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Counterexamples in Analysis (Dover Books on Mathematics)

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Counterexamples in Analysis (Dover Books on Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Book News Annotation:

While most mathematical textbooks are devoted to the proof of true statements, this text focuses on counterexamples for proving statements are false. The 13 chapters cover differentiation, Riemann integration, sequences, infinite series, sets of real numbers, functions of two variables, and metric and topological spaces. Originally published by Holden-Day in 1964. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Most mathematical examples illustrate the truth of a statement; counterexamples demonstrate the falsity of a statement. 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. Undergraduate-level text.

Synopsis:

These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.

Table of Contents

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.

9. Functions of Two Variables.

10. Plane Sets.

11. Area.

12. Metric and Topological Spaces.

13. Function Spaces.

  Bibliography. Special Symbols. Index.

Product Details

ISBN:
9780486428758
Author:
Gelbaum, Bernard R.
Publisher:
Dover Publications
Author:
Olmsted, John M. H.
Author:
Mathematics
Author:
ohn M. H.
Author:
Olmsted, J
Location:
Mineola, N.Y.
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
Applied
Subject:
General Mathematics
Subject:
Mathematics-Calculus
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
GTR-9
Publication Date:
20030631
Binding:
TRADE PAPER
Language:
English
Illustrations:
12 Figs.
Pages:
218
Dimensions:
8.5 x 5.38 in 0.62 lb

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Counterexamples in Analysis (Dover Books on Mathematics) New Trade Paper
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Product details 218 pages Dover Publications - English 9780486428758 Reviews:
"Synopsis" by , Most mathematical examples illustrate the truth of a statement; counterexamples demonstrate the falsity of a statement. 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. Undergraduate-level text.
"Synopsis" by ,
These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
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