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).
