Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Multiple integral notation (or abuse of?)

  1. Jan 23, 2012 #1
    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:
    [tex]\iiint_W \rho\, d V[/tex]
    but somehow once we start doing E&M and QM, professors often just drop the extra integral signs:
    [tex]\int_W \rho\, d V[/tex]
    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:
    [tex]\int \frac{1}{|\vec{r}-\vec{r'}|} \, d^3 r'[/tex]
    Is there some particular reason why this is used over something simpler [itex]dV'[/itex]?

    Maybe I'm just being too picky/OCD about notations, I dunno.
  2. jcsd
  3. Jan 23, 2012 #2


    User Avatar
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook