Mathematical Analysis An Introduction

ISBN-10: 0387946144

ISBN-13: 9780387946146

Edition: 1996

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Description:

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.
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Book details

List price: $64.95
Copyright year: 1996
Publisher: Springer
Publication date: 1/25/2001
Binding: Hardcover
Pages: 335
Size: 6.50" wide x 9.75" long x 1.00" tall
Weight: 1.672
Language: English

Real Functions
Sequences and Series
Continuous Functions on Intervals
Differentiation
The Riemann Integral
Topology
Function Spaces
Differentiable Maps
Measures
Integration
Manifolds
Multilinear Algebra
Differential Forms
Integration on Manifolds
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