Real Analysis
Real Analysis
$74.99
USDThis course in real analysis is directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something of value to specialists and nonspecialists alike. The text covers three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal, down-to-earth style, the author gives motivation and overview of new ideas, while still supplying full details and complete proofs. He provides a great many exercises and suggestions for further study.
- Many more exercises than are commonly found at this level
- Historical commentary
- Many references to both original and secondary sources, including expository and survey articles which are accessible to students
Reviews & endorsements
'… extremely well written: very entertaining and motivating.' Adhemar Bultheel, Bulletin of the London Mathematical Society
'The author writes lucidly in a friendly, readable style and he is strong at motivating, anticipating and reviewing the various themes that permeate the text … The overwhelming impression is that Real analysis was a labour of love for the author, written with a genuine reverence for both its beautiful subject matter and its creators, refiners and teachers down the ages. As such - and high praise indeed - it will sit very happily alongside classics such as Apostol's Mathematical analysis, Royden's Real analysis, Rudin's Real and complex analysis and Hewitt and Stromberg's Real and abstract analysis.' The Mathematical Gazette
Product details
August 2013Adobe eBook Reader
9781139632430
0 pages
0kg
45 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Preface
- Part I. Metric Spaces:
- 1. Calculus review
- 2. Countable and uncountable sets
- 3. Metrics and norms
- 4. Open sets and closed sets
- 5. Continuity
- 6. Connected sets
- 7. Completeness
- 8. Compactness
- 9. Category
- Part II. Function Spaces:
- 10. Sequences of functions
- 11. The space of continuous functions
- 12. The Stone-Weierstrass theorem
- 13. Functions of bounded variation
- 14. The Riemann-Stieltjes integral
- 15. Fourier series
- Part III. Lebesgue Measure and Integration:
- 16. Lebesgue measure
- 17. Measurable functions
- 18. The Lebesgue integral
- 19. Additional topics
- 20. Differentiation
- References
- Index.
