Crossword clues for differential
differential
Longman Dictionary of Contemporary English
The Collaborative International Dictionary
differential \dif`fer*en"tial\, a. [Cf. F. diff['e]rentiel.]
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Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate.
For whom he produced differential favors.
--Motley. (Math.) Of or pertaining to a differential, or to differentials.
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(Mech.) Relating to differences of motion or leverage; producing effects by such differences; said of mechanism. Differential calculus. (Math.) See under Calculus. Differential coefficient, the limit of the ratio of the increment of a function of a variable to the increment of the variable itself, when these increments are made indefinitely small. Differential coupling, a form of slip coupling used in light machinery to regulate at pleasure the velocity of the connected shaft. Differential duties (Polit. Econ.), duties which are not imposed equally upon the same products imported from different countries. Differential galvanometer (Elec.), a galvanometer having two coils or circuits, usually equal, through which currents passing in opposite directions are measured by the difference of their effect upon the needle. Differential gearing, a train of toothed wheels, usually an epicyclic train, so arranged as to constitute a differential motion. Differential motion, a mechanism in which a simple differential combination produces such a change of motion or force as would, with ordinary compound arrangements, require a considerable train of parts. It is used for overcoming great resistance or producing very slow or very rapid motion. Differential pulley. (Mach.)
A portable hoisting apparatus, the same in principle as the differential windlass.
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A hoisting pulley to which power is applied through a differential gearing.
Differential screw, a compound screw by which a motion is produced equal to the difference of the motions of the component screws.
Differential thermometer, a thermometer usually with a U-shaped tube terminating in two air bulbs, and containing a colored liquid, used for indicating the difference between the temperatures to which the two bulbs are exposed, by the change of position of the colored fluid, in consequence of the different expansions of the air in the bulbs. A graduated scale is attached to one leg of the tube.
Differential windlass, or Chinese windlass, a windlass whose barrel has two parts of different diameters. The hoisting rope winds upon one part as it unwinds from the other, and a pulley sustaining the weight to be lifted hangs in the bight of the rope. It is an ancient example of a differential motion.
Douglas Harper's Etymology Dictionary
1640s, from Medieval Latin differentialis, from Latin differentia (see difference). Related: Differentially.
Wiktionary
a. 1 of, or relating to a difference 2 dependent on, or making a difference; distinctive 3 having differences in speed or direction of motion 4 (context mathematics English) of, or relating to differentiation, or the differential calculus n. 1 the differential gear in an automobile etc 2 a qualitative or quantitative difference between similar or comparable things 3 (context mathematics English) an infinitesimal change in a variable, or the result of differentiation 4 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 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.
WordNet
adj. relating to or showing a difference; "differential treatment"
involving or containing one or more derivatives; "differential equation"
n. the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx [syn: derived function, derivative, differential coefficient, first derivative]
a quality that differentiates between similar things
a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves [syn: differential gear]
Wikipedia
A differential is a gear train with three shafts that has the property that the angular velocity of one shaft is the average of the angular velocities of the others, or a fixed multiple of that average.
Differential may refer to:
In mathematics, differential refers to infinitesimal differences or to the derivatives of functions. This article links to differentials in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology.
The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in the variable x. The idea of an infinitely small or infinitely slow change is extremely useful intuitively, and there are a number of ways to make the notion mathematically precise.
Using calculus, it is possible to relate the infinitely small changes of various variables to each other mathematically using derivatives. If y is a function of x, then the differential dy of y is related to dx by the formula
$\mathrm{d}y = \frac{\mathrm{d}y}{\mathrm{d}x} \,\mathrm{d}x,$where dy/dx denotes the derivative of y with respect to x. This formula summarizes the intuitive idea that the derivative of y with respect to x is the limit of the ratio of differences Δy/Δx as Δx becomes infinitesimal.
There are several approaches for making the notion of differentials mathematically precise.
- Differentials as linear maps. This approach underlies the definition of the derivative and the exterior derivative in differential geometry.
- Differentials as nilpotent elements of commutative rings. This approach is popular in algebraic geometry.
- Differentials in smooth models of set theory. This approach is known as synthetic differential geometry or smooth infinitesimal analysis and is closely related to the algebraic geometric approach, except that ideas from topos theory are used to hide the mechanisms by which nilpotent infinitesimals are introduced.
- Differentials as infinitesimals in hyperreal number systems, which are extensions of the real numbers that contain invertible infinitesimals and infinitely large numbers. This is the approach of nonstandard analysis pioneered by Abraham Robinson.
These approaches are very different from each other, but they have in common the idea to be quantitative, i.e., to say not just that a differential is infinitely small, but how small it is.
Usage examples of "differential".
Springs, alembics, coils of copper tubing, buckled sheets of metal, gear systems both rack-and-pinion and epicyclic, pendulums, levers, cams, cranks, differentials, bearings, pulleys, assorted tools, and stone jars containing alkahest and corrosive substances crowded every horizontal surface.
Once there is established the differential between the pure, civilized European and the corrupt, barbarous Other, there is possible not only a civilizing process from disease to health, but also ineluctably the reverse process, from health to disease.
He had a guiding principle: nature seemed to like equations stated in covariant differential forms.
His blood chemistry and differential leucocyte count remained normal, and a series of nerve conduction studies indicated that his peripheral nerves were functioning properly.
He improved the differential calculus, solved the isoperimetrical problem and discovered the properties of the logarithmic spiral.
Stop having children until ontogenesis can be described by a set of differential equations?
Edwards had designed the special instrumentation for the Barracuda and the Bluefin that monitored the thermal variations in the water surrounding the submarine, giving the skipper a constant readout of temperature differentials.
The hydrothermal instrumentation in the two blisters on the sail keep us informed of the temperature differentials between the currents, and by sailing the Barracuda directly in the interface zone we are effectively shielded from detection.
I kept the Barracuda directly in the interface between two temperature differentials.
The ringing sets up something similar to a mental moire fringe interference pattern from which an experienced man can read the time differential with almost micrometer accuracy.
When a pilot returns from the manifold years older or younger than his lover, as Soli recently had, the differential aging-we call it crueltime-can destroy them.
I always thought of things like the subjunctive case and differential calculus and chemical symbols as totally useless.
The sunlight sets up a temperature differential - tiny, but enough to get superfluid helium pumping up through the roots.
If the differential and integral calculus or transfinite arithmetic had been invented in Greece in the fifth century B.
It is merely because a stepping-stone, here and there, is heedlessly left unsupplied in our road to the Differential Calculus, that this latter is not altogether as simple a thing as a sonnet by Mr.