A Course in Mathematical Analysis
Complex Analysis, Measure and Integration
(Sprache: Englisch)
The third volume of three providing a full and detailed account of undergraduate mathematical analysis.
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Produktinformationen zu „A Course in Mathematical Analysis “
The third volume of three providing a full and detailed account of undergraduate mathematical analysis.
Klappentext zu „A Course in Mathematical Analysis “
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.
Inhaltsverzeichnis zu „A Course in Mathematical Analysis “
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.
Autoren-Porträt von D. J. H. Garling
Garling, D. J. H.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.
Bibliographische Angaben
- Autor: D. J. H. Garling
- 329 Seiten, Kartoniert (TB), Englisch
- Verlag: Cambridge University Press
- ISBN-10: 110766330X
- ISBN-13: 9781107663305
Sprache:
Englisch
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