Divergence Theorem and Variations

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online