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Calculus of variations
(gcide) | Variation \Va`ri*a"tion\, n. [OE. variatioun, F. variation, L.
variatio. See Vary.]
1. The act of varying; a partial change in the form,
position, state, or qualities of a thing; modification;
alteration; mutation; diversity; deviation; as, a
variation of color in different lights; a variation in
size; variation of language.
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The essences of things are conceived not capable of
any such variation. --Locke.
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2. Extent to which a thing varies; amount of departure from a
position or state; amount or rate of change.
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3. (Gram.) Change of termination of words, as in declension,
conjugation, derivation, etc.
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4. (Mus.) Repetition of a theme or melody with fanciful
embellishments or modifications, in time, tune, or
harmony, or sometimes change of key; the presentation of a
musical thought in new and varied aspects, yet so that the
essential features of the original shall still preserve
their identity.
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5. (Alg.) One of the different arrangements which can be made
of any number of quantities taking a certain number of
them together.
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Annual variation (Astron.), the yearly change in the right
ascension or declination of a star, produced by the
combined effects of the precession of the equinoxes and
the proper motion of the star.
Calculus of variations. See under Calculus.
Variation compass. See under Compass.
Variation of the moon (Astron.), an inequality of the
moon's motion, depending on the angular distance of the
moon from the sun. It is greater at the octants, and zero
at the quadratures.
Variation of the needle (Geog. & Naut.), the angle included
between the true and magnetic meridians of a place; the
deviation of the direction of a magnetic needle from the
true north and south line; -- called also {declination of
the needle}.
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Syn: Change; vicissitude; variety; deviation.
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Calculus of variations
(gcide) | Calculus \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.
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2. (Math.) A method of computation; any process of reasoning
by the use of symbols; any branch of mathematics that may
involve calculation.
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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.
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calculus of variations
(wn) | calculus of variations
n 1: the calculus of maxima and minima of definite integrals |
| | podobné slovo | definícia |
calculus of variations
(wn) | calculus of variations
n 1: the calculus of maxima and minima of definite integrals |
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