Real Analysis A First Course

ISBN-10: 0201437279

ISBN-13: 9780201437270

Edition: 2nd 2002 (Revised)

List price: $117.80
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Book details

List price: $117.80
Edition: 2nd
Copyright year: 2002
Publisher: Addison Wesley
Publication date: 6/1/2001
Binding: Paperback
Pages: 400
Size: 6.50" wide x 9.25" long x 0.75" tall
Weight: 1.496
Language: English

Real Numbers
What Is a Real Number?
Absolute Value, Intervals, and Inequalities
The Completeness Axiom
Countable and Uncountable Sets
Real-Valued Functions
Sequences
Convergent Sequences
Monotone Sequences and Cauchy Sequences
Subsequences
Supplementary Exercises
Limits and Continuity
The Limit of a Function
Continuous Functions
Intermediate and Extreme Values
Uniform Continuity
Monotone Functions
Supplementary Exercises
Differentiation
The Derivative of a Function
The Mean Value Theorem
Further Topics on Differentiation
Supplementary Exercises
Integration
The Riemann Integral
Conditions for Riemann Integrability
The Fundamental Theorem of Calculus
Further Properties of the Integral
Numerical Integration
Supplementary Exercises
Infinite Series
Convergence of Infinite Series
The Comparison Tests
Absolute Convergence
Rearrangements and Products
Supplementary Exercises
Sequences and Series of Functions
Pointwise Convergence
Uniform Convergence
Uniform Convergence and Inherited Properties
Power Series
Taylor's Formula
Several Miscellaneous Results
Supplementary Exercises
Point-Set Topology
Open and Closed Sets
Compact Sets
Continuous Functions
Miscellaneous Results
Metric Spaces
Mathematical Logic
Mathematical Theories
Statements and Connectives
Open Statements and Quantifiers
Conditional Statements and Quantifiers
Negation of Quantified Statements
Sample Proofs
Some Words of Advice
Sets and Functions
Sets
Functions
Mathematical Induction
Three Equivalent Statements
The Principle of Mathematical Induction
The Principle of Strong Induction
The Well-Ordering Property
Some Comments on Induction Arguments
Bibliography
Index
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