Definition & Meaning | English word DIFFERENTIAL

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Definitions of DIFFERENTIAL

1. 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.
2. 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.
3. Of or pertaining to a difference.
4. Dependent on, or making a difference; distinctive.
5. Having differences in speed or direction of motion.
6. The differential gear in an automobile, etc.
7. A qualitative or quantitative difference between similar or comparable things.
8. (calculus) 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 .
9. (calculus, of a univariate differentiable function ) A function giving the change in the linear approximation of at a point over a small interval or , the function being called the differential of and denoted , , or simply .
10. (multivariable calculus) The Jacobian matrix of a function of several variables.
11. (differential geometry, of a smooth map between smooth manifolds) The pushforward or total derivative of : a linear map from the tangent space at a point in 's domain to the tangent space at which is, in a technical sense, the best linear approximation of at ; denoted .
12. (mathematics) 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.
13. (mathematics) Of or pertaining to differentiation or the differential calculus.

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Examples of Using DIFFERENTIAL in a Sentence

• Jensen was known for his work in psychometrics and differential psychology, the study of how and why individuals differ behaviorally from one another.
• Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
• In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which form a necessary and sufficient condition for a complex function of a complex variable to be complex differentiable.
• Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions.
• In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds.
• Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
• Differential psychology studies the ways in which individuals differ in their behavior and the processes that underlie it.
• When converted to an equivalent system of three ordinary first-order non-linear differential equations, jerk equations are the minimal setting for solutions showing chaotic behaviour.
• This gives the transform many applications in science and engineering, mostly as a tool for solving linear differential equations and dynamical systems by simplifying ordinary differential equations and integral equations into algebraic polynomial equations, and by simplifying convolution into multiplication.
• Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits.
• Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models.
• A metric tensor, in differential geometry, which allows defining lengths of curves, angles, and distances in a manifold.
• Natural selection is the differential survival and reproduction of individuals due to differences in phenotype.
• Also, the domain of an operator is often difficult to characterize explicitly (for example in the case of an integral operator), and may be extended so as to act on related objects (an operator that acts on functions may act also on differential equations whose solutions are functions that satisfy the equation).
• An operational amplifier (often op amp or opamp) is a DC-coupled electronic voltage amplifier with a differential input, a (usually) single-ended output, and an extremely high gain.
• Partial differential equation, differential equation involving partial derivatives (of a function of multiple variables).
• Separable ordinary differential equation, a class of equations that can be separated into a pair of integrals.
• Stability theory, the study of the stability of solutions to differential equations and dynamical systems.
• In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
• While underway a submerged seal in a missile hatch cover failed, allowing high-pressure seawater to enter the missile tube and owing to the pressure differential ruptured the missile fuel tanks, allowing the missile's liquid fuel to mix and ultimately combust.

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