A Course in Mathematical Analysis: Volume 3, Complex Analysis, Measure and Integration
1st Edition
Published on 31. December 2013
978-1-107-59654-2 (ISBN)
Description
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.
More details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Professional and scholarly
Illustrations
Worked examples or Exercises; 5 Halftones, unspecified; 15 Line drawings, unspecified
File size
2,54 MB
ISBN-13
978-1-107-59654-2 (9781107596542)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
D. J. H. Garling
A Course in Mathematical Analysis
Book
05/2014
Cambridge University Press
€186.10
Shipment within 15-20 days
D. J. H. Garling
A Course in Mathematical Analysis: Volume 3, Complex Analysis, Measure and Integration
Book
05/2014
Cambridge University Press
€65.00
Shipment within 15-20 days
Person
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.
Content
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.
