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Counterexamples in Analysis
ISBN-13:
9780486134918
Veröffentl:
2012
Seiten:
224
Autor:
Bernard R. Gelbaum
Serie:
Dover Books on Mathematics
eBook Typ:
EPUB
eBook Format:
EPUB
Kopierschutz:
2 - DRM Adobe
Sprache:
Englisch
Beschreibung:
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.
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.
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