calculus of variations


From The Collaborative International Dictionary of English v.0.48:

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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.

From The Collaborative International Dictionary of English v.0.48:

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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