differential

Meanings

Plural: differentials

Noun

• the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
• a quality that differentiates between similar things
• a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
• 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.
• 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.
• 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.
• 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.
• The Jacobian matrix of a function of several variables.
• 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.
• 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

• relating to or showing a difference
  • "differential treatment"
• involving or containing one or more derivatives
  • "differential equation"

Adj

• Of or pertaining to a difference.
• Dependent on, or making a difference; distinctive.
• Having differences in speed or direction of motion.
• Of or pertaining to differentiation or the differential calculus.

Synonyms

derivative, derived function, differential coefficient, differential gear, first derivative

Related Words

differ, difference, different, differentiate, differentiation

Anagrams of differential