出版社: Princeton University Press
出版年: 2003-4-7
ISBN: 9780691113852
页数: 400
装帧: Hardcover
定价: USD 90.00
丛书: Princeton Lectures in Analysis
内容简介 · · · · · ·
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic ...
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, "Complex Analysis" will be welcomed by students of mathematics, physics, engineering and other sciences. "The Princeton Lectures in Analysis" represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which "Complex Analysis" is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing "Fourier" series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Complex Analysis的创作者
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伊莱亚斯 M. 斯坦恩 作者
丛书信息
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Complex Analysis的书评 · · · · · · ( 全部 8 条 )
一本好书是怎么被翻译成垃圾的
翻译极其极其烂,千千万万别买!
> 更多书评 8篇
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在这本书的论坛里发言这本书的其他版本 · · · · · · ( 全部7 )
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世界图书出版公司 (2007)9.5分 2457人读过
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世界图书出版公司 (2013)9.5分 25人读过
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机械工业出版社 (2017)5.2分 25人读过
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0 有用 Amnesia 2012-05-05 02:49:14
写的东西有点少,不过很直观,顺序安排非常合理
0 有用 Das 2022-05-24 15:57:29
stein shows the structure of proofs,in his textsbook,almost every proof is elegant and clear. this book dont contain the theme of continual analysis.But rarely he gave two chapter for elliptic functio... stein shows the structure of proofs,in his textsbook,almost every proof is elegant and clear. this book dont contain the theme of continual analysis.But rarely he gave two chapter for elliptic function and theta function. Left 10. (展开)
0 有用 。 2017-06-23 12:14:27
很自然
0 有用 滴滴 2014-08-09 20:06:35
在老师引导下尝试接触,收益颇丰。
2 有用 梅花伞 2019-04-15 21:07:55
复分析真美好