so I googled up a proof of te divergence theorem, and plan to explain it....I want to make sure I am understanding the whole proof before I make a fool of myself.(adsbygoogle = window.adsbygoogle || []).push({});

here is a link to the proof I found. It is section 7.2

http://www.enm.bris.ac.uk/admin/courses/EMa2/Lecture Notes 04-05/vcalc7.pdf

ok, so basically, I"m gonna start out and give the formula for divergence, and I will try to prove it.

-so let F = Fi + Fj + Fk, and I"m gonna divde this solid into N small cubes, of volume del(V). so the volume of each cube is devl(V)

-so if we can show that it holds for each little cube, then the proof is done.

because: the volume is equal to the sum, and (1)each little cube will be either inside, or (2) each will be part of the surface.

(in the pdf, it states that in (1), the flux integeral is exactly canceled by the flux integeral of the neighboring cub. I dont know what that means actually...can someone simplify that meaning for me....because it seems important, and if I dont know what it means, then I dont know how to explain it to the class. And in (2), all these contributions sum to the toal flux of intergral of S. again, dunno what that means....)

-so I consider a cube. I will label each face S1, 2, 3, 4, 5, S6.

so for S1, ndS = idydz, and double integeral of F * ndA = integeral from (zi-del(z) to zi +del(z) and integeral (yi-del(y) + yi+del(y) of F1(xi + del x, y, z)dydz.

now, first, I dont know what this integeral is saying. what are we computing here? and where is all the liimits coming from? it's been a while for me since calc class, so I really forgot what n and the del's are.

and then, we take S2 and do the same, w/ the corresponding limits, and different function.

so first of all, where are the functions coming from?

anyways, once we get S1 and S2, we add them up, and by FTC, we get triple integeral partial F/partial x, dV.

and we do the same for S3 + S4, and S5 + S6.

and then we add them all up and get the divergence theorem.

so my final question is, when we did the integeration, what did we integerate exactly...and why when we added them all up, did it prove the divergence theorem.

I really wan't to undersand this, so if someone can help..that would be great.

thanx

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# Help me understand this proof, so I can present it

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