Helmholtz decomposition
In physics and mathematics , in the area of vector calculus , Helmholtz's theorem , also known as the fundamental theorem of vector calculus , states that any sufficiently smooth , rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational ( curl-free ) vector field and a solenoidal ( divergence-free ) vector field; this is known as the Helmholtz decomposition or Helmholtz representation . 
<triplet> vector field <subj> vector calculus <obj> studied by