# differential

## Definitions

• WordNet 3.6
• adj differential relating to or showing a difference "differential treatment"
• adj differential involving or containing one or more derivatives "differential equation"
• n differential 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
• n differential a quality that differentiates between similar things
• n differential the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
• ***
Webster's Revised Unabridged Dictionary
• Differential (Elec) 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.
• Differential A small difference in rates which competing railroad lines, in establishing a common tariff, allow one of their number to make, in order to get a fair share of the business. The lower rate is called a differential rate. Differentials are also sometimes granted to cities.
• Differential (Math) An increment, usually an indefinitely small one, which is given to a variable quantity.
• differential (Math) Of or pertaining to a differential, or to differentials.
• Differential (Elec) 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.
• differential (Mech) Relating to differences of motion or leverage; producing effects by such differences; said of mechanism.
• differential 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."
• ***
Century Dictionary and Cyclopedia
• differential Making or exhibiting a difference or distinction; discriminating; distinguishing; special.
• differential Having or exhibiting a difference.
• differential In mathematics, pertaining to a differential or differentials, or to mathematical processes in which they are employed.
• n differential In math.: An infinitesimal difference between two values of a variable quantity. In the differential and integral calculus, if two or more quantities are dependent on one another, and subject to variations of value, their corresponding differentials are any other quantities whose ratios to one another are the limits to which the ratios of the variations approximate, as these variations are reduced nearer and nearer to zero; but the differentials are commonly understood to be infinitesimal.
• n differential A logarithmic tangent.
• n differential In boil., a morphological difference; a distinction or distinctive characteristic of form or structure: correlated with equivalent.
• differential In mech.: So constructed that the resulting motion is the algebraic sum of two unequal motions in opposite directions. The resistance moves through a path which is the difference of two velocities impressed by the applied force. Hence a slow motion of the resistance is the consequence of the moving force acting through a considerable space, and a small moving force overcomes great resistance. Used in hoisting-pulleys, double screws, and similar devices.
• differential Having differing velocities, as automobile driving-shafts when rounding corners and curves, and rollers for grinding grain.
• differential Selective; having different effects upon different kinds of material: as, differential weathering.
• ***
Chambers's Twentieth Century Dictionary
• adj Differential creating a difference: special:
• adj Differential (math.) pertaining to a quantity or difference infinitely small (see Calculus)
• ***

## Quotations

• Anatole France
“An education isn't how much you have committed to memory, or even how much you know. It's being able to differentiate between what you do know and what you don't.”
• Rebecca West
“People call me feminist whenever I express sentiments that differentiate me from a doormat or a prostitute.”

## Etymology

Webster's Revised Unabridged Dictionary
Cf. F. différentiel,
Chambers's Twentieth Century Dictionary
L. differredif (= dis), apart, ferre, to bear.

## Usage

### In literature:

It means at first no more than a period of modification and differentiation.
"Anticipations" by Herbert George Wells
It is a question of the terms of specialization or differentiation.
"Woman and Womanhood" by C. W. Saleeby
When these two clearly differentiated species were firmly established, the frottola disappeared.
"Some Forerunners of Italian Opera" by William James Henderson
Coquetry, flirtation and coyness, differentiated, xiii, 235.
"Little Journeys to the Homes of the Great - Volume 14" by Elbert Hubbard
In the third Scholion he elaborates this thought and shows that differentiation takes place in triple wise.
"Form and Function" by E. S. (Edward Stuart) Russell
The differentiation of the arts, and the assignment of a patron to each branch, reflect the thoughts and the aspirations of a later age.
"The Religion of Babylonia and Assyria" by Morris Jastrow
Lord John said that if they were beaten on differentiating the tax, they would have to dissolve.
"The Life of William Ewart Gladstone, Vol. 1 (of 3)" by John Morley
But the question now arises, is this differentiation logical?
The internal organs are partially formed, it begins to assume a human shape, but the sex cannot yet be differentiated.
"Woman" by William J. Robinson
The minister, I believe, has written learnedly on the Differential Calculus.
"The Short-story" by William Patterson Atkinson
The organs are not so well differentiated.
"How to Add Ten Years to your Life and to Double Its Satisfactions" by S. S. Curry
But the diverse character of the objects on which they fall suffices to differentiate the virtues.
"On Prayer and The Contemplative Life" by St. Thomas Aquinas
The most important factor in differentiation of language is local differentiation.
"Human Traits and their Social Significance" by Irwin Edman
The symptoms closely resemble those of a "loose body," and it is often difficult to differentiate between them.
"Manual of Surgery Volume Second: Extremities--Head--Neck. Sixth Edition." by Alexander Miles
As children become physically differentiated in respect of sex, so also does a mental differentiation ensue.
"Introduction to the Science of Sociology" by Robert E. Park
There is, however, one outstanding matter that differentiates our present occasion from those that have gone before.
"Herbert Hoover" by Vernon Kellogg
This differentiation upon differentiation is just what takes place during the evolution of a civilized society.
"Essays: Scientific, Political, & Speculative, Vol. I" by Herbert Spencer
A good home trade connexion is considered an extremely valuable asset, and as the trade is highly differentiated the profits are usually good.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 5" by Various
This is known as Lagrange's linear partial differential equation of the first order.
"Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 4" by Various
This made for greater differentiation between individuals than was possible in the village.
"Area Handbook for Bulgaria" by Eugene K. Keefe, Violeta D. Baluyut, William Giloane, Anne K. Long, James M. Moore, and Neda A. Walpole
***

### In poetry:

For, as their nurses dandle them
They crow binomial theorem,
With views (it seems absurd to us)
On differential calculus.
"My Dream" by William Schwenck Gilbert
Remember, truth draws upward. This to us
Of steady happiness should be a cause
Beyond the differential calculus
Or Kant’s dull dogmas and mechanic laws.
"Faith in God" by Henry Kendall

### In news:

Plasticell and Sigma-Aldrich Partner on Stem Cell Differentiation Tools.
Using Senses for Differentiation .
Eager to differentiate itself in this competitive landscape, Richfield, Minn.-based Best Buy Co. We chose to differentiate ourselves around customer centricity and a superior customer experience.
In an effort to differentiate their products from competitors.
Instead, everyone is trying to differentiate themselves.
All the wholesalers, though, are providing more services to differentiate themselves.
Induction of Pancreatic Differentiation by Signals from Blood Vessels E Lammert, O.
It was her accountant who urged her to treat the incident as an impetus to differentiate her business.
Aggressive Differentiation In the Offing.
Perspectives on Supplier Differentiator , Part II.
Self Checkout A Service Differentiator , Survey Says.
What are some of the specifics for keeping that temperature differential in the 20° range.
Why sell a commodity ingredient to foodservice clients when you can provide an ask-for brand that differentiates the restaurant, too.
Google executive chairman Eric Schmidt raised eyebrows when he appeared at the Consumer Electronics Show in January and argued that Android is not fragmented but "differentiated.".
Festival participants at a yoga class in one of the outdoor studios that differentiate yoga festivals, like Hanuman , from daily studio practice.
***

### In science:

The analog of V here is the chain complex of M , it is a differential module over the differential algebra C∗ (G) of chains on G.
Quantum Field Theory and Representation Theory: A Sketch
Bott, R., The index theorem for homogeneous differential operators, in: Differential and Combinatorial Topology: A Symposium in honor of Marston Morse, Princeton University Press, 1965, 167-186.
Quantum Field Theory and Representation Theory: A Sketch
First of all, it is easy to see that the pullback of the bundle of the logarithmic differentials on Z is the bundle of logarithmic differentials on ˆZ .
McKay correspondence for elliptic genera
Then it is straightforward to calculate the ratio of Chern classes for the bundles of logarithmic differentials and usual differentials for a variety with the normal crossing divisor.
McKay correspondence for elliptic genera
Indeed, each γ -differentiation of the terms in the square brackets in Eq.(B.6) brings a factor of the order of N , which is much larger compared to the result of differentiating the factor Fκ (γ )∆(γ ).
Random Matrices close to Hermitian or unitary: overview of methods and results
On the other hand, imitating the de Rham differential on the space Ω∗ (M ), we deﬁne the differential of the Lie algebroid A, d: Γ(∧kA∗ ) → Γ(∧k+1A∗ ), as follows.
Jacobi groupoids and generalized Lie bialgebroids
Leung, Counting curves on irrational surfaces, Surveys in differential geometry: differential geometry inspired by string theory, 313-339, Surv.
Family Gromov-Witten Invariants for Kahler Surfaces
We have relaxed the condition in [St] that the pull-back of a differential of E is a non-zero multiple of the differential on X1 (N ) associated to a newform (see [St] for ﬁne conjectures about these constants).
Belyi parametrisations of elliptic curves and congruence defects
The expression cdga will always refer to a non-positively graded commutative differential graded algebra over C with differential of degree 1.
From HAG to DAG: derived moduli spaces
This will have a differential induced by the differential on U (g[ǫ]) and the differential on L∗ .
Deformation Quantization of Endomorphism Bundles
We now consider the differential graded algebra k [η ], where η has degree one, η 2 = 0 and the differential is given by ∂η .
Deformation Quantization of Endomorphism Bundles
For a differential graded algebra A we deﬁne A[η ] to be A ⊗ k [η ], where ⊗ is the tensor product of differential graded algebras.
Deformation Quantization of Endomorphism Bundles
First we show that the differential equation in η of ˆB η ˆak ˆB †η is the same as the differential equation for the transformed mode operators with matrix S η .
Quantum Physics of Simple Optical Instruments
Next, Df S (f ) ∈ E T is the differential of the functional S (f ), D2S (f ) is the second differential of the functional S (f ).
Geometry of irreversibility: The film of nonequilibrium states
The linear map u is continuous by Lemma (2.1), hence differentiable, while v is differentiable by hypothesis.
Manifold structures for sets of solutions of the general relativistic constraint equations
***