Medal by PACM and the 2009 Computational and Applied Sciences Award by

the United States Association for Computational Mechanics (USACM).

Table of Contents

Preliminaries

Elementary Logic and Set Theory

Relations; Functions

Cardinality of Sets

Foundations of Abstract Algebra

Elementary Topology in Rn

Elements of Differential and Integral Calculus

Linear Algebra

Vector Spaces—The Basic Concepts

Linear Transformations

Algebraic Duals; Euclidean Spaces

Lebesgue Measure and Integration

Lebesgue Measure

Lebesgue Integration Theory

Topological and Metric Spaces

Elementary Topology

Theory of Metric Spaces

Banach Spaces

Topological Vector Spaces

Hahn–Banach Extension Theorem

Bounded (Continuous) Linear Operators on Normed Spaces

Closed Operators

Topological Duals

Weak Compactness

Closed Range Theorem

Solvability of Linear Equations

Hilbert Spaces

Basic Theory

Duality in Hilbert Spaces

Elements of Spectral Theory

References

What People are Saying About This

From the Publisher

The textbook is designed to drive a crash course for beginning graduate students majoring in something besides mathematics, introducing mathematical foundations that lead to classical results in functional analysis. More specifically, Oden and Demkowicz want to prepare students to learn the variational theory of partial differential equations, distributions, and Sobolev spaces and numerical analysis with an emphasis on finite element methods. The 1996 first edition has been used in a rather intensive two-semester course.
—Book News, June 2010

Editorial Reviews

Introduces the fundamental topics in functional analysis important in mathematical modeling and computer simulations, for graduate students in engineering and science with no training in advanced mathematics. Features extensive examples; exercises; narrative, intuition-building presentation; and gradual progression from elementary set theory to advanced topics including Hilbert spaces and spectral theory of linear operators. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

The textbook is designed to drive a crash course for beginning graduate students majoring in something besides mathematics, introducing mathematical foundations that lead to classical results in functional analysis. More specifically, Oden and Demkowicz want to prepare students to learn the variational theory of partial differential equations, distributions, and Sobolev spaces and numerical analysis with an emphasis on finite element methods. The 1996 first edition has been used in a rather intensive two-semester course.
—Book News, June 2010

From the Publisher