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A First Course in Real Analysis : Undergraduate Texts in Mathematics - Murray H. Protter

A First Course in Real Analysis

Undergraduate Texts in Mathematics


Published: 1st April 1997
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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.

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
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387974378
ISBN-10: 0387974377
Series: Undergraduate Texts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 536
Published: 1st April 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 3.18
Weight (kg): 0.95
Edition Number: 2
Edition Type: Revised