Divergence Theorem and Variations

F a n ds f a dv v v f a f a dv v f

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Unformatted text preview: ming the first, apply the first with F = f a, where a is any constant vector. ˆ f a · n dS = ∇ · (f a) dV V ∂V = (∇f ) · a + f ∇ · a dV V = (∇f ) · a dV V To get the second line, we used vector identity # 8. To get the third line, we just used that a is a constant, so that it is annihilated by all derivatives. Since a is a constant, we can factor it out of both integrals, so ˆ f n dS = a · a· ∇ f dV V ∂V ˆ f n dS − =⇒ a · ∇f dV =0 V ∂V March 3, 2013 Divergence Theorem and Variations...
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This note was uploaded on 02/13/2014 for the course MATH 227 taught by Professor Joelfeldman during the Fall '13 term at UBC.

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