differential

Etymology

Definitions

1. 1

   Of or pertaining to a difference.

   • differential characteristics
   • I saved disk space by taking differential backups, which only stored the data that had changed.
2. 2

   Dependent on, or making a difference

   Dependent on, or making a difference; distinctive.

3. 3

   Having differences in speed or direction of motion.

4. ›+ 10 more definitionsshow fewer

   1. 4

      Of or pertaining to differentiation or the differential calculus.

   2. 5

      The differential gear in an automobile, etc.

   3. 6

      A qualitative or quantitative difference between similar or comparable things.

   4. 7

      One of two coils of conducting wire so related to one another or to a magnet or armature…

      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.

   5. 8

      A form of conductor used for dividing and distributing the current to a series of…

      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.

   6. 9

      A quantity representing an infinitesimal change in a variable, now only used as a…

      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.

   7. 10

      A function giving the change in the linear approximation of f at a point x over a small…

      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.
   8. 11

      The Jacobian matrix of a function of several variables.

   9. 12

      The pushforward or total derivative of ϕ

      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. 13

       Any of several generalizations of the concept(s) above

       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.

The neighborhood

• neighbordiffer
• neighbordifference
• neighbordifferent
• neighbordifferentiate
• neighbordifferentiation