Calculus of variations

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 them; as, biliary calculi; urinary calculi, etc. [1913 Webster]

2. (Math.) A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation. [1913 Webster]

{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. [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 — 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 — 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;… …   The Collaborative International Dictionary of English

  • 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 — 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

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

  • 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 (disambiguation) — Calculus is Latin for pebble, and has a number of meanings in English: In mathematics and computer science Calculus , in its most general sense, is any method or system of calculation. To modern theoreticians the answer to the question what is a… …   Wikipedia