proof of divergence theorem in n_dimension?

Answer 1

here is a good beginning:
http://mathworld.wolfram.com/DivergenceTheorem.html
http://en.wikipedia.org/wiki/Stokes_theorem
.

Answer 2

It's *way* too involved to try and reproduce it here. Find a good text on multidimensional Calculus and/or Projective Geometry. Most people have a difficult time following the proof going from a triple integral over a closed surface (in 3-space) to a double integral in a plane. Going from an arbitrary n-space to n-1 space is even more abstract.

Good luck ☺


Doug

Answer 3

my suggestion is
look up a book on 'tensors'
they will give u proof and derivation of divergence
in a generalized coordinates system which could be n dim
also need not be a orthogonal system
just that the system or the basis needs to be linearly independent
the proof is lennnngthy!!