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differential

From Wiktionary, the free dictionary

English

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EnglishWikipedia has an article on:
Wikipedia
EnglishWikipedia has an article on:
Wikipedia

Etymology

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Morphologicallydifferent +‎-ial.

Pronunciation

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Adjective

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differential (comparativemoredifferential,superlativemostdifferential)

  1. Of or pertaining to adifference.
    differential characteristics
    I saved disk space by takingdifferentialbackups, which only stored the data that had changed.
    • 1856,John Lothrop Motley,The Rise of the Dutch Republic: A History, volume 1:
      [Caspar Schetz, Baron of Grobbendonck] was regularly in the pay of Sir Thomas Gresham, to whom he produceddifferential favours, and by whose government he was rewarded by gold chains and presents of hard cash, bestowed as secretly as the equivalent was conveyed adroitly.
  2. Dependent on, ormaking a difference;distinctive.
  3. Having differences inspeed ordirection ofmotion.
  4. (mathematics) Of or pertaining todifferentiation or thedifferential calculus.

Derived terms

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Translations

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relating to a difference
dependent on, distinctive
having differences in speed or direction
relating to differentiation or differential calculus

Noun

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differential (pluraldifferentials)

  1. Thedifferential gear in anautomobile, etc.
  2. Aqualitative orquantitative difference betweensimilar orcomparable things.
  3. One of twocoils ofconductingwire so related to one another or to amagnet orarmature common to both, that one coil producespolar action contrary to that of the other.
  4. A form ofconductor used for dividing and distributing thecurrent to a series of electric lamps so as to maintain equal action in all.[1]
  5. (calculus) A quantity representing aninfinitesimal change in avariable, now only used as aheuristic aid except innonstandard analysis but considered rigorous until the 20th century; afluxion inNewtonian calculus, now usually written inLeibniz's notation asdx{\displaystyle \operatorname {d} \!x}.
  6. (calculus, of aunivariatedifferentiablefunctionf(x){\displaystyle f(x)}) A function giving the change in thelinearapproximation off{\displaystyle f} at a pointx{\displaystyle x} over a small intervalΔx{\displaystyle \Delta x} ordx{\displaystyle \operatorname {d} \!x}, the function being called thedifferential off{\displaystyle f} and denoteddf(x,Δx){\displaystyle \operatorname {d} \!f(x,\Delta x)},df(x){\displaystyle \operatorname {d} \!f(x)}, or simplydf{\displaystyle \operatorname {d} \!f}.
    1. Any of severalgeneralizations of this concept to functions of several variables or to higherorders: thepartial differential,total differential,Gateaux differential,etc.
  7. (multivariable calculus) TheJacobianmatrix of a function of several variables.
  8. (differential geometry, of asmoothmapϕ{\displaystyle \phi } betweensmooth manifolds) Thepushforward ortotal derivative ofϕ{\displaystyle \phi }: a linear map from thetangent space at a pointx{\displaystyle x} inϕ{\displaystyle \phi }'s domain to the tangent space atϕ(x){\displaystyle \phi (x)} which is, in a technical sense, the best linear approximation ofϕ{\displaystyle \phi } atx{\displaystyle x}; denoteddϕx{\displaystyle \operatorname {d} \!\phi _{x}}.
  9. (mathematics) Any of severalgeneralizations of the concept(s) above: e.g. theKähler differential in the setting ofschemes, thequadratic differential in the theory ofRiemann surfaces, etc.

Derived terms

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Translations

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differential gearseedifferential gear
difference between similar or comparable things
infinitesimal change

Related terms

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References

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  1. ^Edward H[enry] Knight (1877), “Differential”, inKnight’s American Mechanical Dictionary. [], volumes I (A–GAS), New York, N.Y.:Hurd and Houghton [],→OCLC.

Swedish

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Noun

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differential c

  1. (mechanics) adifferential gear
  2. (mathematics) an infinitesimal change
  3. (mathematics) thedifferential operator

Declension

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Declension ofdifferential
nominativegenitive
singularindefinitedifferentialdifferentials
definitedifferentialendifferentialens
pluralindefinitedifferentialerdifferentialers
definitedifferentialernadifferentialernas
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