differential

1. The differential gear in an automobile, etc.

2. A qualitative or quantitative difference between similar or comparable things.

   a quality that differentiates between similar 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.

   дифференциа́лdifferenciál

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.

   If f(x)#61;x², the differential of f is the function #92;operatorname#123;d#125;#92;#33;f(x,#92;Deltax)#61;f'(x)#92;Deltax#61;2x#92;Deltax.

7. 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.

   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.

1. He didn't understand the concept of differential equations.

   Он совершенно не понимал, что такое дифференциальное уравнение.

   deEr verstand nicht, was Differentialgleichungen sind.

   CC BY · Tatoeba · kerbear407 · B2Открыть на TatoebaСообщить о проблеме

2. Resolving a differential equation means finding the functions that satisfy it.

   Решение дифференциального уравнения означает нахождение функции, удовлетворяющей ему.

   deEine Differentialgleichung lösen heißt die Funktionen finden, die sie erfüllen.

   CC BY · Tatoeba · marcelostockle · B2Открыть на TatoebaСообщить о проблеме

3. Tom's favourite pastime was solving differential expressions, while Mary preferred sex.

   Любимым занятием Тома было решение дифференциальных уравнений, в то время как Мэри предпочитала секс.

   ukУлюбленим заняттям Тома було вирішення диференціальних рівнянь, у той час як Мері надавала перевагу сексу.

   CC0 · Tatoeba · deniko · C1Открыть на TatoebaСообщить о проблеме

4. Tom loves non-linear differential equations.

   ukТом обожнює нелінійні диференціальні рівняння.

   CC0 · Tatoeba · deniko · C1Открыть на TatoebaСообщить о проблеме

5. Can you help me with differential equations?

   CC BY · Tatoeba · rul · B2Открыть на TatoebaСообщить о проблеме

правильный