A Course in Mathematical Analysis 3 Volume Set
A Course in Mathematical Analysis 3 Volume Set
$393.00
USDThe 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
Product details
June 2016Multiple copy pack
9781107625341
986 pages
252 × 177 × 68 mm
2.22kg
55 b/w illus. 890 exercises
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.
