Talk:Complex analysis

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 Field: Analysis

The plot is not in traditional sense[edit]

Have anyone notice that the plot of the function is not in the traditional way? What I mean is that, in the plot, positive x-axis points left and positive y-axis points down. I discovered that when I copied the code in the plot's description page and tried to use the code for other functions. Should this be rectified? Billyauhk (talk) 13:14, 17 December 2009 (UTC)

Philosophical impact[edit]

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)

Complex Variables[edit]

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)

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.

Too Technical[edit]

The claim that "in real analysis, the limit can only be approached by moving along the one dimensional number line" needs be elaborated since students often confuse it with directional derivatives. It may be explained that in directional derivatives, one still moves along the one dimensional x line but it can be in "discrite" units; that is, if one follows y = x2 line, that does not mean that one is moving on the plane (instead of the one dimensional x line) but means that one is approaching in steps of discrete units. - Vvelup, Canada, 10 Apr 2008.

Euler's equation[edit]

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".

This is disgraceful[edit]

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)

Complex Functions Section[edit]

The section "Complex Functions" uses the terms "dependent variable" and "independent variable". It seems like domain and codomain would be more suitable, since this is a mathematics-oriented page and not a scientific one. It could even be made more succinct saying a complex function is a function C -> C.

If that terminology seems within reason to others, there are other issues with this section. It uses the phrase "(in)dependent variable" twice, which is not very good style. Then, it defines the functions "more precisely" by letting complex functions being functions from a subset of the complex plane, which would suggest the author is describing partial functions. They randomly threw in using an otherwise unreferenced variable omega. And lastly, the word "range" is used where codomain is more precise. —Preceding unsigned comment added by Tac-Tics (talkcontribs) 18:05, 11 March 2008 (UTC)

Complex manifolds?[edit]

Shouldn´t there be mention of complex manifolds in this article, with a link to the complex manifold article? Alterationx10 (talk) 20:41, 18 June 2008 (UTC)

Article short but good summary[edit]

I found that the Complex Analysis article I am commenting on was a good summarized article for the topic if I was in a masters or PhD program in pure mathematics. However, most people looking this article up are probably going to be engineers or in physics, and as such, need to know certain pieces of information either not directly in or not linked in the article. That information mostly includes a complex integral table, if someone happens to have one available, as these are hard to come by and to my knowledge wikipedia does not have such a table of integration online. Adding either this table or even a link to one to this article would be extremely beneficial to both the article and its readers. NOTE_ I BELIEVE THAT: THERE İS ONE NUMBER SPACE,İT İS MORE POWERFUL THAN COMPLEX ANALYSİS,NAMELY TİHİS İS META COMPLEX NUMBERS!Skywatcher365 (talk) 17:16, 28 August 2008 (UTC)

Assessment comment[edit]

The comment(s) below were originally left at Talk:Complex analysis/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Needs information on motivation and examples; sections on history and holomorphic functions need expanding. Tompw 17:46, 7 October 2006 (UTC)

Last edited at 12:02, 16 April 2007 (UTC). Substituted at 01:54, 5 May 2016 (UTC)