differential operator
Noun
Meaning
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}
.
Related terms
Examples
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.
Euler's notation Euler 's notation uses a differential operator D, which is applied to a function f to give the first derivative Df.
The idea is that a velocity field can also be understood as a first order differential operator acting on functions.