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Helmholtz theorem derivation question

  1. Dec 15, 2014 #1
    http://en.wikipedia.org/wiki/Helmholtz_decomposition#Derivation
    how do we go from
    f8d3b3e44dfc58f31df26e57c121a22f.png
    to

    6f79acfa5e48004f3a3d8c262d7205db.png

    also on the next step
    f87a951aa4c1323f4886374808b14276.png
    ∇' just means the gradient with respect to r', right?
    Also, why do i have to use the dirac delta function? i thought it was only used to deal with discontinuities?

    also when we say
    gif.gif
    gif.gif
    the volume integral of a vector field just means we do the triple integral on each component of the vector field independently right?
     
    Last edited: Dec 15, 2014
  2. jcsd
  3. Dec 15, 2014 #2

    jedishrfu

    Staff: Mentor

    Last edited: Dec 15, 2014
  4. Dec 15, 2014 #3
    del is an operator though? if i applied that to this case then id get stuff like gif.gif or gif.gif

    i dont know why theyd explain each step then leave one completely mising
     
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