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Calculus of functionsCalculus Cal"cu*lus, n.; pl. Calculi. [L, calculus. See
Calculate, and Calcule.]
1. (Med.) Any solid concretion, formed in any part of the
body, but most frequent in the organs that act as
reservoirs, and in the passages connected with them; as,
biliary calculi; urinary calculi, etc.
2. (Math.) A method of computation; any process of reasoning
by the use of symbols; any branch of mathematics that may
involve calculation.
Barycentric calculus, a method of treating geometry by
defining a point as the center of gravity of certain other
points to which co["e]fficients or weights are ascribed.
Calculus of functions, that branch of mathematics which
treats of the forms of functions that shall satisfy given
conditions.
Calculus of operations, that branch of mathematical logic
that treats of all operations that satisfy given
conditions.
Calculus of probabilities, the science that treats of the
computation of the probabilities of events, or the
application of numbers to chance.
Calculus of variations, a branch of mathematics in which
the laws of dependence which bind the variable quantities
together are themselves subject to change.
Differential calculus, a method of investigating
mathematical questions by using the ratio of certain
indefinitely small quantities called differentials. The
problems are primarily of this form: to find how the
change in some variable quantity alters at each instant
the value of a quantity dependent upon it.
Exponential calculus, that part of algebra which treats of
exponents.
Imaginary calculus, a method of investigating the relations
of real or imaginary quantities by the use of the
imaginary symbols and quantities of algebra.
Integral calculus, a method which in the reverse of the
differential, the primary object of which is to learn from
the known ratio of the indefinitely small changes of two
or more magnitudes, the relation of the magnitudes
themselves, or, in other words, from having the
differential of an algebraic expression to find the
expression itself. Circular functionsCircular Cir"cu*lar, a. [L. circularis, fr. circulus circle:
cf. F. circulaire. See Circle.]
1. In the form of, or bounded by, a circle; round.
2. repeating itself; ending in itself; reverting to the point
of beginning; hence, illogical; inconclusive; as, circular
reasoning.
3. Adhering to a fixed circle of legends; cyclic; hence,
mean; inferior. See Cyclic poets, under Cyclic.
Had Virgil been a circular poet, and closely adhered
to history, how could the Romans have had Dido?
--Dennis.
4. Addressed to a circle, or to a number of persons having a
common interest; circulated, or intended for circulation;
as, a circular letter.
A proclamation of Henry III., . . . doubtless
circular throughout England. --Hallam.
5. Perfect; complete. [Obs.]
A man so absolute and circular In all those
wished-for rarities that may take A virgin captive.
--Massinger.
Circular are, any portion of the circumference of a circle.
Circular cubics (Math.), curves of the third order which
are imagined to pass through the two circular points at
infinity.
Circular functions. (Math.) See under Function.
Circular instruments, mathematical instruments employed for
measuring angles, in which the graduation extends round
the whole circumference of a circle, or 360[deg].
Circular lines, straight lines pertaining to the circle, as
sines, tangents, secants, etc.
Circular note or letter.
(a) (Com.) See under Credit.
(b) (Diplomacy) A letter addressed in identical terms to a
number of persons.
Circular numbers (Arith.), those whose powers terminate in
the same digits as the roots themselves; as 5 and 6, whose
squares are 25 and 36. --Bailey. --Barlow.
Circular points at infinity (Geom.), two imaginary points
at infinite distance through which every circle in the
plane is, in the theory of curves, imagined to pass.
Circular polarization. (Min.) See under Polarization.
Circular or Globular sailing (Naut.), the method of
sailing by the arc of a great circle.
Circular saw. See under Saw. Defunct
Defunct De*funct", n.
A dead person; one deceased.
Defunction
Defunction De*func"tion, n. [L. defunctio performance, death.]
Death. [Obs.]
After defunction of King Pharamond. --Shak.
Defunctive
Defunctive De*func"tive, a.
Funereal. [Obs.] ``Defunctive music.' --Shak.
Discontinuous functionDiscontinuous Dis`con*tin"u*ous, a.
1. Not continuous; interrupted; broken off.
A path that is zigzag, discontinuous, and
intersected at every turn by human negligence. --De
Quincey.
2. Exhibiting a dissolution of continuity; gaping.
``Discontinuous wound.' --Milton.
Discontinuous function (Math.), a function which for
certain values or between certain values of the variable
does not vary continuously as the variable increases. The
discontinuity may, for example, consist of an abrupt
change in the value of the function, or an abrupt change
in its law of variation, or the function may become
imaginary. Explicit functionExplicit Ex*plic"it, a. [L. explicitus; p. p. of explicare to
unfold: cf. F. explicite. See Explicate, Exploit.]
1. Not implied merely, or conveyed by implication; distinctly
stated; plain in language; open to the understanding;
clear; not obscure or ambiguous; express; unequivocal; as,
an explicit declaration.
The language of the charter was too explicit to
admit of a doubt. --Bancroft.
2. Having no disguised meaning or reservation; unreserved;
outspoken; -- applied to persons; as, he was earnest and
explicit in his statement.
Explicit function. (Math.) See under Function.
Syn: Express; clear; plain; open; unreserved; unambiguous.
Usage: Explicit, Express. Explicit denotes a setting
forth in the plainest language, so that the meaning
can not be misunderstood; as, an explicit promise.
Express is stronger than explicit: it adds force to
clearness. An express promise or engagement is not
only unambiguous, but stands out in bold relief, with
the most binding hold on the conscience. An explicit
statement; a clear and explicit notion; explicit
direction; no words can be more explicit. An explicit
command; an express prohibition. ``An express
declaration goes forcibly and directly to the point.
An explicit declaration leaves nothing ambiguous.'
--C. J. Smith. force functionPotential Po*ten"tial, n.
1. Anything that may be possible; a possibility; potentially.
--Bacon.
2. (Math.) In the theory of gravitation, or of other forces
acting in space, a function of the rectangular coordinates
which determine the position of a point, such that its
differential coefficients with respect to the
co["o]rdinates are equal to the components of the force at
the point considered; -- also called potential function,
or force function. It is called also Newtonian
potential when the force is directed to a fixed center
and is inversely as the square of the distance from the
center.
3. (Elec.) The energy of an electrical charge measured by its
power to do work; hence, the degree of electrification as
referred to some standard, as that of the earth;
electro-motive force. functionFluent Flu"ent, n.
1. A current of water; a stream. [Obs.]
2. [Cf. F. fluente.] (Math.) A variable quantity, considered
as increasing or diminishing; -- called, in the modern
calculus, the function or integral. FunctionalFunctional Func"tion*al, a.
1. Pertaining to, or connected with, a function or duty;
official.
2. (Physiol.) Pertaining to the function of an organ or part,
or to the functions in general.
Functional disease (Med.), a disease of which the symptoms
cannot be referred to any appreciable lesion or change of
structure; the derangement of an organ arising from a
cause, often unknown, external to itself opposed to
organic disease, in which the organ itself is affected. Functional diseaseFunctional Func"tion*al, a.
1. Pertaining to, or connected with, a function or duty;
official.
2. (Physiol.) Pertaining to the function of an organ or part,
or to the functions in general.
Functional disease (Med.), a disease of which the symptoms
cannot be referred to any appreciable lesion or change of
structure; the derangement of an organ arising from a
cause, often unknown, external to itself opposed to
organic disease, in which the organ itself is affected. Functionalize
Functionalize Func"tion*al*ize, v. t.
To assign to some function or office. [R.]
Functionally
Functionally Func"tion*al*ly, adv.
In a functional manner; as regards normal or appropriate
activity.
The organ is said to be functionally disordered.
--Lawrence.
FunctionariesFunctionary Func"tion*a*ry, n.; pl. Functionaries. [Cf. F.
fonctionnaire.]
One charged with the performance of a function or office; as,
a public functionary; secular functionaries. FunctionaryFunctionary Func"tion*a*ry, n.; pl. Functionaries. [Cf. F.
fonctionnaire.]
One charged with the performance of a function or office; as,
a public functionary; secular functionaries. Functionless
Functionless Func"tion*less, a.
Destitute of function, or of an appropriate organ. Darwin.
Hyperbolic functionsHyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression.
``This hyperbolical epitaph.' --Fuller.
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector. Implicit functionImplicit Im*plic"it, a. [L. implicitus, p. p. of implicare to
entwine, entangle, attach closely: cf. F. implicite. See
Implicate.]
1. Infolded; entangled; complicated; involved. [Obs.]
--Milton.
In his woolly fleece I cling implicit. --Pope.
2. Tacitly comprised; fairly to be understood, though not
expressed in words; implied; as, an implicit contract or
agreement. --South.
3. Resting on another; trusting in the word or authority of
another, without doubt or reserve; unquestioning;
complete; as, implicit confidence; implicit obedience.
Back again to implicit faith I fall. --Donne.
Implicit function. (Math.) See under Function. Perfunctorily
Perfunctorily Per*func"to*ri*ly, adv.
In a perfunctory manner; formally; carelessly. --Boyle.
Perfunctoriness
Perfunctoriness Per*func"to*ri*ness, n.
The quality or state of being perfunctory.
PerfunctoryPerfunctory Per*func"to*ry, a. [L. perfunctorius, fr.
perfunctus dispatched, p. p. of perfungi to discharge,
dispatch; per (see Per) + fungi to perform. See
Function.]
1. Done merely to get rid of a duty; performed mechanically
and as a thing of rote; done in a careless and superficial
manner; characterized by indifference; as, perfunctory
admonitions. --Macaulay.
2. Hence: Mechanical; indifferent; listless; careless.
``Perfunctory in his devotions.' --Sharp. Perfuncturate
Perfuncturate Per*func"tu*rate, v. t.
To perform in a perfunctory manner; to do negligently. [R.]
potential functionPotential Po*ten"tial, n.
1. Anything that may be possible; a possibility; potentially.
--Bacon.
2. (Math.) In the theory of gravitation, or of other forces
acting in space, a function of the rectangular coordinates
which determine the position of a point, such that its
differential coefficients with respect to the
co["o]rdinates are equal to the components of the force at
the point considered; -- also called potential function,
or force function. It is called also Newtonian
potential when the force is directed to a fixed center
and is inversely as the square of the distance from the
center.
3. (Elec.) The energy of an electrical charge measured by its
power to do work; hence, the degree of electrification as
referred to some standard, as that of the earth;
electro-motive force. Sustentative functionsSustentative Sus"ten*ta*tive, a.
Adapted to sustain, strengthen, or corroborate; as,
sustentative citations or quotations.
Sustentative functions (Physiol.), those functions of the
body which affect its material composition and thus
determine its mass. Thermodynamic functionThermodynamic Ther`mo*dy*nam"ic, a. [Thermo- + dynamic.]
(Physics)
Relating to thermodynamics; caused or operated by force due
to the application of heat.
Thermodynamic function. See Heat weight, under Heat. Theta functionTheta The"ta, n. [L., fr. Gr. qh^ta, the Greek letter [theta],
[Theta].]
A letter of the Greek alphabet corresponding to th in
English; -- sometimes called the unlucky letter, from being
used by the judges on their ballots in passing condemnation
on a prisoner, it being the first letter of the Greek
qa`natos, death.
Theta function (Math.), one of a group of functions used in
developing the properties of elliptic functions. Transcendental functionTrancscendental Tranc`scen*den"tal, a. [Cf. F. transcendantal,
G. transcendental.]
1. Supereminent; surpassing others; as, transcendental being
or qualities.
2. (Philos.) In the Kantian system, of or pertaining to that
which can be determined a priori in regard to the
fundamental principles of all human knowledge. What is
transcendental, therefore, transcends empiricism; but is
does not transcend all human knowledge, or become
transcendent. It simply signifies the a priori or
necessary conditions of experience which, though affording
the conditions of experience, transcend the sphere of that
contingent knowledge which is acquired by experience.
3. Vaguely and ambitiously extravagant in speculation,
imagery, or diction.
Note: In mathematics, a quantity is said to be transcendental
relative to another quantity when it is expressed as a
transcendental function of the latter; thus, a^x,
10^2x, log x, sin x, tan x, etc., are transcendental
relative to x.
Transcendental curve (Math.), a curve in which one ordinate
is a transcendental function of the other.
Transcendental equation (Math.), an equation into which a
transcendental function of one of the unknown or variable
quantities enters.
Transcendental function. (Math.) See under Function.
Syn: Transcendental, Empirical.
Usage: These terms, with the corresponding nouns,
transcendentalism and empiricism, are of comparatively
recent origin. Empirical refers to knowledge which is
gained by the experience of actual phenomena, without
reference to the principles or laws to which they are
to be referred, or by which they are to be explained.
Transcendental has reference to those beliefs or
principles which are not derived from experience, and
yet are absolutely necessary to make experience
possible or useful. Such, in the better sense of the
term, is the transcendental philosophy, or
transcendentalism. Each of these words is also used in
a bad sense, empiricism applying to that one-sided
view of knowledge which neglects or loses sight of the
truths or principles referred to above, and trusts to
experience alone; transcendentalism, to the opposite
extreme, which, in its deprecation of experience,
loses sight of the relations which facts and phenomena
sustain to principles, and hence to a kind of
philosophy, or a use of language, which is vague,
obscure, fantastic, or extravagant. Vital functionsVital Vi"tal, a. [F., fr. L. vitalis, fr. vita life; akin to
vivere to live. See Vivid.]
1. Belonging or relating to life, either animal or vegetable;
as, vital energies; vital functions; vital actions.
2. Contributing to life; necessary to, or supporting, life;
as, vital blood.
Do the heavens afford him vital food? --Spenser.
And vital virtue infused, and vital warmth.
--Milton.
3. Containing life; living. ``Spirits that live throughout,
vital in every part.' --Milton.
4. Being the seat of life; being that on which life depends;
mortal.
The dart flew on, and pierced a vital part. --Pope.
5. Very necessary; highly important; essential.
A competence is vital to content. --Young.
6. Capable of living; in a state to live; viable. [R.]
Pythagoras and Hippocrates . . . affirm the birth of
the seventh month to be vital. --Sir T.
Browne.
Vital air, oxygen gas; -- so called because essential to
animal life. [Obs.]
Vital capacity (Physiol.), the breathing capacity of the
lungs; -- expressed by the number of cubic inches of air
which can be forcibly exhaled after a full inspiration.
Vital force. (Biol.) See under Force. The vital forces,
according to Cope, are nerve force (neurism), growth force
(bathmism), and thought force (phrenism), all under the
direction and control of the vital principle. Apart from
the phenomena of consciousness, vital actions no longer
need to be considered as of a mysterious and unfathomable
character, nor vital force as anything other than a form
of physical energy derived from, and convertible into,
other well-known forces of nature.
Vital functions (Physiol.), those functions or actions of
the body on which life is directly dependent, as the
circulation of the blood, digestion, etc.
Vital principle, an immaterial force, to which the
functions peculiar to living beings are ascribed.
Vital statistics, statistics respecting the duration of
life, and the circumstances affecting its duration.
Vital tripod. (Physiol.) See under Tripod.
Vital vessels (Bot.), a name for latex tubes, now disused.
See Latex.
Meaning of Funct from wikipedia
