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Help with Beginner Index Notation

  1. Dec 20, 2009 #1
    Okay, so I'm learning some basic index notation, and I have a few questions...
    1. The problem statement, all variables and given/known data
    f= scalar field
    F = vector field

    so, we are supposed to show that curl(fF) = fcurl(F) + ([tex]\nabla[/tex]f) x F

    3. The attempt at a solution

    curl(fF) = [[tex]\nabla[/tex] x (fF))][tex]_{k}[/tex] = [tex]\in[/tex][tex]_{ijk}[/tex](f[tex]\partial[/tex][tex]_{i}[/tex]F[tex]_{j}[/tex] + F[tex]_{j}[/tex][tex]\partial[/tex][tex]_{i}[/tex]f)

    any help??

    (all the superscripts are supposed to be subscripts, i dunno)
     
  2. jcsd
  3. Dec 20, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi fttteotd! Welcome to PF! :smile:

    (have a curly d: ∂ and a nabla: ∇ and an epsilon: ε and use itex rather than tex in the middle of a line :wink:)

    [∇ x (fF)]i = εijkj(fFk) …

    and now use the chain rule! :wink:
     
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