Introduction to Real Analysis

Name: Introduction to Real Analysis
Price: 60.36 USD
Availability: InStock
ISBN: 9780471321484

ISBN-10: 0471321486

ISBN-13: 9780471321484

Edition: 3rd 2000 (Revised)

Authors: Robert G. Bartle, Donald R. Sherbert

List price: $195.95

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Description:

This text covers the concepts & techniques of real analysis for students of mathematics, economics & management science, the physical sciences, engineering & computer science. It contains an introduction to infinite series & Riemann integrals.

Book details

List price: $195.95
Edition: 3rd
Copyright year: 2000
Publisher: John Wiley & Sons, Incorporated
Publication date: 10/5/1999
Binding: Hardcover
Pages: 400
Size: 7.25" wide x 10.25" long x 0.75" tall
Weight: 1.892




Preliminaries



Sets and Functions



Mathematical Induction



Finite and Infinite Sets



The Real Numbers



The Algebraic and Order Properties of R



Absolute Value and the Real Line



The Completeness Property of R



Applications of the Supremum Property



Intervals



Sequences and Series



Sequences and Their Limits



Limit Theorems



Monotone Sequences



Subsequences and the Bolzano-Weierstrass Theorem



The Cauchy Criterion



Properly Divergent Sequences



Introduction to Infinite Series



Limits



Limits of Functions



Limit Theorems



Some Extensions of the Limit Concept



Continuous Functions



Continuous Functions



Combinations of Continuous Functions



Continuous Functions on Intervals



Uniform Continuity



Continuity and Gauges



Monotone and Inverse Functions



Differentiation



The Derivative



The Mean Value Theorem



L'Hospital's Rules



Taylor's Theorem



The Riemann Integral



Riemann Integral



Riemann Integrable Functions



The Fundamental Theorem



The Darboux Integral



Approximate Integration



Sequences of Functions



Pointwise and Uniform Convergence



Interchange of Limits



The Exponential and Logarithmic Functions



The Trigonometric Functions



Infinite Series



Absolute Convergence



Tests for Absolute Convergence



Tests for Nonabsolute Convergence



Series of Functions



The Generalized Riemann Integral



Definition and Main Properties



Improper and Lebesgue Integrals



Infinite Intervals



Convergence Theorems



A Glimpse into Topology



Open and Closed Sets in R



Compact Sets



Continuous Functions



Metric Spaces



Logic and Proofs



Finite and Countable Sets



The Riemann and Lebesgue Criteria



Approximate Integration



Two Examples


References


Photo Credits


Hints for Selected Exercises


Index