Talk:Complex analysis

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Revision as of 03:39, 22 February 2011 by imported>Daniele Tampieri (Changed the definition of the entry)
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 Definition:  Field of mathematics, precisely of mathematical analysis, that studies those properties which characterize functions of complex variables. [d] [e]
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started this page

This is some material that used to be in the complex number article, but I felt an entire article on complex analysis would be the better place for it. However all I did was cut and paste from there to here, so this article doesn't have a good structure yet. Feel free to attack it! - Greg Martin 18:53, 29 April 2007 (CDT)

Reworked introduction

Hi,

I've reworked the introduction to the article, to clarify that complex analysis really involves functions satisfying complex differentiability conditions, rather than just complex-valued functions. Also, a brief note on a comparison between complex analysis and real analysis. This reflects what could be thought of as a personal opinion, but I think the opinion is generally echoed in the math community. Vipul Naik 19:28, 27 February 2008 (CST)

Definitely an improvement (in my opinion), so thanks for that. I think the comparison between real and complex analysis is acceptable, though there is a tension with the Neutrality Policy and this comparison should ideally be worked out later in the article. There is a slight danger that the introduction is seen to imply that complex analysis concerns only analytic (or meromorphic) functions, but I can't see a way to improve that without destroying the flow of the text. -- Jitse Niesen 08:22, 28 February 2008 (CST)

Changed slightly the definition

Hello, I changed slightly the definition of the entry, since there are two points that need to be clarified by such a definition:

  1. Complex analysis deals not only with functions of one variable, but also with functions of several variables: this last branch is specifically identified by the name "several complex variables". Some times, university course topics identified with the name "complex analysis" deal only with functions of one complex variable, but this in some sense an "abuse of notation".
  2. The functions studied in the field of complex analysis need not to be defined on the whole complex plane or complex euclidean space: they can be defined only on subdomains of these two sets.

Please contact me if there is any problem related to this change that anyone would like to discuss. Daniele Tampieri 09:39, 22 February 2011 (UTC)

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