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Math Help - Why isn't Stokes Theorem taught as follows?

  1. #1
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    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..
    Last edited by shilz222; December 1st 2007 at 02:25 PM.
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    Because then you need to learn what differencial forms are. And that is graduate level math.
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  3. #3
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    That's not graduate level math. See Advanced Calculus: A differential forms approach by edwards. Or Spivak's calculus of manifolds.
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    Quote Originally Posted by shilz222 View Post
    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.
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