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Functional analysis arose from traditional topics of calculus and integral and differential equations. This accessible text by an internationally renowned teacher and author starts with problems in numerical analysis and shows how they lead naturally to the concepts of functional analysis.
Suitable for advanced undergraduates and graduate students, this book provides coherent explanations for complex concepts. Topics include Banach and Hilbert spaces, contraction mappings and other criteria for convergence, differentiation and integration in Banach spaces, the Kantorovich test for convergence of an iteration, and Rall's ideas of polynomial and quadratic operators. Numerous examples appear throughout the text.
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About the Author
Internationally renowned for his innovative teaching methods, the late W. W. Sawyer was a Professor of Mathematics and Education at the University of Toronto. Dover has reprinted Sawyer's The Mathematician's Delight, which has been in print continuously since 1943 and has sold over 500,000 copies.
Table of Contents
1. A First Course in Functional Analysis
2. Old Ideas in New Contexts
3. Iteration and Contraction Mappings
4. Minkowski Spaces
5. Linear Operators and their Norms
6. Differentiation and Integration
7. Further Developments
8. Euclidean Space
9. Some Tools of the Trade
10. Some Bridgeheads