A First Course in Real Analysis

by Protter, Murray H.; Morrey, Charles B., Jr.

• ISBN13: 9780387974378
• ISBN10: 0387974377
• Edition: 2nd
• Format: Hardcover
• Copyright: 1991-05-01
• Publisher: Springer Verlag
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Summary

This book is designed for a first course in real analysis following the standard course in elementary calculus. Since many students encounter rigorous mathematical theory for the first time in this course, the authors have included such elementary topics as the axioms of algebra and their immediate consequences as well as proofs of the basic theorems on limits. The pace is deliberate, and the proofs are detailed. The emphasis of the presentation is on theory, but the book also contains a full treatment (with many illustrative examples and exercises) of the standard topics in infinite series, Fourier series, multidimensional calculus, elements of metric spaces, and vector field theory. There are many exercises that enable the student to learn the techniques of proofs and the standard tools of analysis.In this second edition, improvements have been made in the exposition, and many of the proofs have been simplified. Additionally, this new edition includes an assortment of new exercises and provides answers for the odd-numbered problems.

Table of Contents

The Real Number System

Continuity and Limits

Basic Properties of Functions on R

Elementary Theory of Differentiation

Elementary Theory of Integration

Elementary Theory of Metric Spaces

Differentiation in R

Integration in R

Infinite Sequences and Infinite Series

Fourier Series

Functions Defined by Integrals; Improper Integrals

The Riemann-Stieltjes Integral and Functions of Bounded Variation

Contraction Mappings, Newton's Method, and Differential Equations

Implicit Function Theorems and Lagrange Multipliers

Functions on Metric Spaces; Approximation

Vector Field Theory; the Theorems of Green and Stokes

Appendices

Table of Contents provided by Publisher. All Rights Reserved.