Talk:Green's identities

Proofs?

Probably would be worth adding, at least from the divergence theorem Eraserhead1 12:15, 25 May 2007 (UTC)

Especially for the second one. I have no idea what they are talking about there.123Mike456Winston789 (talk) 20:27, 16 October 2011 (UTC) Actually, it's looking like the theorems are pretty evident if you just work them out.123Mike456Winston789 (talk) 20:33, 16 October 2011 (UTC)

Direction of contour integral

I was just reading this page to try and work out which direction the contour integral has to be taken with and the page does not tell me. I think this should be made clear. —Preceding unsigned comment added by Kiwimhm (talk • contribs) 07:02, 10 November 2007 (UTC)

First, the integral over the boundary need not be a contour. If U is in 3D, its boundary would be a surface.

Clarified: U is a region in R³. TomyDuby (talk) 15:00, 12 July 2008 (UTC)

About the orientation of the contour, the standard way is I think that you take the outer normal to the boundary, then rotate it 90 degree counterclockwise. That will show which direction the contour goes. So, if your domain is a disk, the contour will go counterclockwise, but if the domain is an annulus, the outer contour will go counterclockwise but the inner contour will be clockwise. At least, that's how I remember it. Oleg Alexandrov (talk) 02:33, 16 April 2008 (UTC)

Psi

The third Green's identity says "if psi is twice continuously differentiable" but psi is not mentioned previously in that section. Overall, this page looks like it needs expansion, correction and tidying up. AstroDave (talk) 19:09, 15 April 2008 (UTC)

Psi is mentinoned right below in the text. It is just an arbitrary smooth function, for which the third Green's identity holds. Oleg Alexandrov (talk) 02:26, 16 April 2008 (UTC)

Range of functions

The text says: "Let φ and ψ be functions defined on some region U in R^3, and suppose that φ is twice continuously differentiable, and ψ is once continuously differentiable." Why is the range for each function not specified? Does it matter whether φ:R^n \rightarrow R^n or φ:R^n \rightarrow R?

The $\oint$ sign

The page uses the $\oint$ notation for a surface integral. It is common to use it for an integral along a closed curve. How common is the use for surfaces? Tkuvho (talk) 11:45, 4 February 2011 (UTC)

Whose crazy idea was it to use psi and phi

Bad choice of symbols, they look near identical. Hai2410 (talk) 22:59, 23 May 2011 (UTC)

They are similar (especially when handwritten) but that kind of notation is pretty standard, and the similarity of the symbols hints that phi and psi are the same type of object here. Khromegnome (talk) 23:57, 24 May 2011 (UTC)

What's more, under "Green's first identity," phi is at first used in the gradient product rule. Then, in writing out Green's first identity, psi takes the place of phi and gradient of phi takes the place of X. This change in notation left me puzzled for a bit, thinking that integration by parts was being used to re-express the equation.--173.244.134.42 (talk) —Preceding undated comment added 15:45, 23 June 2020 (UTC)

Any assumption on the boundary?

Am I wrong or there should be some assumption concerning the regularity of the boundary? Something like piecewise smooth? — Preceding unsigned comment added by 129.16.128.48 (talk) 16:41, 4 November 2011 (UTC)

I think so: it should have piecewise smooth boundary, and also the region should be a compact region (as in the divergence theorem). Am I right? Gim²y (talk) 15:31, 20 February 2018 (UTC)

epsilon

Epsilon is not defined, i think — Preceding unsigned comment added by 62.31.80.113 (talk) 21:59, 12 April 2012 (UTC)