1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook