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. Tom loves non-linear differential equations.

   Том обожнює нелінійні диференціальні рівняння.

   CC0 · Tatoeba · deniko · C1Open on TatoebaReport a problem

2. The only class Tom has ever failed was differential equations.

   Єдиний предмет, який Том коли-небудь не здавав, — це диференціальні рівняння.

   CC0 · Tatoeba · deniko · B2Open on TatoebaReport a problem

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

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

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

   CC0 · Tatoeba · deniko · C1Open on TatoebaReport a problem

4. Tom's favorite pastime was solving differential expressions, while Mary preferred sex.

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

   CC0 · Tatoeba · deniko · C1Open on TatoebaReport a problem

5. Can you help me with differential equations?

   CC BY · Tatoeba · rul · B2Open on TatoebaReport a problem

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