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Mathematics
Differential Geometry
Integration of differential forms
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[QUOTE="JonnyG, post: 6419264, member: 547631"] ##dt## is a covector field and evaluated at a point, gives you a covector, which then acts on a tangent vector. So if we are evaluating ##F \cdot dt## at a point ##t_0##, then we get ##F(t_0) dt_{t_0}##, which is a real number multiplied by a covector. I don't see how it makes sense to sum a bunch of covectors to obtain a real number. I hope that clears up my question. But then this is just the usual thing you're told in elementary calculus: the ##dt## tells you what variable to integrate over, so then it seems kind of pointless to have created the theory of differential forms. Differential forms are supposed to be giving meaning to the ##dt##, but with this viewpoint I am just circling back to "it's the variable to integrate over". [/QUOTE]
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