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March 30th, 2014, 03:53 PM   #1
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Diffential elements and analysis dimensional

The definition for volume element is simples, is , ok. But, if you integrate this you'll have problems, because no make sense in the right side of equation and, on the other hand, no make sense in the left side of equation... so, this problem is eliminated if you define the volume element like , now the tiple integral make sense:


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.
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March 31st, 2014, 01:02 PM   #2
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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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