Definition of Partial differentials. Meaning of Partial differentials. Synonyms of Partial differentials
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Definition of Partial differentials
Partial differentialsPartial Par"tial, 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 partial eclipse
of the moon. ``Partial dissolutions of the earth.' --T.
2. Inclined to favor one party in a cause, or one side of a
question, more then the other; baised; not indifferent;
as, a judge should not be partial.
Ye have been partial in the law. --Mal. ii. 9.
3. Having a predelection for; inclined to favor unreasonably;
foolishly fond. ``A partial parent.' --Pope.
Not partial to an ostentatious display. --Sir W.
4. (Bot.) Pertaining to a subordinate portion; as, a compound
umbel is made up of a several partial umbels; a leaflet is
often supported by a partial petiole.
Partial differentials, Partial differential coefficients,
Partial differentiation, etc. (of a function of two or more
variables), the differentials, differential coefficients,
differentiation etc., of the function, upon the hypothesis
that some of the variables are for the time constant.
Partial fractions (Alg.), fractions whose sum equals a
Partial tones (Music), the simple tones which in
combination form an ordinary tone; the overtones, or
harmonics, which, blending with a fundamental tone, cause
its special quality of sound, or timbre, or tone color.
See, also, Tone. Partial differentialDifferential Dif`fer*en"tial, n.
1. (Math.) An increment, usually an indefinitely small one,
which is given to a variable quantity.
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.
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.
(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.
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.
Meaning of Partial differentials from wikipedia
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