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Table of contents (14 chapters)
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About this book
Reviews
This is a very good textbook presenting a modern course in analysis both at the advanced undergraduate and at the beginning graduate level. It contains 14 chapters, a bibliography, and an index. At the end of each chapter interesting exercises and historical notes are enclosed.\par From the cover: ``The book begins with a brief discussion of sets and mappings, describes the real number field, and proceeds to a treatment of real-valued functions of a real variable. Separate chapters are devoted to the ideas of convergent sequences and series, continuous functions, differentiation, and the Riemann integral (of a real-valued function defined on a compact interval). The middle chapters cover general topology and a miscellany of applications: the Weierstrass and Stone-Weierstrass approximation theorems, the existence of geodesics in compact metric spaces, elements of Fourier analysis, and the Weyl equidistribution theorem. Next comes a discussion of differentiation of vector-valued functions of several real variables, followed by a brief treatment of measure and integration (in a general setting, but with emphasis on Lebesgue theory in Euclidean spaces). The final part of the book deals with manifolds, differential forms, and Stokes' theorem [in the spirit of M. Spivak's: ``Calculus on manifolds'' (1965; Zbl 141.05403)] which is applied to prove Brouwer's fixed point theorem and to derive the basic properties of harmonic functions, such as the Dirichlet principle''. ZENTRALBLATT MATH
A. Browder
Mathematical Analysis
An Introduction
"Everything needed is clearly defined and formulated, and there is a reasonable number of examples…. Anyone teaching a year course at this level to should seriously consider this carefully written book. In the reviewer's opinion, it would be a real pleasure to use this text with such a class."—MATHEMATICAL REVIEWS
Authors and Affiliations
Bibliographic Information
Book Title: Mathematical Analysis
Book Subtitle: An Introduction
Authors: Andrew Browder
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-0715-3
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1996
Hardcover ISBN: 978-0-387-94614-6Published: 15 December 1995
Softcover ISBN: 978-1-4612-6879-6Published: 08 October 2012
eBook ISBN: 978-1-4612-0715-3Published: 06 December 2012
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: XIV, 335
Topics: Analysis, Real Functions, Manifolds and Cell Complexes (incl. Diff.Topology)