differentials

核心释义

A difference between similar or comparable things.

1. 1.

   汽车等中的差速器。

   The differential gear in an automobile, etc.

2. 2.

   相似或可比事物之间质或量的差异。

   A qualitative or quantitative difference between similar or comparable things.

3. 3.

   两个线圈之一,彼此或与共同磁铁或电枢相关,使一个线圈产生与另一个相反的极性作用。

   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. 4.

   一种导体形式,用于将电流分流到一系列电灯以保持各灯作用相等。

   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. 5.

   代表变量无穷小变化的量,在非标准分析之外仅作启发式工具,但在20世纪前被认为是严谨的；牛顿微积分中的流数,现通常用莱布尼茨记法写作 d x。

   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. 6.

   给出 f 在点 x 处关于小增量 Δx 或 dx 的线性近似变化量的函数,称为 f 的微分,记作 df(x,Δx)、df(x) 或 df。

   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. 7.

   多元函数的雅可比矩阵。

   The Jacobian matrix of a function of several variables.

8. 8.

   φ 的前推或全导数:从 φ 定义域中点 x 的切空间到 φ(x) 处切空间的线性映射,在技术意义上为 φ 在 x 处的最佳线性近似；记作 dφ_x。

   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.

9. 9.

   上述概念的若干推广之一,例如概形中的Kähler微分、Riemann曲面理论中的二次微分等。

   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.

差速器；微分；差动线圈；分流器；汽车等中的差速器。；相似或可比事物之间质或量的差异。