A Course in Mathematical Analysis

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

D. J. H. Garling (Author)

9781107032040, Cambridge University Press

Hardback, published 22 May 2014

332 pages, 20 b/w illus. 270 exercises
24.4 x 17 x 1.9 cm, 0.73 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 the 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. Volume 1 focuses on the analysis of real-valued functions of a real variable. Volume 2 goes on to consider metric and topological spaces. This third volume develops the classical theory of functions of a complex variable. It carefully establishes the properties of the complex plane, including a proof of the Jordan curve theorem. Lebesgue measure is introduced, and is used as a model for other measure spaces, where the theory of integration is developed. The Radon–Nikodym theorem is proved, and the differentiation of measures discussed.

Introduction
Part I. Complex Analysis: 1. Holomorphic functions and analytic functions
2. The topology of the complex plane
3. Complex integration
4. Zeros and singularities
5. The calculus of residues
6. Conformal transformations
7. Applications
Part II. Measure and Integration: 8. Lebesgue measure on R
9. Measurable spaces and measurable functions
10. Integration
11. Constructing measures
12. Signed measures and complex measures
13. Measures on metric spaces
14. Differentiation
15. Applications
Index.

Subject Areas: Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB], Mathematics [PB]