Mathematical Analysis: An Introduction / Edition 1

Mathematical Analysis: An Introduction / Edition 1

by Andrew Browder
     
 

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

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Overview

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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Product Details

ISBN-13:
9780387946146
Publisher:
Springer New York
Publication date:
12/15/1995
Series:
Undergraduate Texts in Mathematics Series
Edition description:
1st ed. 1996. Corr. 3rd printing 2001
Pages:
335
Product dimensions:
9.21(w) x 6.14(h) x 0.88(d)

Table of Contents

1 Real Functions 2 Sequences and Series 3 Continuous Functions on Intervals 4 Differentiation 5 The Riemann Integral 6 Topology 7 Function Spaces 8 Differentiable Maps 9 Measures 10 Integration 11 Manifolds 12 Multilinear Algebra 13 Differential Forms 14 Integration on Manifolds

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