A Course in Mathematical Analysis 3 Volume Set
Published on 24. July 2014
Book
986 pages
978-1-107-62534-1 (ISBN)
Description
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.
More details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Professional and scholarly
Illustrations
Worked examples or Exercises; 5 Halftones, unspecified; 50 Line drawings, unspecified
Dimensions
Height: 252 mm
Width: 177 mm
Thickness: 68 mm
Weight
2220 gr
ISBN-13
978-1-107-62534-1 (9781107625341)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Complete work / Part of the work
D. J. H. Garling
A Course in Mathematical Analysis
Book
05/2014
Cambridge University Press
€186.10
Shipment within 15-20 days
D. J. H. Garling
A Course in Mathematical Analysis
Book
01/2014
Cambridge University Press
€151.60
Shipment within 15-20 days
D. J. H. Garling
A Course in Mathematical Analysis
Book
04/2013
Cambridge University Press
€171.30
Shipment within 15-20 days
Person
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.
Content
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.