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Infinitesimal volume using differentials

  1. Oct 13, 2013 #1
    Hi, I don't understand why in some texts they put that infinitesimal volume dV = dx dy dz. If V = x y z, infinitesimal volume should be dV = y z dx + x z dy + x y dz, by partial differentiation. Thanks
  2. jcsd
  3. Oct 13, 2013 #2


    Staff: Mentor

    Because the dimensions of the box are dx, dy, and dz. The volume of this box is dV, which is dx * dy * dz.
    This would be the change in volume of a box whose dimensions are x, y, and z, and whose dimensions change by dx, dy, and dz.
  4. Oct 13, 2013 #3


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    It's for the same reason that dA = dx*dy.
  5. Oct 13, 2013 #4


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    dx dy dx dz are three independent small changes in the axis variables. You can think of the as spanning a small rectangular solid.
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