Multiple integral notation (or abuse of?)

[Freiddie]

So I've seen quite a variety of notations that deviate from what we've learned in our "normal" math courses.

In math classes we write a volume integral as:
$$\iiint_W \rho\, d V$$
but somehow once we start doing E&M and QM, professors often just drop the extra integral signs:
$$\int_W \rho\, d V$$
Is this justifiable? Or just a short-hand? I've seen this happen to both volume and surface integrals.

Then there's this stranger notation which is more rarely used:
$$\int \frac{1}{|\vec{r}-\vec{r'}|} \, d^3 r'$$
Is there some particular reason why this is used over something simpler $dV'$?

Maybe I'm just being too picky/OCD about notations, I dunno.

 

[mathman]

It is just notation. There is no deep meaning to the differences. The important thing is the differential. dV means your integrating over volume. d³r implies 3 one-d differentials to get volume.