Helmholtz theorem derivation question

  • #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:

Answers and Replies

  • #3
image-jpg.jpg
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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