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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 may refer to: Genetic variation Human genetic variation Genetic diversity, differences within a species.variation may be defined as the differences...

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

- Somaclonal variation is the variation seen in plants that have been produced by plant tissue culture. Chromosomal rearrangements are an important source...

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

- Segura. It is one of the most po****r openings, with such a vast number of variations that in the Encyclopaedia of Chess Openings (ECO) all codes from C60 to...

- Magnetic declination, or magnetic variation, is the angle on the horizontal plane between magnetic north (the direction the north end of a magnetized...

- Genetics is a branch of biology concerned with the study of genes, genetic variation, and heredity in organisms. Gregor Mendel, a scientist and Augustinian...

- Genetic variation means that biological systems – individuals and po****tions – are different over space. Each gene pool includes various alleles of genes...

- for solidity and resilience, although some lines such as the Winawer Variation can lead to sharp complications. Black's position is often somewhat cramped...

- explained variation measures the proportion to which a mathematical model accounts for the variation (dispersion) of a given data set. Often, variation is quantified...

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

- Somaclonal variation is the variation seen in plants that have been produced by plant tissue culture. Chromosomal rearrangements are an important source...

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

- Segura. It is one of the most po****r openings, with such a vast number of variations that in the Encyclopaedia of Chess Openings (ECO) all codes from C60 to...

- Magnetic declination, or magnetic variation, is the angle on the horizontal plane between magnetic north (the direction the north end of a magnetized...

- Genetics is a branch of biology concerned with the study of genes, genetic variation, and heredity in organisms. Gregor Mendel, a scientist and Augustinian...

- Genetic variation means that biological systems – individuals and po****tions – are different over space. Each gene pool includes various alleles of genes...

- for solidity and resilience, although some lines such as the Winawer Variation can lead to sharp complications. Black's position is often somewhat cramped...

- explained variation measures the proportion to which a mathematical model accounts for the variation (dispersion) of a given data set. Often, variation is quantified...

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