Definiciones
1.AdjectiveOf or pertaining to a difference."differential characteristics; I saved disk space by taking differential backups, which only stored the data that had changed."
2.AdjectiveDependent on, or making a difference; distinctive.
3.AdjectiveHaving differences in speed or direction of motion.
4.AdjectiveOf or pertaining to differentiation or the differential calculus.
5.NounThe differential gear in an automobile, etc.
6.NounA qualitative or quantitative difference between similar or comparable things.
7.NounOne of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
8.NounA form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
9.NounA quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but considered rigorous until the 20th century; a fluxion in Newtonian calculus, now usually written in Leibniz's notation as
d
x
{\displaystyle \operatorname {d} \!x}
.
10.NounA function giving the change in the linear approximation of
f
{\displaystyle f}
at a point
x
{\displaystyle x}
over a small interval
Δ
x
{\displaystyle \Delta x}
or
d
x
{\displaystyle \operatorname {d} \!x}
, the function being called the differential of
f
{\displaystyle f}
and denoted
d
f
(
x
,
Δ
x
)
{\displaystyle \operatorname {d} \!f(x,\Delta x)}
,
d
f
(
x
)
{\displaystyle \operatorname {d} \!f(x)}
, or simply
d
f
{\displaystyle \operatorname {d} \!f}
."If
f
(
x
)
=
x
2
{\displaystyle f(x)=x^{2}}
, the differential of
f
{\displaystyle f}
is the function
d
f
(
x
,
Δ
x
)
=
f
′
(
x
)
Δ
x
=
2
x
Δ
x
{\displaystyle \operatorname {d} \!f(x,\Delta x)=f'(x)\Delta x=2x\Delta x}
."
11.NounAny of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
12.NounThe Jacobian matrix of a function of several variables.
13.NounThe pushforward or total derivative of
ϕ
{\displaystyle \phi }
: a linear map from the tangent space at a point
x
{\displaystyle x}
in
ϕ
{\displaystyle \phi }
's domain to the tangent space at
ϕ
(
x
)
{\displaystyle \phi (x)}
which is, in a technical sense, the best linear approximation of
ϕ
{\displaystyle \phi }
at
x
{\displaystyle x}
; denoted
d
ϕ
x
{\displaystyle \operatorname {d} \!\phi _{x}}
.
14.NounAny of several generalizations of the concept(s) above: e.g. the Kähler differential in the setting of schemes, the quadratic differential in the theory of Riemann surfaces, etc.