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 teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.
- Developed from the author's own undergraduate courses taught at the University of Cambridge
- Over 250 exercises challenge the reader to learn through practice
- Useful background reading for a wide range of courses in mathematics
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Product details
- Date Published: January 2014
- format: Paperback
- isbn: 9781107675322
- length: 336 pages
- dimensions: 247 x 174 x 18 mm
- weight: 0.6kg
- contains: 15 b/w illus. 280 exercises
- availability: Available
Table of Contents
Introduction
Part I. Metric and Topological Spaces:
1. Metric spaces and normed spaces
2. Convergence, continuity and topology
3. Topological spaces
4. Completeness
5. Compactness
6. Connectedness
Part II. Functions of a Vector Variable:
7. Differentiating functions of a vector variable
8. Integrating functions of several variables
9. Differential manifolds in Euclidean space
Appendix A. Linear algebra
Appendix B. Quaternions
Appendix C. Tychonoff's theorem
Index.
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Author
D. J. H. Garling, University of Cambridge
D. J. H. Garling is Emeritus Reader in Mathematical Analysis at the University of Cambridge. He has 50 years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.