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
