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Problem with Vector Calculus

  1. May 13, 2005 #1
    I'm doing an assignment where the lecturer has said scalar fucntion g(x,y,z) = x^3 + y + z^2

    and vector field F = (2xz,sin y,e^y)

    and asked find


    a) grad g


    which is fairly easy, but then

    b) div g

    and my understanding was that you can only find the divergence of a vector field not a scalar function.

    Am I right an theres been a typo and he meant div F, or can you actually find div g, Because theres no actually mention of F in any of the questions, which is odd.
     
  2. jcsd
  3. May 13, 2005 #2
    You're entirely right. It's a typo.
     
  4. May 14, 2005 #3

    dextercioby

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    Science Advisor
    Homework Helper

    The scalars don't have a divergence.The divergence is a differntial operator which,applied on a tensor of rank "n",reduces the rank by a unit,namely to "n-1".Since the scalar has already rank "0",you see that it makes no sense to apply the divergence.

    Daniel.
     
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