Editing Differential operator (section)

{{Short description|Typically linear operator defined in terms of differentiation of functions}}
{{Use American English|date = January 2019}}
[[Image:Laplace's equation on an annulus.svg|right|thumb|300px|A harmonic function defined on an [[Annulus (mathematics)|annulus]]. Harmonic functions are exactly those functions which lie in the [[kernel (linear algebra)|kernel]] of the [[Laplace operator]], an important differential operator.]]

In [[mathematics]], a '''differential operator''' is an [[Operator (mathematics)|operator]] defined as a function of the [[derivative|differentiation]] operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a [[function (mathematics)|function]] and returns another function (in the style of a [[higher-order function]] in [[computer science]]).

This article considers mainly [[linear map|linear]] differential operators, which are the most common type. However, non-linear differential operators also exist, such as the [[Schwarzian derivative]].