Why isn't Stokes Theorem taught as follows?

• December 1st 2007, 12:55 PM
shilz222
Why isn't Stokes Theorem taught as follows?
Stokes Theorem: $\boxed{\int_{\partial S} \omega = \int_{S} d \omega}$.

Isn't this the more natural way of writing it? It's also easier to remember. From this one statement, we can get Green's Theorem, the Fundamental Theorem of Calculus, etc..
• December 1st 2007, 02:10 PM
ThePerfectHacker
Because then you need to learn what differencial forms are. And that is graduate level math.
• December 1st 2007, 02:21 PM
shilz222
That's not graduate level math. See Advanced Calculus: A differential forms approach by edwards. Or Spivak's calculus of manifolds.
• December 1st 2007, 02:24 PM
ThePerfectHacker
Quote:

Originally Posted by shilz222
That's not graduate level math. See Advanced Calculus: A differential forms approach by edwards. Or Spivak's calculus of manifolds.

I do not imagine that is taught in any undergraduate analysis course eventhough it might be in the book.