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Counterexamples in Analysis

By: Bernard R.GelbaumContributor(s): Olmsted, John M.HMaterial type: Text

TextPublication details: Mineola, N.Y. : Dover Publications, 2003Description: xxiv, 195 pages : illustrationsISBN: 9780486428758; 0486428753 Subject(s): Mathematical analysisDDC classification: 515

Contents:

Part I. Functions of a Real Variable -- 1. The Real Number System -- 2. Functions and Limits -- 3. Differentiation -- 4. Riemann Integration -- 5. Sequences -- 6. Infinite Series -- 7. Uniform Convergence -- 8. Sets and Measure on the Real Axis -- Part II. Higher Dimensions -- 9. Functions of Two Variables -- 10. Plane Sets -- 11. Area -- 12. Metric and Topological Spaces -- 13. Function Spaces.

Summary: These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing higher dimensions, examines functions of two variables, plane sets, area, metric and topological spaces, and function spaces. This volume contains much that will prove suitable for students who have not yet completed a first course in calculus, and ample material of interest to more advanced students of analysis as well as graduate students. 12 figures. Bibliography. Index. Errata.

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Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Reference Books	Main Library Reference	Reference	515 GEL (Browse shelf(Opens below))	Available		009813

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" ... an unabridged, slightly corrected republication of the 1965 second printing of the work originally published in 1964 by Holden-Day, Inc., San Francisco [in the Mathesis series]"--Title page verso.

Part I. Functions of a Real Variable --
1. The Real Number System --
2. Functions and Limits --
3. Differentiation --
4. Riemann Integration --
5. Sequences --
6. Infinite Series --
7. Uniform Convergence --
8. Sets and Measure on the Real Axis --
Part II. Higher Dimensions --
9. Functions of Two Variables --
10. Plane Sets --
11. Area --
12. Metric and Topological Spaces --
13. Function Spaces.

These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing higher dimensions, examines functions of two variables, plane sets, area, metric and topological spaces, and function spaces. This volume contains much that will prove suitable for students who have not yet completed a first course in calculus, and ample material of interest to more advanced students of analysis as well as graduate students. 12 figures. Bibliography. Index. Errata.

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