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Homework Help: Vector Calculus Identities

  1. Sep 19, 2014 #1
    1. The problem statement, all variables and given/known data

    div(øu) = ødivu + ugradø

    2. Relevant equations

    divergence of scalar field = f,ii
    divergence of vector field = ui,i

    3. The attempt at a solution

    I've heard this is a simple proof, but this is my first one of 8 or so proofs I need to complete for homework, and I'm really not sure where to start. I know that div v = ∇ . v, but that's as far as I've gotten. We need to use Index Notation. Thoughts on where to start?
  2. jcsd
  3. Sep 20, 2014 #2


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    Gold Member

    Why not start by applying the definition of the divergence of a vector field to ##\phi\mathbf u##? Please don't use the empty set symbol instead of ##\phi##. I found it very confusing, and it took me some time to understand what you meant. If you don't use LaTeX, and can't find another way to type a ##\phi##, then just call the scalar field f or something like that.
  4. Sep 20, 2014 #3
    Sorry for the confusion. I'll be more careful with the lettering in the future. I've actually figured this one out now. It was the product rule that I wasn't sure about, now that I've worked it through (and several other identity proofs). Now, I'm on the divergence of (u cross v) identity.

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