# A Course in Mathematical Analysis: 2

Cambridge University Press, 1/23/2014

EAN 9781107675322, ISBN10: 1107675324

Paperback, 334 pages, 24.4 x 17 x 1.9 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 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.