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Differential of a 2-form

  1. Apr 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Compute the differentials of the following form:

    2. Relevant equations

    f = exy dy ^ dz

    3. The attempt at a solution

    I'm a little confused on how to work with the wedge product. If I'm looking for df, should I start by calculating the dual f*? Or does the dual not come into play?
     
  2. jcsd
  3. Apr 15, 2012 #2

    HallsofIvy

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    Science Advisor

    No, there is no reason to worry about the dual. For any f, [itex]df= (\partial f/\partial x)dx+ (\partial f/\partial y)dy+ (\partial f/\partial z)dz[/itex].

    If
    [itex]f= e^{xy} dy^dz[/itex] then
    [tex]df= (\partial e^{xy}/\partial x)dx\^dy\^dz+ (\partial e^{xy}/\partial y)dy\^dy\^dz+ (\partial e^{xy}/\partial z)dz\^dy\^dz[/tex]
    Remember, of course, that the wedge product is "anti-symmetric".
     
  4. Apr 15, 2012 #3
    So

    df = yexy dx ^ dy ^ dz + xexy dy ^ dy ^ dz ? Is that the answer?
     
    Last edited: Apr 15, 2012
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