3rd Edition

Applied Functional Analysis

By J. Tinsley Oden, Leszek Demkowicz Copyright 2018
    632 Pages 55 B/W Illustrations
    by CRC Press

    632 Pages 55 B/W Illustrations
    by Chapman & Hall

    632 Pages 55 B/W Illustrations
    by Chapman & Hall

    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.



    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

    Biography

    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).