Infinitesimal volume using differentials

[girolamo]

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

 

[Mark44]

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.

 

[SteamKing]

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.

 

[lavinia]

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