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Green's, Gauss divergence and Stoke's theorems

  1. Jan 17, 2012 #1

    sharks

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    Gold Member

    The problem statement, all variables and given/known data
    What's the difference between Green's theorem, Gauss divergence theorem and Stoke's theorem?

    The attempt at a solution
    I'm struggling to understand when i should apply each of those theorems.

    Here is what i understand. Please correct my statements below, if needed.

    Green's theorem is for evaluating the surface area of a region in a 2D plane, bounded by a simple closed curve.

    Gauss divergence theorem is for evaluating the flux in 3D of a surface bounded by a closed curve.

    Stoke's theorem is for evaluating the surface area in 3D bounded by a simple closed curve.

    It's all a bit mixed in my mind, so i'm not sure which theorem to use, but i've been trying to distinguish between those 3 theorems.
     
    Last edited: Jan 17, 2012
  2. jcsd
  3. Jan 17, 2012 #2
    I think it might help to get an intriductory book on manifolds, for instance the one by Tu. You'll find out that these theorems are in fact all examples of stokes' theorem.

    For now:
    the divergence theorem says that everything escaping a certain volume goes through the surface. So is you're integrating the divergence you might as well integrate the field itself over the (2-D) boundary.

    Green's theorem says basically the same thing but one dimension lower

    and Stokes' theorem is a generalization of these
     
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