A Course in Mathematical Analysis: Volume 2, Metric and Topological Spaces, Functions of a Vector Variable

The second volume of three providing a full and detailed account of undergraduate mathematical analysis.

D. J. H. Garling (Author)

9781107675322, Cambridge University Press

Paperback / softback, published 23 January 2014

336 pages, 15 b/w illus. 280 exercises
24.7 x 17.4 x 1.8 cm, 0.6 kg

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.

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.

Subject Areas: Topology [PBP], Geometry [PBM], Mathematics [PB]