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

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis
Cover of the book A Course in Mathematical Analysis: Volume 3, Complex Analysis, Measure and Integration by D. J. H. Garling, Cambridge University Press
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Author: D. J. H. Garling ISBN: 9781107702837
Publisher: Cambridge University Press Publication: May 22, 2014
Imprint: Cambridge University Press Language: English
Author: D. J. H. Garling
ISBN: 9781107702837
Publisher: Cambridge University Press
Publication: May 22, 2014
Imprint: Cambridge University Press
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 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.

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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.

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