Calculus of variations
Variation Va`ri*a"tion, n. [OE. variatioun, F. variation, L. variatio. See {Vary}.] [1913 Webster] 1. The act of varying; a partial change in the form, position, state, or qualities of a thing; modification; alternation; mutation; diversity; deviation; as, a variation of color in different lights; a variation in size; variation of language. [1913 Webster]

The essences of things are conceived not capable of any such variation. --Locke. [1913 Webster]

2. Extent to which a thing varies; amount of departure from a position or state; amount or rate of change. [1913 Webster]

3. (Gram.) Change of termination of words, as in declension, conjugation, derivation, etc. [1913 Webster]

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. [1913 Webster]

5. (Alg.) One of the different arrangements which can be made of any number of quantities taking a certain number of them together. [1913 Webster]

{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}. [1913 Webster]

Syn: Change; vicissitude; variety; deviation. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

### Look at other dictionaries:

• Calculus of variations — is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite …   Wikipedia

• Calculus of variations — 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… …   The Collaborative International Dictionary of English

• calculus of variations — n. the branch of mathematics that tries to determine a function so as to satisfy specified conditions and to maximize (or minimize) a quantity which depends on the function …   English World dictionary

• calculus of variations — the branch of mathematics that deals with the problem of finding a curve or surface that maximizes or minimizes a given expression, usually with several restrictions placed on the desired curve. [1830 40] * * * ▪ mathematics       branch of… …   Universalium

• calculus of variations — noun the calculus of maxima and minima of definite integrals • Topics: ↑mathematics, ↑math, ↑maths • Hypernyms: ↑calculus, ↑infinitesimal calculus …   Useful english dictionary

• calculus of variations — noun The form of calculus that deals with the maxima and minima of definite integrals of functions of many variables …   Wiktionary

• calculus of variations — Date: 1837 a branch of mathematics concerned with applying the methods of calculus to finding the maxima and minima of a function which depends for its values on another function or a curve …   New Collegiate Dictionary

• Direct method in the calculus of variations — In the calculus of variations, a topic in mathematics, the direct method is a general method for constructing a proof of the existence of a minimizer for a given functional,[1] introduced by Zaremba and David Hilbert around 1900. The method… …   Wikipedia

• Fundamental lemma of calculus of variations — In mathematics, specifically in the calculus of variations, the fundamental lemma in the calculus of variations is a lemma that is typically used to transform a problem from its weak formulation (variational form) into its strong formulation… …   Wikipedia

• Calculus of functions — 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… …   The Collaborative International Dictionary of English