differential
IPA: dɪfɝˈɛnʃʌɫ
noun
- The differential gear in an automobile, etc.
- A qualitative or quantitative difference between similar or comparable things.
- 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.
- 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.
- (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.
- (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.
- Any of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- (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.
- (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.
adjective
- Of or pertaining to a difference.
- Dependent on, or making a difference; distinctive.
- Having differences in speed or direction of motion.
- (mathematics) Of or pertaining to differentiation or the differential calculus.
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Examples of "differential" in Sentences
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