Analysis
An Introduction

This book is an extensive introductory text to mathematical analysis for graduate students and advanced undergraduates, complete with 500 exercises and numerous examples.

Richard Beals (Author)

9780521600477, Cambridge University Press

Paperback, published 13 September 2004

272 pages, 11 b/w illus. 502 exercises
25.2 x 17.7 x 1.7 cm, 0.49 kg

'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

This 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.

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.

Subject Areas: Functional analysis & transforms [PBKF], Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB]