Talk:Surface integral
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[edit] 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)
[edit] Notation
Am I wrong, or is the 
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 "
" 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)
[edit] 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)
