Mathematical Analysis - An Introduction (Paperback, Softcover reprint of the original 1st ed. 1996)

This is a textbook containing more than enough material for a year-long course in analysis at the advanced undergraduate or beginning graduate level. 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. 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 space). The final part of the book deals with manifolds, differential forms, and Stokes' theorem, which is applied to prove Brouwer's fixed point theorem and to derive the basic properties of harmonic functions, such as the Dirichlet principle.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Undergraduate Texts in Mathematics
Release date:	December 2012
First published:	1996
Authors:	Andrew Browder
Dimensions:	235 x 155 x 18mm (L x W x T)
Format:	Paperback
Pages:	335
Edition:	Softcover reprint of the original 1st ed. 1996
ISBN-13:	978-1-4612-6879-6
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis Books > Science & Mathematics > Mathematics > Geometry > Analytic geometry
LSN:	1-4612-6879-6
Barcode:	9781461268796

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