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Notational problem in tensor calculus

  1. Feb 10, 2008 #1
    Using the Einstein convention, is this about right? (indexes run from 1 to 3):

  2. jcsd
  3. Feb 10, 2008 #2


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    The partial derivatives are take wrt what variable ? x or a ?
  4. Feb 10, 2008 #3
    it's said x above the exercises [tex]\partial_{j}=\frac{\partial}{\partial x_{j}}}[/tex]

    and the question is:

    calculate explicitly: [tex]\nabla \bullet (x_{i}\vec{a})[/tex], where a is a constant vector....

    my attempt is way off, but I don't feel at home in these new symbols enough to get the right answer.
    Last edited: Feb 10, 2008
  5. Feb 10, 2008 #4


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    [tex]x_i{\vec a}[/tex] is not clear notation. Does it mean the i component of a tensor
    [xa], or does it mean [tex]{\vec\hat i}\cdot{\vec r}{\vec a}[/tex]?
  6. Feb 10, 2008 #5


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    You are right that it means [tex] \partial_{j} (a_{j}x_{i}) [/tex] But the components of a are constants so this is equal to [tex]a_j \partial_{j} x_{i} [/tex] Now, what does [tex] \partial_{j} x_{i} [/tex]give ?
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