Talk:Surface integral

Accuracy
Is the comment at the end of the first section accurate? "Note that because of the presence of the cross product, the above formulas only work for surfaces embedded in three dimensional space." If an n-dimensional surface is embedded in (n+1)-dimensional space then the partial derivatives will be vectors in (n+1)-space and there will be n of them. The cross product of a set of n vectors in (n+1)-space is well defined so the formula could still be grammatically sensible. It seems likely that it would still be correct as well. Is there a more general theorem we could reference? —Preceding unsigned comment added by 24.4.97.134 (talk) 07:28, 16 June 2009 (UTC)

Not pleased
I'm not pleased with the section on surface integrals of vector fields. It talks about these things before giving the definition. This is thoroughly confusing to people who have just read the section on surface integrals of scalar functions. They will have no idea what the "surface integral of a vector field" means, and then they will have a definition "derived" for them based on facts derived from a non-existent definition. Revolver 18:31, 17 January 2006 (UTC)
 * In my original formulation I meant to start with an intuitive idea of the integral of a vector field, the same thing I did for the integral of a scalar field. I did not mention flux at all. Then Patrick came a long and did some more edits too. So I guess you don't like the end result. If I look at the diff between my last edit and the current version here, I will argue that what I wrote (left column) makes sense. No? Oleg Alexandrov (talk) 01:33, 18 January 2006 (UTC)
 * Yes, your original way looks okay. I just have a problem when it appears that two things are defined, and each in terms of the other, which is how it looked when I saw it. I did not look at the history close enough. Revolver 23:27, 27 January 2006 (UTC)

Notation
Am I wrong, or is the $$\oint_{S}$$ notation used for surface integrals? My understanding of path and surface integrals, so I'm not sure exactly how this notation is used, but I had thought that it might even be used for both surface and path integrals. If so, it should be noted what say "$$\oint_S$$" means. Fresheneesz 07:13, 9 February 2006 (UTC)
 * I believe that notiation is used for integrals on closed curves and/or closed surfaces. But I am not sure. I don't know if it is worth the trouble mentioning that in the article. Oleg Alexandrov (talk) 16:28, 9 February 2006 (UTC)


 * Oh, that sounds right. But I do think that a small note is due just because one might expect to find an explanation of it here. Fresheneesz 20:10, 9 February 2006 (UTC)

If we think of S as made of some material, and for each x in S the number f(x) is the density of material at x, then the surface integral of f over S is the mass per unit thickness of S. May S be thought of as a hollow object, such as a bubble or a vase? --Abdull 16:45, 30 May 2006 (UTC)


 * I think the notation with an ellipse/"o"/circle on it is for closed surfaces (sphere, as opposed to a ball or plane). but maybe it requires 2 of these "$$\int$$" thingies within the ellipse/circle/"o".  Is there a code for it?  K61824 (talk) 01:25, 14 July 2009 (UTC)


 * In a physics textbook I have, electric flux over a closed surface is written simply $$\oint \mathbf{E} \cdot d\mathbf{A}$$, which I vehemently criticize as both inaccurate and misleading (we can argue that $$\oint$$ can replace, as many people do one symbol regardless of the number of dimensions, but either way, this notation doesn't specify the domain of integration!).--Jasper Deng (talk) 09:18, 23 November 2013 (UTC)

Simpler proof for vector fields?
to prove integral (A.dS) = integral (del.A dV) Let A (Ax,Ay,Az)

RHS =integral (pd/dx . i + pd/dy .j + pd/dz .k)(Ax i + Ay j + Az k)dV

= int(int(int((pd Ax/dx + pd Ay/dy + pd Az/dz).dx.dy.dz))

= int(int(int (pd Ax. dy.dz + pd Ay.dx.dz + pd Az.dx.dy)))

= int(int (Ax.dy.dz + Ay.dx.dz + Az.dx.dy)

= int (A.dS)
 * No, that is not a correct formulation of the divergence theorem.--Jasper Deng (talk) 09:12, 23 November 2013 (UTC)

Cross Product
Hi, This article gives definitions in terms of cross products, which means that they are only applicable in 3 dimensional space. The article does mention this restriction, but it would be good to also have a section that gives the/a generalisation to n-dimensional spaces. Cheers, Nathanielvirgo (talk) 15:58, 29 July 2009 (UTC)

Area element
How come that this article does not link to the area element??? And I hope someone can write something to relate them. Jackzhp (talk) 02:38, 19 March 2011 (UTC)


 * Now it's linked, but I think the whole section about Area element belongs here rather than where it is. fgnievinski (talk) 02:35, 6 December 2023 (UTC)

The notation is a mess
For someone who doesn't already know what is going on, the notation is very very confusing. Some letters are bold, some are not (this is probably vector x scalar quantity difference), but what are the dimensions of domains/codomains? It can be guessed and then verified to "sort of make sense" if one has some intuition, but in general, I find that the weakest point of the article.

It would be beneficial if someone who understands the topic added the domains/codomains or explanations of what are f,x,v,n,u,v,r (which seems to be x from the example just before!) and other symbols used in the first two sections. Thanks 94.112.136.34 (talk) 14:08, 24 June 2014 (UTC)

Advanced issues section is Original Research
The whole area of advanced issues reads like original research and is completely unreferenced.I think we need to find a source for it. — Preceding unsigned comment added by Loneather (talk • contribs) 18:18, 16 December 2017 (UTC)

Please define f subscript x and f subscript y
There is no definition of what f refers to when subscripted by either x or y. Please define. Jim Bowery (talk) 00:07, 6 April 2022 (UTC)