Analysis
Analysis
AUD$89.95
exc GSTThis self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.
- Self-contained coverage of basic analysis, from fundamentals to more advanced topics
- Designed to enhance understanding through numerous remarks, examples, and 500 exercises
- Clear but concise treatment of many interesting examples and applications
Reviews & endorsements
'The self-contained text, suitable for advanced undergraduates, provides an extensive introduction into mathematical analysis, from the fundamentals to more advanced material.' Zentralblatt fur Didaktik der Mathematik
Product details
January 2005Paperback
9780521600477
272 pages
252 × 177 × 17 mm
0.49kg
11 b/w illus. 502 exercises
Available
Table of Contents
- 1. Introduction
- 2. The real and complex numbers
- 3. Real and complex sequences
- 4. Series
- 5. Power series
- 6. Metric spaces
- 7. Continuous functions
- 8. Calculus
- 9. Some special functions
- 10. Lebesgue measure on the line
- 11. Lebesgue integration on the line
- 12. Function spaces
- 13. Fourier series
- 14. Applications of Fourier series
- 15. Ordinary differential equations
- Appendix: the Banach-Tarski paradox
- Hints for some exercises.
