Real analysis

By: Frank MorganMaterial type: TextTextPublication details: Rhode Island, American Matematical Society: [c2005]Description: 151 pISBN: 9780821852224Subject(s): MathematicsLOC classification: QA300
Contents:
Part I. Real Numbers and Limits Part II. Topology Part III. Calculus Part IV. Metric Spaces
Summary: Intended for undergraduates studying real analysis, this book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in Rn. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as "closed and bounded," via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem.This concise text not only provides efficient proofs, but also shows students how to derive them. The excellent exercises are accompanied by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester.---Summary provided by publisher
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Part I. Real Numbers and Limits
Part II. Topology
Part III. Calculus
Part IV. Metric Spaces

Intended for undergraduates studying real analysis, this book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in Rn. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as "closed and bounded," via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem.This concise text not only provides efficient proofs, but also shows students how to derive them. The excellent exercises are accompanied by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester.---Summary provided by publisher

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