Green, Stokes and Gauss

[MindShadowfax]

Hi there everybody! I'm having trouble with this hw my teacher gave and i'd like you to help me as it's been quite difficult to find anything with Google. I'm supposed to get information about Green, Stokes and Gauss' theorems on: How could you relate them (at least in pairs) and some applications they have.

I know that if my surface is plane and parallel to the coordinate axes Stokes = Greens.

Another thing I've already got is that Green applied to a 1 is the curve-length , Stokes would give the surface and Gauss the volume, correct me if i'm wrong.

 

So i'd basically be needing some real applications like in physics or any other field where it is used.

 

 

Thank you very much,

Merry xmas and happy new year to everyone!

[ajb]

These things come up in electromagnetic theory and fluid dynamics, for example. In modern mathematics these ideas are usually discussed in therms of differential forms.

[elfmotat]

You use the Stokes and Gauss theorems to switch back and forth between the integral and differential forms of Maxwell's equations. Stokes also pops up a lot (the 4-d version of it) when varying Lagrange densities, so you can use it to eliminate boundary terms.

 

The usual 3-d Stokes and Gauss theorems actually fall out of the generalized Stokes theorem, i.e. they're both consequences of a more general theorem.

[overtone]

Sometimes, once a student has a rudimentary physical intuition of some approach or basis for these mathematical theorems, they can find applications and comparisons easily on their own. They know where to look.

 

If that is so of you, maybe something like this site would be of help: http://mathinsight.org/stokes_theorem_idea