Talk:Complex analysis

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	This article is within the scope of WikiProject Mathematics.
	Mathematics grading:	B Class	Mid Importance	Field: Analysis
Needs information on motivation and examples; sections on history and holomorphic functions need expanding. Tompw 17:46, 7 October 2006 (UTC)

the emergence of complex analysis is a vast change in the truth structure of mathematics, and it is incorrect to introduce it without some mention of its impact on the w:philosophy of mathematics

Please provide references for this claim. AxelBoldt 21:44 Jan 10, 2003 (UTC)

Contents 1 Complex Variables 2 Too Technical 3 Euler's equation 4 This is disgraceful

[edit] Complex Variables

Does anyone know a terminological difference, if any, between complex analysis and so-called complex variables? I am under an impression that the latter is more elemental stuff. Though complex variable is redirected here, as it should be, I would love to see some mention of this matter in the article. -- Taku 09:54, 19 October 2005 (UTC)

[edit] Too Technical

I restructured the article and added some introductory material to try to make the content more accessible, but I didn't feel particularly qualified to modify most of what was already there. I may tackle it later unless someone else goes first.

Taku, I don't know if 'complex variables' is a distinct subject -- I did add a section defining complex functions (functions of complex variables). Hope that is helpful.--andersonpd 21:52, 20 October 2005 (UTC)

The problem I have here is I want to see what is actual complex analysis. It includes Cauchy-Riemann equations, integrations and the problem of how to define functions like e, sin, cos of complex variables. One of the marvelous is, in a sense, complex analysis is more elegant analysis than real one. For instance, the proof for C-R equations doesn't belong here but I want to see the point of this in the context of complex analysis. -- Taku 23:09, 20 October 2005 (UTC)

I agree. The current article jumps too quickly into fairly high level results of complex analysis without enough foundation. A discussion of complex differentiation and integration seems in order and some attention should be given to more elementary complex analysis -- definitions of the exponential and logarithm functions, power series, etc. Most of that info is available on Wikipedia in other articles but there should be at least a summary of some of the simpler aspects of the subject here.--andersonpd 01:35, 21 October 2005 (UTC)

Actually, the article, in my opinion, lacks both elementary and advanced stuff. For example, Runge's approximation theorem is very important result but it is not mentioned even a bit. A complex function of several variables should be discussed somehow at least. In any rate, I don't think anyone disagree that we need more substantial improvement and whining doesn't do this job. -- Taku 09:33, 21 October 2005 (UTC)

There needs to be a separate article on "differentiability." This term is used without definition.

[edit] Euler's equation

The equation e^((pi)*i)=-1 is one of the most important equations in mathematics, shouldn't it be produced in full here?

Fephisto 01:27, 19 January 2006 (UTC)

I believe it shows up at complex number. That may be enough I think. Oleg Alexandrov (talk) 02:02, 19 January 2006 (UTC)

There is a separate article about it, called Euler's identity. As that article states, Euler's identity is also sometimes called "Euler's equation". I think that there should be a disambiguation page for "Euler's equation": leading to either "Euler's equations" or "Euler's identity".

[edit] This is disgraceful

In my opinion, this article is a disgrace to Wikipedia. Complex analysis is indeed a wonderful subject, including such notable mathematical achievements as the Fundamental Theorem of Algebra. It has also motivated a large number of extensions, such as cyclotomic fields, the quaternions, etc. To a very great extent, one might say that mathematical analysis is complex analysis.

I've put this one on my to-do list. If anyone else wants to help improve this article, feel free to contact me. DavidCBryant 12:34, 4 December 2006 (UTC)

I've begun to flesh out this article. I added a new section on the derivative and the Cauchy-Riemann equations today. More coming soon! DavidCBryant 20:24, 7 December 2006 (UTC)