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Other titles in the Dover Books on Mathematics series:
A First Look at Numerical Functional Analysis First Look at Numerical Functional Analysisby W. W. Sawyer
Synopses & Reviews
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.
Dover (2010) unabridged republication of the edition published by Oxford University Press, Oxford, 1978.
Elements of the Theory of Functions and Functional Analysis, A. N. Kolmogorov. 288pp. 53/8 x 81/2. 0-486-40683-0
Functional Analysis, Frigyes Riesz. 491pp. 53/8 x 81/2. 0-486-66289-6
Elementary Functional Analysis, Georgi E. Shilov. 352pp. 53/8 x 81/2. 0-486-68923-9
For current price information write to Dover Publications, or log on to www.doverpublications.com and see every Dover book in print.
Book News Annotation:
Sawyer (1911-2008) introduces the theorems of classical analysis, reviews their original role in the historical setting, and explains their application in modern analysis. Intended for math majors familiar with linear algebra, the textbook discusses the Cauchy test for convergence of a sequence, Banach spaces, Minkowski spaces, linear operators, the Newton-Raphson method, the Taylor series, and Hilbert space. This volume is an unabridged reprint of the work originally published in 1978 by Oxford University Press. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
Text by renowned educator shows how problems in numerical analysis lead to concepts of functional analysis. Topics include Banach and Hilbert spaces, contraction mappings, convergence, differentiation and integration, and Euclidean space. 1978 edition.
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
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