D. J. H. Garling

A Course in Mathematical Analysis

• Broschiertes Buch

Produktbeschreibung

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 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 336
• Erscheinungstermin: 23. Januar 2014
• Englisch
• Abmessung: 244mm x 170mm x 18mm
• Gewicht: 614g
• ISBN-13: 9781107675322
• ISBN-10: 1107675324
• Artikelnr.: 36956730

Autorenporträt

D. J. H. Garling is Emeritus Reader in Mathematical Analysis at the University of Cambridge. He has 50 years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.

Inhaltsangabe

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.

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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.

Rezensionen

'Garling is a gifted expositor and the book under review really conveys the beauty of the subject, not an easy task. [It] comes with appropriate examples when needed and has plenty of well-chosen exercises as may be expected from a textbook. As the author points out in the introduction, a newcomer may be advised, on a first reading, to skip part one and take the required properties of the ordered real field as axioms; later on, as the student matures, he/she may go back to a detailed reading of the skipped part. This is good advice.' Felipe Zaldivar, MAA Reviews