American Mathematical Soc., 2005 - Mathematics - 151 pages
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 givesthe 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. Theexcellent 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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Capítulo 17: Sequencias de funções

### Contents

 III 3 IV 9 V 13 VI 21 VII 25 VIII 27 IX 33 X 35
 XXIII 81 XXIV 85 XXV 89 XXVII 93 XXVIII 99 XXIX 105 XXX 109 XXXI 111

 XI 37 XII 41 XIII 45 XIV 47 XV 49 XVI 53 XVII 59 XVIII 61 XIX 65 XX 71 XXII 75
 XXXII 115 XXXIII 119 XXXIV 121 XXXV 125 XXXVI 129 XXXVII 133 XXXVIII 137 XXXIX 147 XL 149 Copyright