Real Analysis A First Course

Name: Real Analysis A First Course
Price: 109.55 USD
Availability: InStock
ISBN: 9780201832105

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'Hï¿½pital'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.