English Explanatory Dictionary

differential

English dictionary entry

Meanings

adj
  1. Of or pertaining to a difference.
  2. Dependent on, or making a difference; distinctive.
  3. Having differences in speed or direction of motion.
  4. 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. 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. 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.
  7. Any of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
  8. The Jacobian matrix of a function of several variables.
  9. 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.
  10. 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.

Pronunciation

[dɪfəˈɹənʃəɫ] en-us-differential.ogg /ɖɪf(ə)ˈrɛnʃ(ɪ)jəl/

Word forms

differential more differential most differential differentials

Etymology

Etymology tree Proto-Indo-European *dwóh₁ Proto-Indo-European *d(w)is- Proto-Italic *dis- Latin dis- Proto-Indo-European *bʰer- Proto-Indo-European *bʰéreti Proto-Italic *ferō Latin ferō Latin differō Latin differēns Proto-Indo-European *-yós Proto-Italic *-ios Old Latin -ios Latin -ius Latin -ia Latin differentia Proto-Indo-European *h₂el-der.? Proto-Italic *-ālis Latin -ālis Latin differentiālislbor. English differential Learned borrowing from Latin differentiālis. By surface analysis, different + -ial.

Related words

differ difference different differentiate differentiation

Derived words

bidifferential codifferential cytodifferential differential grasshopper differentialize differentially differential privacy differential racialization differintegral multidifferential nondifferential paradifferential pseudodifferential subdifferential subdifferentially thermodifferential time differential transdifferential ultradifferential undifferential absolute differential calculus affine differential geometry delay differential equation differential amplifier differential analyzer differential coefficient differential diagnosis differential equation differential form differential gear differential geometry differential lock differential medium differential piece work differential psychologist differential psychology differential scanning calorimetry differential screw differential steering differential structure differential thermal analysis differential thermometer differential topology integro-differential Legendre's differential equation limited-slip differential locking differential open differential ordinary differential equation partial differential partial differential equation stochastic differential equation
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