具体描述
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).
作者简介
Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings. His proof with colleagues and students of the Double Bubble Connecture is featured at the NSF Discoveries site. He has six books: Geometric Measure Theory: a Beginner's Guide (4th ed. 2009), Calculus Lite 2001, Riemannian Geometry: a Beginner's Guide 1998, The Math Chat Book 2000, based on his live, call-in Math Chat TV show and Math Chat column, Real Analysis 2005, and Real Analysis and Applications 2005.
Morgan went to MIT and Princeton, where his thesis advisor, Fred Almgren, introduced him to minimal surfaces. He then taught for ten years at MIT, where he served for three years as Undergraduate Mathematics Chairman, received the Everett Moore Baker Award for excellence in undergraduate teaching, and held the Cecil and Ida Green Career Development Chair. He spent leave years at Rice, Stanford, and the Institute for Advanced Study. He served on the NSF Math Advisory Committee from 1994-97, and as chair of the Hudson River Undergraduate Mathematics Conference in 1997. In January, 1993, he received an inaugural MAA national award for distinguished teaching. In 1995 he represented mathematics research at the exhibition for Congress by the Coalition for National Science Funding. He received the Allen High School Distinguished Alumni Award and an honorary doctorate from Cedar Crest College. For 1997-98 he held the first Visiting Professorship for Distinguished Teaching at Princeton University. From 2000-2002 he served as Second Vice-President of the Mathematical Association of America. He is currently (2009-2012) Vice-President of the American Mathematical Society and has launched the AMS Graduate Student Blog, by and for mathematics graduate students.
Morgan served at Williams as Mathematics Department Chair and founding director of an NSF undergraduate research project. He is currently Webster Atwell '21 Professor of Mathematics at Williams College.
See also Wikipedia and "A Math Chat with Frank Morgan" by Donald J. Albers, Math Horizons, The Mathematical Association of America, September 1997, 14-17.
目录信息
錯誤修正
Preface, line 5: "and that a function with a positive derivative can decrease?"
Page 48, line 1, inside the braces after "min": "/2" should apply to the whole delta, not just the subscript.
Page 71, 16.1. Replace "[a,b]" with "an open interval containing [a,b]".
Page 99, (2). Inside the integrals for An and Bn, insert "f(x)".
Page 100, line 4. "Theorem 24.1"
Page 101, Figure 22.1. The graph at height 0 should extend leftward to -pi instead of just to -3.
Page 103. Delete 2 from denominator in equations for An and Bn (but not A0).
Page 115, line 2. Replace "R" with "r".
Page 135, Exercise 5. Insert "a multiple of" before "arclength".
Thanks to Art Benjamin, Bob Burckel, Diana Davis.
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