1: A Course in Mathematical Analysis: Volume 1
Cambridge University Press, 4/25/2013
EAN 9781107614185, ISBN10: 110761418X
Paperback, 318 pages, 24.7 x 17.4 x 1.7 cm
Language: English
The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration.
Introduction
Part I. Prologue
The Foundations of Analysis
1. The axioms of set theory
2. Number systems
Part II. Functions of a Real Variable
3. Convergent sequences
4. Infinite series
5. The topology of R
6. Continuity
7. Differentiation
8. Integration
9. Introduction to Fourier series
10. Some applications
Appendix
Zorn's lemma and the well-ordering principle
Index.