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. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. Volume 2 goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. Volume 3 covers complex analysis and the theory of measure and integration.
- Developed from the author's own undergraduate courses taught at the University of Cambridge
- Over 850 exercises challenge the reader to learn through practice
- Useful background reading for a wide range of courses in mathematics
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Product details
- Date Published: July 2014
- format: Multiple copy pack
- isbn: 9781107625341
- length: 986 pages
- dimensions: 252 x 177 x 68 mm
- weight: 2.22kg
- contains: 55 b/w illus. 890 exercises
- availability: Temporarily unavailable - available from TBC
Table of Contents
Volume 1: Introduction
Part I. Prologue: The Foundations of Analysis:
1. The axioms of set theory
2. Number systems
Part II. Functions of a Real Variable:
3. Convergent sequences
4. Infinite series
5. The topology of R
6. Continuity
7. Differentiation
8. Integration
9. Introduction to Fourier series
10. Some applications
Appendix: Zorn's lemma and the well-ordering principle
Index. Volume 2: Introduction
Part I. Metric and Topological Spaces:
1. Metric spaces and normed spaces
2. Convergence, continuity and topology
3. Topological spaces
4. Completeness
5. Compactness
6. Connectedness
Part II. Functions of a Vector Variable:
7. Differentiating functions of a vector variable
8. Integrating functions of several variables
9. Differential manifolds in Euclidean space
Appendix A. Linear algebra
Appendix B. Quaternions
Appendix C. Tychonoff's theorem
Index. Volume 3: 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.

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Author
D. J. H. Garling, University of Cambridge
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.