First Course in Real Analysis

ISBN-10: 0387974377
ISBN-13: 9780387974378
Edition: 2nd 1991 (Revised)
List price: $74.95 Buy it from $18.59
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Description: 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  More...

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Book details

List price: $74.95
Edition: 2nd
Copyright year: 1991
Publisher: Springer
Publication date: 3/7/1997
Binding: Hardcover
Pages: 536
Size: 6.50" wide x 9.75" long x 1.25" tall
Weight: 1.936
Language: English

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
Appendices

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