عنوان

A course in mathematical analysis

9781107032033 (hardback)

IR

41237

انگلیسی

IR

A course in mathematical analysis

[Book]

/ D. J. H. Garling

Cambridge

: Cambridge university press

, 2013.

volumes ; 26 cm

Language: انگلیسی

Print

Includes bibliographical references and index.

"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 I 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: differentiation is developed in a co-ordinate free way, while integration (the Riemann integral) is established for functions defined on subsets of Euclidean space. 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 III covers complex analysis and the theory of measure and integration. "--Provided by publisher. v. 2. Metric and topological spaces, functions of a vector variable Machine generated contents note: 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.

Metric spaces

Topological spaces

Vector valued functions

MATHEMATICS / Mathematical Analysis.--bisacsh

Garling, D. J. H

ایران

QA611.28 .G37 2013

old catalog

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