Noun
differential operator (plural differential operators)
(mathematics, mathematical analysis) An operator defined as a function of the differentiation operator (the operator which maps functions to their derivatives).
Define
P
(
D
)
{\displaystyle P(D)}
to be the differential operator given by
P
(
D
)
=
D
2
+
5
D
+
6
{\displaystyle P(D)=D^{2}+5D+6}
, where
D
{\displaystyle D}
is the differentiation operator. Then
P
(
D
)
(
sin
(
x
)
)
=
−
sin
(
x
)
+
5
cos
(
x
)
+
6
{\displaystyle P(D)(\sin(x))=-\sin(x)+5\cos(x)+6}
.
In most cases of practical interest, the orthonormal basis comes from an integral or differential operator, in which case the series converges in the distribution sense. Source: Internet
Euler's notation Euler 's notation uses a differential operator D, which is applied to a function f to give the first derivative Df. Source: Internet
The idea is that a velocity field can also be understood as a first order differential operator acting on functions. Source: Internet