Analysis
著者
書誌事項
Analysis
（Texts and readings in mathematics, 38）
Hindustan Book Agency, c2014
3rd ed
- 2
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注記
"Corrected reprint, 2017"--T.p. verso
Includes index
内容説明・目次
内容説明
This is part two of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning - the construction of the number systems and set theory - then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.
The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
In the third edition, several typos and other errors have been corrected and a few new exercises have been added.
目次
1. Metric spaces
2. Continuous functions on metric spaces
3. Uniform convergence
4. Power series
5. Fourier series
6. Several variable differential calculus
7. Lebesgue measure
8. Lebesgue integration
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