Counterexamples in Analysis 豆瓣阅读 英文原版 数学分析中的反例 Bernard R. Gelbaum and John M. H. Olmsted

基本信息

By (author) Bernard R. Gelbaum , By (author) John M. H. Olmsted

Format Paperback | 218 pages

Dimensions 162 x 215 x 12mm | 254g

Publication date 04 Jun 2003

Publisher Dover Publications Inc.

Publication City/Country New York, United States

Language English

Illustrations note Illustrations, unspecified

ISBN10 0486428753

ISBN13 9780486428758

页面参数仅供参考，具体以实物为准

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. 12 figures. Bibliography. Index. Errata.

这些根据难度或复杂程度排列的反例主要处理从演算级别开始的分析部分，即“实际变量”。本书的前半部分介绍了实变量的功能。主题包括实数系统，函数和极限，微分，Riemann积分，序列，无穷级数，一致收敛以及实轴上的集合和度量。下半部分涵盖了更高的维度，研究了两个变量的功能，即平面集，面积，度量和拓扑空间以及函数空间。该卷包含许多内容，将证明它们适合尚未完成微积分第一门课程的学生，并且对于高级分析学生和研究生也有足够的兴趣。12位。参考书目。指数。勘误

书籍目录

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.