'Applied Funcitonal Analysis' introduces in a connected and unified manner the fundamental topics in functional analysis important in mathematical modeling and computer simulations. Modern mathematics, linear algebra in both finite and infinite dimensions, a course on Lebesque measure and integration, and a presentation of elementary topology, as well as the theory of linear operators in Banach spaces, are covered in this book.
'Applied Funcitonal Analysis' introduces in a connected and unified manner the fundamental topics in functional analysis important in mathematical modeling and computer simulations. Modern mathematics, linear algebra in both finite and infinite dimensions, a course on Lebesque measure and integration, and a presentation of elementary topology, as well as the theory of linear operators in Banach spaces, are covered in this book.
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Inhaltsangabe
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
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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