Real Analysis A First Course

Name: Real Analysis A First Course
Price: 39.23 USD
Availability: InStock
ISBN: 9780201437270

ISBN-10: 0201437279

ISBN-13: 9780201437270

Edition: 2nd 2002 (Revised)

Authors: Russell Gordon

List price: $146.65

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Book details

List price: $146.65
Edition: 2nd
Copyright year: 2002
Publisher: Pearson Education
Publication date: 6/1/2001
Binding: Paperback
Pages: 400
Size: 6.30" wide x 9.25" long x 0.79" tall
Weight: 1.716
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