differential

comparative more differential · superlative most differential

1. Of or pertaining to a difference.

   differential characteristics

   2 more examples

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

   [Caspar Schetz, Baron of Grobbendonck] was regularly in the pay of Sir Thomas Gresham, to whom he produced differential favours, and by whose government he was rewarded by gold chains and presents of hard cash, bestowed as secretly as the equivalent was conveyed adroitly.

   1856, John Lothrop Motley, The Rise of the Dutch Republic: A History, volume 1

2. Dependent on, or making a difference; distinctive.
3. Having differences in speed or direction of motion.
4. mathematicsOf or pertaining to differentiation or the differential calculus.

plural differentials

1. The differential gear in an automobile, etc.
2. A qualitative or quantitative difference between similar or comparable 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. calculusA 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. calculusA 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.

   1. calculusAny of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
7. The Jacobian matrix of a function of several variables.
8. differential geometryThe 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. mathematicsAny 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.