Counterexamples in Analysis

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丛书名：Dover Books on Mathematics
作者：Bernard R. Gelbaum, John M. H. Olmsted
文件大小：49.7MB
文件类型：扫描版PDF
语言：英语
出版：Dover Publications, Inc.，2003年
页数：218
书签：无

内容简介：
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.

目录
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.

地址：
http://u.115.com/file/dn4c3ko2#