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Real Analysis A First Course

ISBN-10: 0201832100
ISBN-13: 9780201832105
Edition: 1997
Authors: Russell Gordon
List price: $99.00
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Book details

List price: $99.00
Copyright year: 1997
Publisher: Addison-Wesley Longman, Incorporated
Publication date: 7/11/1996
Binding: Hardcover
Pages: 304
Size: 6.50" wide x 9.50" long x 0.50" tall
Weight: 1.188
Language: English

Real Numbers
What is a Real Number? The Completeness Axiom
Some Miscellaneous Results
Countable and Uncountable Sets
The Uncountability of the Set of Real Numbers
Sequences
Convergent Sequences
Algebraic Properties and Monotone Sequences
Cauchy Sequences
The Bolzano-Weierstrass Theorem
Limits
The Limit of a Function
The Algebra of Limits
One-sided Limits and Infinite Limits
Continuity
Continuous Functions
Intermediate and Extreme Values
Monotone Functions and Inverse Functions
Uniform Continuity
Differentiation
The Derivative of a Function
The Chain Rule
Further Results on Derivatives
The Mean Value Theorem
L'H�pital's Rule
Integration
The Riemann Integral
Properties of the Riemann Integral
Types of Riemann Integrable Functions
The Fundamental Theorem of Calculus
Additional Algebraic Properties
Infinite Series
Convergence of Infinite Series
Two Classes of Infinite Series
The Comparision Tests
Absolute Convergence
The Root and Ratio Tests
Sequences and Series of Functions
Sequences of Functions
Uniform Convergence
Uniform Convergence and Inherited Properties
Series of Functions
Two Miscellaneous Results
Power Series
Taylor Series
Point-Set Topology
Open and Closed Sets
Limit Points
Compact Sets
The Heine-Borel Theorem
Continuous Functions
Continuous Functions and Compact Sets
Some Deeper Results
The Set of Points of Continuity of a Function
The Baire Category Theorem
Baire Class One Functions
Continuity Properties of Baire One Functions.

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