Applied functional analysis
著者
書誌事項
Applied functional analysis
（Textbooks in mathematics）
CRC Press, c2018
3rd ed
- : hardback
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注記
"A Chapman & Hall book"
Includes bibliographical references (p. 599) and index
内容説明・目次
内容説明
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.
目次
- 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
「Nielsen BookData」 より
