My Math Forum Diffential elements and analysis dimensional

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 March 30th, 2014, 03:53 PM #1 Senior Member   Joined: Nov 2013 Posts: 137 Thanks: 1 Diffential elements and analysis dimensional The definition for volume element is simples, is $dV=dxdydz$, ok. But, if you integrate this you'll have problems, because $\int dV= \int dxdydx$ no make sense in the right side of equation and, on the other hand, $\iiint dV=\iiint dxdydx$ no make sense in the left side of equation... so, this problem is eliminated if you define the volume element like $d^3V= dxdydz$, now the tiple integral make sense: $\iiint d^3V= \iiint dxdydz$ However, to think if a quantity physical, in infinitesimal size, have simple, double, triple, ..., differential is non-intuitive, is a concept very analytical. But, ignore this information is metematically wrong. So, which is correct form for deal with this? Last edited by Jhenrique; March 30th, 2014 at 03:55 PM.
 March 31st, 2014, 01:02 PM #2 Global Moderator   Joined: May 2007 Posts: 6,806 Thanks: 716 You seem to be hung up on notation. If V stands for volume, then dV is understood to mean volume element, putting in 3 as an exponent doesn't change the meaning.

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