Talk:Methods of contour integration

WikiProject Mathematics (Rated C-class, Low-priority)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 C Class
 Low Priority
Field: Analysis

In my university's adv. calculus course number 4 was called "Pacman rule". Is it popular imformal name or just local name?

Hehe. Sounds like it's an informal (and local - I've never heard of it) name. Dysprosia 10:22, 3 September 2005 (UTC)

Embarrassing

I'm going to go ahead and delete Example V which has a number of serious problems. Later on, if I have the time, I'll replace it with another example demonstrating the use of keyhole contours.

The problems I see with this example are the following.

1. There is a completely irrelevant remark at the beginning about the computer program MAPLE. This has nothing to do with with the choice of branch cut in this example. The reason for choosing this particular branch cut is that the avoids the integration contour.

2. It is claimed that the integral over the circular arcs tends to zero, but the only estimate actually shown in the article is the large R limit, and it's much less obvious that the integral over the small arc tends to zero as well.

3. In fact, its not even clear what small circular arc we're looking at since the picture of the contour does not match up with the computation a few lines later. Judging from the computation, the contour should contain two segments parallel to the negative x-axis, but instead the picture shows two lines emanating from the origin at an angle.

3. In the sixth line of displayed mathematics, the letter z is being used for three different things.

4. The word "or" is used indiscriminately in going from one line of computation to the next. In the first instance, it suggests equality, while in the second instance it seems to be saying "When we take the small-epsilon limit, we get..." Also, no justification is given for the limit taken in this line, which requires interchanging a limit with an improper integral.

5. I cant solve integral of (1+z)/z, where C is the right half of the circle |z| = 1 from z = -i to z = i. — Preceding unsigned comment added by 174.117.247.151 (talk) 15:42, 7 December 2011 (UTC)

In summary, I find this example to be an embarrassing example of poor mathematical writing. I haven't read the rest of the article, but if it contains the same basic errors, then I think it may need attention from an expert. 208.46.240.2 (talk) 20:42, 8 August 2011 (UTC)

I have restored it, minus the Maple sentence (which is ridiculous). While I agree with most of your points, I do not agree that this makes it unhelpful; indeed, I found the section quite helpful, and think that cleanup is more appropriate than deletion. Leaving it here with a discussion here directing somebody to clean it up, change the image, etc., will be more helpful than removing it, since the core content is quite good. --74.196.121.135 (talk) 19:51, 11 August 2011 (UTC)

Yes. Please don't delete things based on what they OMIT. That makes no sense whatsoever. Add to them. Harsimaja (talk) 01:29, 24 December 2011 (UTC)

The first sentence is inaccurate

The first sentence says

"In complex analysis, contour integration is a method of evaluating certain integrals of real-valued functions along intervals on the real line that are not readily found by using only real variables."

This is an overly restrictive definition of what contour integration is, because it can be applied to complex-valued functions as well. I would suggest rewording this to

"In complex analysis, contour integration is a method of evaluating certain integrals along closed paths in the complex plane. This can be useful for evaluating integrals along the real line that are not readily found by using only real variables."

--Plasma g (talk) 16:49, 12 April 2008 (UTC)

there's a minor error

When it gives cos[theta]=(1/2)(z+1/z), it first states cos[theta] as (1/2)e^{i theta) +e^(-i theta). The 1/2 should multiply both exponents. Minor error, but worth fixing whenever anyone reads this that knows how to edit the math. And when you fix it, please delete my comment =)

Nelson

I thought I'd mention that this appears to have been fixed by now.

Here is my site with contour integration example problems. Someone please put this link in the external links section if you think it's helpful and relevant. Tbsmith

http://www.exampleproblems.com/wiki/index.php/Complex_Variables#Complex_Integrals

Some of the text in this page doesn't wrap properly around the figures in my browser (Firefox 1.0.4). Anyone else see this problem/know how to fix it?

Yeah I get the same problem.ACielecki 02:07, 12 April 2006 (UTC)

I saw that there was no page for "Estimation lemma" which is linked to, so I created the page. It's the first one I've ever made so would appreciate help with it if you see room for improvement. For the example I used the same integral used in the example on this page, which I thought fit well.

Who creates the graphics? The "estimation lemma" could use an upper half-circle contour of radius 'a' and Γ near it to name the contour. --Menorman 07:25, 23 June 2006 (UTC)

Redirecting "Complex Integration" here

I added a redirect from Complex Integration to this page. Hope it's alright. Etnoy (talk) 22:31, 3 November 2008 (UTC)

NPOV/Accuracy

See [1]. The tags should remain until this is clarified. Headbomb {ταλκκοντριβς – WP Physics} 01:28, 22 February 2010 (UTC)

Nonsense! Count Iblis (talk) 01:41, 22 February 2010 (UTC)
The sources seem to be on-topic, professionally published sources. As described at WP:SCG, this article seems to footnote several general sources on the first line that can be used to verify statements lower down.
Unless there are specific concerns, I don't see any glaring difficulties with the sources. — Carl (CBM · talk) 02:48, 22 February 2010 (UTC)
Alright, CBM's vouching is good enough for me. Headbomb {ταλκκοντριβς – WP Physics} 03:10, 22 February 2010 (UTC)
Actually, CMB vouching or not should be completely irrelevant. This article contains a large number of derivations which themselves cannot be directly sourced. Of course, it would be plaigiarism if they could be directly sourced. I think this article is fine. But according to Headbomb's logic used in the infraparticle page discussion, this article should be very problematic. People who are not fluent in maths cannot verify this article from the sources.
B.t.w., I do think one needs to explain the residue at infinity either by giving a source for that specific statement or an argument that explains why it is defined in that way (no source would be ok with me in the latter case). I do myself understand this, but I know that many people who know the basics of complex analysis do not. Count Iblis (talk) 13:11, 22 February 2010 (UTC)
Please note that the article's verifiability is perfectly adequate. Charles Matthews (talk) 13:18, 22 February 2010 (UTC)
I agree 100%. Count Iblis (talk) 13:45, 22 February 2010 (UTC)

Not a mathematical toolbox

A prod was stuck on saying 'Wikipedia is not meant to be a mathematical toolbox. That is true all right but I think all that is wrong with this article currently is the tone, That methods of contour integration is a notable subject in itself and most of the article could be kept. I think most of the problems could be removed by changing the tone so the descriptive bits don't say things like 'we will evaluate'. Dmcq (talk) 16:56, 23 July 2010 (UTC)

Nothing wrong with adding the occasional 'toolbox' article - the book-form Britannica includes such articles too - it helps more people than are grievously offended by its existence, so this person can lighten up. Same goes for the article on vector calculus in various coordinate systems. I'm thinking of adding a similar one myself. Harsimaja (talk) 01:27, 24 December 2011 (UTC)

What is a contour integral?

Contour integral redirects here; yet the text appears to assume that the reader already knows what a contour integral is: the term is used without further explanation.  --Lambiam 21:06, 23 October 2011 (UTC)

There did not seem to be a page that appropriately introduces the contour integral on Wikipedia, so I started such sections here. I believe that they are of admissible quality, but will require a bit of work to become what I would consider complete. In the future I could see these sections, as well as some of the general discussion of the intro, becoming their own page (such as Contour Integration). However, for now, considering their length I think this location is appropriate, especially considering that all related links currently direct readers to this page. Particular improvements I hope to do to these sections are to lengthen the conceptual discussion and add more references. Also, I would like to see the subsection Methods of contour integration#Generalization of the Riemann Integral to be mathematically precise (and thus longer). Further results such as independence of path should be included, as well as a short discussion of other results which should link to appropriate pages (such as Cauchy integral formula and Cauchy integral theorem).Brent Perreault (talk) 18:29, 17 December 2012 (UTC)

Independent of path?

At the bottom of Contour integrals, it states: That is, the result is independent of the curve chosen.[6] In the case where the real integral on the right side does not exist the integral along γ is said not to exist.

I assume it was meant to be independent of PARAMETRIZATION, since the example just a little bit down shows the reader that the integral of 1/z over the complex unit circle is 2πi, contradicting the statement that there is an independence of PATH.

Svein Olav Nyberg (talk) 06:02, 20 March 2013 (GMT+1)

Use log for complex logarithm and ln for the real one

I think this would be useful, now some of the steps are a bit confusing. I've seen this convention in a couple books and also in some wikipedia articles. — Preceding unsigned comment added by 94.112.136.34 (talk) 20:43, 7 June 2014 (UTC)