Suitable for undergraduates studying real analysis, this book presents the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. Num Pages: 151 pages, illustrations. BIC Classification: PBKB. Category: (P) Professional & Vocational. Dimension: 259 x 183 x 15. Weight in Grams: 539. . 2005. Hardcover. . . . . Books ship from the US and Ireland.

Bestandsnummer des Verk�ufers V9780821836705

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Bibliografische Details

Titel: Real Analysis
Verlag: American Mathematical Society
Erscheinungsjahr: 2005
Sprache: Englisch
ISBN-10: 0821836706
ISBN-13: 9780821836705
Einband: Hardcover
Zustand: New

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Inhaltsangabe

This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style. 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 $\mathbb{R}^n$. 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. Frank Morgan received the first Haimo Award for distinguished college teaching from the Mathematical Association of America. He has also garnered top teaching awards from Rice University (Houston, TX) and MIT (Cambridge, MA).

Rese�a del editor

This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style. 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 $\mathbf{R n$. 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 at the back of the book by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester. Frank Morgan received the first national Haimo teaching award from the Mathematical Association of America. He has also garnered top teaching awards from Rice University (Houston, TX) and MIT (Cambridge, MA).

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