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Differential

/[dɪfəˈɹənʃəɫ]/ adj, noun

Definitions

Adjective
  1. 1
    Of or pertaining to a difference.

    "differential characteristics"

  2. 2
    Dependent on, or making a difference; distinctive.
  3. 3
    Having differences in speed or direction of motion.
  4. 4
    Of or pertaining to differentiation or the differential calculus.
Adjective
  1. 1
    relating to or showing a difference wordnet
  2. 2
    involving or containing one or more derivatives wordnet
Noun
  1. 1
    The differential gear in an automobile, etc.
  2. 2
    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 wordnet
  3. 3
    A qualitative or quantitative difference between similar or comparable things.
  4. 4
    a quality that differentiates between similar things wordnet
  5. 5
    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.
Show 8 more definitions
  1. 6
    the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx wordnet
  2. 7
    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.
  3. 8
    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.
  4. 9
    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."

  5. 10
    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.
  6. 11
    The Jacobian matrix of a function of several variables.
  7. 12
    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.
  8. 13
    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.

Etymology

Etymology 1

Morphologically different + -ial.

Etymology 2

Morphologically different + -ial.

See also for "differential"

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