Applied Functional Analysis
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Applied Functional Analysis

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Description

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.
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Product details

  • Hardback | 610 pages
  • 178 x 254 x 35.56mm | 1,247g
  • Productivity Press
  • Portland, United States
  • English
  • New edition
  • 3rd New edition
  • 15 Tables, black and white; 55 Illustrations, black and white
  • 1498761143
  • 9781498761147
  • 1,754,556

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
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About J. Tinsley Oden

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 Academiques 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).
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