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In mathematics, the term differential has several meanings. ==Basic notions== * In calculus, the differential represents a change in the linearization of a function. * * The total differential is its generalization for functions of multiple variables. * In traditional approaches to calculus, the differentials (e.g. d''x'', d''y'', d''t'', etc.) are interpreted as infinitesimals. There are several methods of defining infinitesimals rigorously, but it is sufficient to say that an infinitesimal number is smaller in absolute value than any positive real number, just as an infinitely large number is larger than any real number. * The differential is another name for the Jacobian matrix of partial derivatives of a function from R''n'' to R''m'' (especially when this matrix is viewed as a linear map). * More generally, the differential or ''pushforward'' refers to the derivative of a map between smooth manifolds and the pushforward operations it defines. The differential is also used to define the dual concept of pullback. * Stochastic calculus provides a notion of stochastic differential and an associated calculus for stochastic processes. * The integrator in a Stieltjes integral is represented as the differential of a function. Formally, the differential appearing under the integral behaves exactly as a differential: thus, the integration by substitution and integration by parts formulae for Stieltjes integral correspond, respectively, to the chain rule and product rule for the differential. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Differential (mathematics)」の詳細全文を読む スポンサード リンク
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