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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. 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.

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. 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.

- Variation or Variations may refer to: Variation (astronomy), any perturbation of the mean motion or orbit of a planet or satellite, particularly of the...

- In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of...

- Variational may refer to: Calculus of variations, a field of mathematical analysis that deals with maximizing or minimizing functionals Variational method...

- In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function...

- the classical Variation; 5...e5, the Sveshnikov Variation; or 5...e6, transposing to the Four Knights Variation. The Sveshnikov Variation was pioneered...

- Goldberg Variations, BWV 988, is a musical composition for keyboard by Johann Sebastian Bach, consisting of an aria and a set of 30 variations. First published...

- In music, variation is a formal technique where material is repeated in an altered form. The changes may involve melody, rhythm, harmony, counterpoint...

- An anatomical variation, anatomical variant, or anatomical variability is a difference between the anatomical structures of animals from the same species...

- Genetic variation is the difference in DNA among individuals or the differences between po****tions. There are multiple sources of genetic variation, including...

- In ballet, a variation (sometimes referred to as a pas seul, meaning to dance alone) is a solo dance. In a classical grand pas de deux, the ballerina...

- In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of...

- Variational may refer to: Calculus of variations, a field of mathematical analysis that deals with maximizing or minimizing functionals Variational method...

- In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function...

- the classical Variation; 5...e5, the Sveshnikov Variation; or 5...e6, transposing to the Four Knights Variation. The Sveshnikov Variation was pioneered...

- Goldberg Variations, BWV 988, is a musical composition for keyboard by Johann Sebastian Bach, consisting of an aria and a set of 30 variations. First published...

- In music, variation is a formal technique where material is repeated in an altered form. The changes may involve melody, rhythm, harmony, counterpoint...

- An anatomical variation, anatomical variant, or anatomical variability is a difference between the anatomical structures of animals from the same species...

- Genetic variation is the difference in DNA among individuals or the differences between po****tions. There are multiple sources of genetic variation, including...

- In ballet, a variation (sometimes referred to as a pas seul, meaning to dance alone) is a solo dance. In a classical grand pas de deux, the ballerina...

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