Introduction to Real Analysis

ISBN-10: 0471321486

ISBN-13: 9780471321484

Edition: 3rd 2000 (Revised)

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.
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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
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
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