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A Course in Mathematical Analysis

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en Limba Engleză Hardback – 23 Jan 2014
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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Specificații

ISBN-13: 9781107032033
ISBN-10: 1107032032
Pagini: 336
Ilustrații: 15 b/w illus. 280 exercises
Dimensiuni: 170 x 244 x 19 mm
Greutate: 0.75 kg
Ediția: New.
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării: New York, United States

Cuprins

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.

Recenzii

'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
'This work is the first in a three-volume set dedicated to real and complex analysis that 'mathematical undergraduates may expect to meet in the first two years or so … of analysis' … The exposition is superb: open and nontelegraphic. Highly recommended. Upper-division undergraduates and graduate students.' D. Robbins, Choice
'These three volumes cover very thoroughly the whole of undergraduate analysis and much more besides.' John Baylis, The Mathematical Gazette