Introduction to Real Analysis

Name: Introduction to Real Analysis
Availability: InStock
ISBN: 9780471433316

ISBN-10: 0471433314

ISBN-13: 9780471433316

Edition: 4th 2011

Authors: Robert G. Bartle, Donald R. Sherbert

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Description:

This book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals,…

Book details

List price: $206.95
Edition: 4th
Copyright year: 2011
Publisher: John Wiley & Sons, Incorporated
Publication date: 3/4/2011
Binding: Hardcover
Pages: 416
Size: 7.10" wide x 10.10" long x 1.10" tall
Weight: 1.980
Language: English




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