Editing Helmholtz decomposition (section)

{{Short description|Certain vector fields are the sum of an irrotational and a solenoidal vector field}}
{{Calculus |expanded=vector}}

In [[physics]] and [[mathematics]], the '''Helmholtz decomposition theorem''' or the '''fundamental theorem of vector calculus'''<ref name="murray1898"/><ref name="gibbs1901"/><ref name="heaviside1893"/><ref name="woolhouse1854"/><ref name="johnson1881"/><ref name="shaw1922"/><ref name="edwards1922"/> states that certain differentiable [[vector field]]s can be resolved into the sum of an [[irrotational vector field|irrotational]] ([[Curl (mathematics)|curl]]-free) vector field and a [[solenoidal]] ([[divergence]]-free) vector field. In [[physics]], often only the decomposition of sufficiently [[smooth function|smooth]], rapidly decaying [[vector field]]s in three dimensions is discussed. It is named after [[Hermann von Helmholtz]].