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Real Analysis : A First Course by Russell Gordon (1996, Hardcover)

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Informazioni su questo prodotto

Product Identifiers

PublisherAddison-Wesley Longman, Incorporated

ISBN-100201832100

ISBN-139780201832105

eBay Product ID (ePID)83507

Product Key Features

Number of Pages304 Pages

LanguageEnglish

Publication NameReal Analysis : a First Course

SubjectGeneral, Mathematical Analysis

Publication Year1996

TypeTextbook

Subject AreaMathematics

AuthorRussell Gordon

FormatHardcover

Dimensions

Item Height0.7 in

Item Weight19.3 Oz

Item Length9.4 in

Item Width6.6 in

Additional Product Features

Intended AudienceCollege Audience

LCCN96-017868

Dewey Edition20

IllustratedYes

Dewey Decimal515

Table Of Content1. 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. 2. Sequences. Convergent Sequences.Algebraic Properties and Monotone Sequences.Cauchy Sequences.The Bolzano-Weierstrass Theorem. 3. Limits. The Limit of a Function.The Algebra of Limits.One-sided Limits and Infinite Limits. 4. Continuity. Continuous Functions.Intermediate and Extreme Values.Monotone Functions and Inverse Functions.Uniform Continuity. 5. Differentiation. The Derivative of a Function.The Chain Rule.Further Results on Derivatives.The Mean Value Theorem.L'Hapital's Rule. 6. Integration. The Riemann Integral.Properties of the Riemann Integral.Types of Riemann Integrable Functions.The Fundamental Theorem of Calculus.Additional Algebraic Properties. 7. Infinite Series. Convergence of Infinite Series.Two Classes of Infinite Series.The Comparision Tests.Absolute Convergence.The Root and Ratio Tests. 8. 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. 9. Point-Set Topology. Open and Closed Sets.Limit Points.Compact Sets.The Heine-Borel Theorem.Continuous Functions.Continuous Functions and Compact Sets. 10. 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.

SynopsisThis text provides the theory behind single variable calculus, including the standard topics on sequences, continuity, differentiation, integration and infinite series. It takes a rigorous approach to the subject, building up student confidence with exercises., This text provides the theory behind single-variable calculus, and includes the topics typically required, such as sequences, continuity, differentiation, integration, and infinite series. The last chapter introduces point-set topology. The author presents his material in a clear, uncluttered manner, keeping a narrative style while focusing on the basic ideas of real analysis.

LC Classification NumberQA300.G593 1996