Morgan builds the theory behind calculus from the basic concepts of real numbers, limits, and open and closed sets, and includes proofs and exercises for the undergraduate student. He covers real numbers and limits, including the concepts of infinity and sequences, topology, including the Cantor set and fractals, and then progresses to calculus, including the Riemann integral, sequences of functions, power and Fourier series and the exponential function, closing with metric spaces, including Ascoli's theorem. Annotation ©2005 Book News, Inc., Portland, OR (booknews.com)
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Book by Frank Morgan
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Hardcover. Condizione: new. Hardcover. 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). 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780821836705
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Condizione: New. 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. . . . . Codice articolo V9780821836705
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