Counterexamples in Analysis

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis
Cover of the book Counterexamples in Analysis by Bernard R. Gelbaum, John M. H. Olmsted, Dover Publications
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Author: Bernard R. Gelbaum, John M. H. Olmsted ISBN: 9780486134918
Publisher: Dover Publications Publication: July 12, 2012
Imprint: Dover Publications Language: English
Author: Bernard R. Gelbaum, John M. H. Olmsted
ISBN: 9780486134918
Publisher: Dover Publications
Publication: July 12, 2012
Imprint: Dover Publications
Language: English

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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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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