A Course in Mathematical Analysis 3 Volume Set
Cambridge University Press
978-1-107-62534-1 (ISBN)
- Keine Verlagsinformationen verfügbar
- Artikel merken
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.
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.
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.
| Erscheint lt. Verlag | 24.7.2014 |
|---|---|
| Zusatzinfo | Worked examples or Exercises; 5 Halftones, unspecified; 50 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 177 x 252 mm |
| Gewicht | 2220 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-107-62534-3 / 1107625343 |
| ISBN-13 | 978-1-107-62534-1 / 9781107625341 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
aus dem Bereich
