D. J. H. Garling

A Course in Mathematical Analysis

• Gebundenes Buch

Produktbeschreibung

The third volume of three providing a full and detailed account of undergraduate mathematical analysis.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 332
• Erscheinungstermin: 1. August 2014
• Englisch
• Abmessung: 250mm x 175mm x 22mm
• Gewicht: 756g
• ISBN-13: 9781107032040
• ISBN-10: 1107032040
• Artikelnr.: 40921353

Autorenporträt

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.

Inhaltsangabe

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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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