Functional analysis-the study of the properties of mathematical functions-is widely used in modern scientific and engineering disciplines, particularly in mathematical modeling and computer simulation. Applied Functional Analysis, the only textbook of its kind, is designed specifically for the graduate student in engineering and science who has little or no training in advanced mathematics. Comprehensive and easy-to-understand, this innovative textbook progresses from the essentials of preparatory mathematics to sophisticated functional analysis. This self-contained presentation requires few mathematical prerequisites and provides students with the fundamental concepts and theorems essential to mathematical analysis and modeling.
Applied Functional Analysis combines various principles of mathematics, computer science, engineering, and science, laying the foundation for further specialty work in partial differential equations, approximation theory, numerical mathematics, control theory, mathematical physics, and related subjects. This new treatment of a classic subject outfits engineering and science majors with a graduate-level mathematics standing, otherwise accessible only through regular mathematics studies.

Contenuti:

Preliminaries
Elementary Set Theory
Elementary Logic
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
Lp-Spaces
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
Index

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