Helmholtz decomposition

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${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus^{[1][2][3][4][5][6][7]} states that certain differentiable vector fields can be resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field. In physics, often only the decomposition of sufficiently smooth, rapidly decaying vector fields in three dimensions is discussed. It is named after Hermann von Helmholtz.