differential
Language: English
Part of speech: noun
Pronunciation: ipa: [dɪfəˈɹənʃəɫ]
note: Indic
ipa: /ɖɪf(ə)ˈrɛnʃ(ɪ)jəl/
Forms: form: differentials
Etymology: Morphologically different + -ial.
Senses: glosses: The differential gear in an automobile, etc.
glosses: A qualitative or quantitative difference between similar or comparable things.
glosses: 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.
glosses: 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.
topics: calculus
mathematics
sciences
glosses: 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.
examples: text: 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.
topics: calculus
mathematics
sciences
glosses: 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.
raw_tags: of a univariate differentiable function f(x)
topics: calculus
mathematics
sciences
glosses: 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.
raw_tags: of a univariate differentiable function f(x)
glosses: The Jacobian matrix of a function of several variables.
qualifier: differential geometry
glosses: 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.
raw_tags: of a smooth map ϕ between smooth manifolds
topics: mathematics
sciences
glosses: 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.
Derived terms: absolute differential calculus
affine differential geometry
delay differential equation
differential amplifier
differential analyzer
differential coefficient
differential diagnosis
differential equation
differential form
differential gear
differential geometry
differential lock
differential medium
differential piece work
differential psychologist
differential psychology
differential scanning calorimetry
differential screw
differential steering
differential structure
differential thermal analysis
differential thermometer
differential topology
integro-differential
Legendre's differential equation
limited-slip differential
locking differential
open differential
ordinary differential equation
partial differential
partial differential equation
stochastic differential equation
Related terms: differ
difference
different
differentiate
differentiation