A Course in Mathematical Analysis: Volume 3, Complex Analysis, Measure and Integration

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D. J. H. Garling (University of Cambridge)

A Course in Mathematical Analysis

Volume 3, Complex Analysis, Measure and Integration

D. J. H. Garling (University of Cambridge)

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English

Cambridge University Press
22 May 2014

Mathematics; Real analysis, real variables; Complex analysis, complex variables

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.

By: D. J. H. Garling (University of Cambridge)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 247mm, Width: 173mm, Spine: 17mm
Weight: 610g
ISBN: 9781107663305
ISBN 10: 110766330X
Pages: 329
Publication Date: 22 May 2014
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

D. J. H. Garling is Emeritus Reader in Mathematical Analysis at the University of Cambridge and Fellow of St John's College, Cambridge. He has fifty years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.