Partial differential
Differential Dif`fer*en"tial, n. 1. (Math.) An increment, usually an indefinitely small one, which is given to a variable quantity. [1913 Webster]

Note: According to the more modern writers upon the differential and integral calculus, if two or more quantities are dependent on each other, and subject to increments of value, their differentials need not be small, but are any quantities whose ratios to each other are the limits to which the ratios of the increments approximate, as these increments are reduced nearer and nearer to zero. [1913 Webster]

2. 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. [1913 Webster]

3. (Elec.) (a) 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. (b) 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. --Knight. [1913 Webster]

{Partial differential} (Math.), the differential of a function of two or more variables, when only one of the variables receives an increment.

{Total differential} (Math.), the differential of a function of two or more variables, when each of the variables receives an increment. The total differential of the function is the sum of all the {partial differentials}. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

### Look at other dictionaries:

• partial differential — Math. an expression obtained from a given function of several variables by taking the partial derivative with respect to one of the variables and multiplying by the increment in that variable. [1810 20] * * * …   Universalium

• partial differential — par′tial differen′tial n. Math. math. an expression obtained from a given function of several variables by taking the partial derivative with respect to one of the variables and multiplying by the increment in that variable • Etymology: 1810–20 …   From formal English to slang

• partial differential — Math. an expression obtained from a given function of several variables by taking the partial derivative with respect to one of the variables and multiplying by the increment in that variable. [1810 20] …   Useful english dictionary

• Partial differential coefficients — partial par tial (p[aum]r shal), a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See {Part}, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a… …   The Collaborative International Dictionary of English

• Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …   Wikipedia

• partial differential equation — Math. a differential equation containing partial derivatives. Cf. ordinary differential equation. [1885 90] * * * In mathematics, an equation that contains partial derivatives, expressing a process of change that depends on more than one… …   Universalium

• partial differential equation — noun Date: 1845 a differential equation containing at least one partial derivative …   New Collegiate Dictionary

• partial differential equation — noun a differential equation that involves the partial derivatives of a function of several variables …   Wiktionary

• partial differential equation — noun a differential equation involving a functions of more than one variable • Hypernyms: ↑differential equation …   Useful english dictionary

• partial differential equation — noun Mathematics an equation containing one or more partial derivatives …   English new terms dictionary

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