| 书目名称 | Real Mathematical Analysis | | 编辑 | Charles C. Pugh | | 视频video | | | 概述 | Elucidates abstract concepts and salient points in proofs with over 150 detailed illustrations.Treats the rigorous foundations of both single and multivariable Calculus.Gives an intuitive presentation | | 丛书名称 | Undergraduate Texts in Mathematics | | 图书封面 |  | | 描述 | .Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis..New to the second edition of .Real Mathematical Analysis. is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini‘s theorem fro | | 出版日期 | Textbook 2015Latest edition | | 关键词 | Brouwer fixed point theorem; Lebesgue integral; Riemann integral; calculus; mathematical analysis; multiv | | 版次 | 2 | | doi | https://doi.org/10.1007/978-3-319-17771-7 | | isbn_softcover | 978-3-319-33042-6 | | isbn_ebook | 978-3-319-17771-7Series ISSN 0172-6056 Series E-ISSN 2197-5604 | | issn_series | 0172-6056 | | copyright | Springer Nature Switzerland AG 2015 |
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发表于 2025-3-21 17:43:55
