Definition of "differential" in Englisch

adjective

1. Of or pertaining to a difference.

   • differential characteristics

2. Dependent on, or making a difference; distinctive.

3. Having differences in speed or direction of motion.

4. (mathematics) Of or pertaining to differentiation or the differential calculus.

noun

1. The differential gear in an automobile, etc.

2. A qualitative or quantitative difference between similar or comparable things.

3. One 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.

4. A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.

5. (calculus) A 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 operatorname d!x.

6. (calculus, of a univariate differentiable function f(x)) A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.

   • If f(x)#61;x², the differential of f is the function #92;operatorname#123;d#125;#92;#33;f(x,#92;Deltax)#61;f'(x)#92;Deltax#61;2x#92;Deltax.

7. (multivariable calculus) The Jacobian matrix of a function of several variables.

8. (differential geometry, of a smooth map ϕ between smooth manifolds) The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.

9. (mathematics) Any 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.