On an alternative Stokes theorem

[curupira]

I find in a homework an alternative Stokes theorem tha i wasn't knew before. I wold like to know that it is really true. Any can give me a proof please?

It is:

Int (line) dℓ′× A = Int (surface)dS′×∇′× A

 

[Danger]

First off, you cannot modify someone else's theorem and still leave his name attached to it (unless you collaborate with him).
Secondly, I think that this belongs in the Homework sub-forum.

 

[Curl]

I can't really read your equation very well but it looks like Stoke's theorem written using alternative notation.

I bet it is equivalent and you can show it with a few lines of manipulation.

 

[Dickfore]

Use the vector field:

[tex]
\vec{F} = \vec{C} \times \vec{A}
[/tex]

where [itex]\vec{C}[/itex] is an arbitrary, but constant vector in the original Stokes' Theorem. Perform some simplifications for:

[tex]
\nabla \times \vec{F}
[/tex]

using nabla calculus and you will arrive at your alternative form of Stokes' Theorem.

 

[curupira]

First off, you cannot modify someone else's theorem and still leave his name attached to it (unless you collaborate with him).
Secondly, I think that this belongs in the Homework sub-forum.

Well, First, I think that you don't understood what I say, because i don't speak english, so its hard but I try to post, others understood me and have answered my question. In fact you don't understood nothing.

Second, It is a general question, and don't a homework question, my homework I solved , but there was a little part incomprehensible to me.

I don't want damage the forum, but think that is possible stay posting here without to know english, cause there's people here that help me, and it is usefull to me.
Thanks!