Infinitesimal volume using differentials

  • Thread starter girolamo
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  • #1
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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
 

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  • #2
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Hi, I don't understand why in some texts they put that infinitesimal volume dV = dx dy dz.
Because the dimensions of the box are dx, dy, and dz. The volume of this box is dV, which is 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

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.
 
  • #3
SteamKing
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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

It's for the same reason that dA = dx*dy.
 
  • #4
lavinia
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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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