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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 their 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 teachers. Volume I focuses on the analysis of real-valued functions of a real variable. Volume II goes on to consider metric and topological spaces. This third volume covers complex analysis and the theory of measure and integration.Read more
- Developed from the author's own undergraduate courses taught at the University of Cambridge
- Over 250 exercises challenge the reader to learn through practice
- Useful background reading for a wide range of courses in mathematics
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- Date Published: May 2014
- format: Hardback
- isbn: 9781107032040
- length: 332 pages
- dimensions: 244 x 170 x 19 mm
- weight: 0.73kg
- contains: 20 b/w illus. 270 exercises
- availability: Available
Table of Contents
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
Part II. Measure and Integration:
8. Lebesgue measure on R
9. Measurable spaces and measurable functions
11. Constructing measures
12. Signed measures and complex measures
13. Measures on metric spaces
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