Дифференциа́л (от лат. differentia — разность, различие) — линейная часть приращения функции.

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  • Дифференциа́л (от лат. differentia — разность, различие) — линейная часть приращения функции.
  • In calculus, the differential represents the principal part of the change in a function y = f(x) with respect to changes in the independent variable. The differential dy is defined bywhere is the derivative of f with respect to x, and dx is an additional real variable (so that dy is a function of x and dx). The notation is such that the equationholds, where the derivative is represented in the Leibniz notation dy/dx, and this is consistent with regarding the derivative as the quotient of the differentials. One also writesThe precise meaning of the variables dy and dx depends on the context of the application and the required level of mathematical rigor. The domain of these variables may take on a particular geometrical significance if the differential is regarded as a particular differential form, or analytical significance if the differential is regarded as a linear approximation to the increment of a function. In physical applications, the variables dx and dy are often constrained to be very small ("infinitesimal").
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prop-fr:contenu
  • Soit L' une application linéaire vérifiant également la définition de la différentielle de f en a. Posons u=L -L' et montrons que u=0 . Soient s un vecteur de norme 1 dans E et V un voisinage de 0F. Puisque , il existe un rayon α>0 tel que . Or par linéarité de u, . Ainsi u est dans tous les voisinages de 0F et donc u = 0F par séparation de F. Par suite u=0 et L=L' .
prop-fr:titre
  • Démonstration de l'unicité
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prop-fr:wikiversity
  • Notions sur les différentielles
prop-fr:wikiversityTitre
  • Notions sur les différentielles
  • Notions sur les différentielles
prop-fr:wiktionary
  • différentielle
dcterms:subject
rdfs:comment
  • Дифференциа́л (от лат. differentia — разность, различие) — линейная часть приращения функции.
  • In calculus, the differential represents the principal part of the change in a function y = f(x) with respect to changes in the independent variable. The differential dy is defined bywhere is the derivative of f with respect to x, and dx is an additional real variable (so that dy is a function of x and dx).
rdfs:label
  • Différentielle
  • Diferencial d'una funció
  • Diferencial de una función
  • Diferenciál (matematika)
  • Differentiaal
  • Differential (Mathematik)
  • Differential of a function
  • Differenziale (matematica)
  • Różniczka
  • Диференциал (математика)
  • Дифференциал (математика)
  • 関数の微分
  • 미분소
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