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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.

- The calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima...

- such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus. Modern calculus was developed in 17th-century...

- Applications of the calculus of variations include: Solutions to the brachistochrone problem, tautochrone problem, catenary problem, and Newton's minimal...

- In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not...

- 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...

- fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic...

- in 1799. Lagrange was one of the creators of the calculus of variations, deriving the Euler–Lagrange equations for extrema of functionals. He also extended...

- development of the calculus of variations. His statement of the problem is a summary of the state-of-the-art (in 1900) of the theory of calculus of variations, with...

- properties of continuous functions on closed and bounded intervals. Weierstr**** also made significant advancements in the field of calculus of variations. Using...

- differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus...

- such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus. Modern calculus was developed in 17th-century...

- Applications of the calculus of variations include: Solutions to the brachistochrone problem, tautochrone problem, catenary problem, and Newton's minimal...

- In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not...

- 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...

- fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic...

- in 1799. Lagrange was one of the creators of the calculus of variations, deriving the Euler–Lagrange equations for extrema of functionals. He also extended...

- development of the calculus of variations. His statement of the problem is a summary of the state-of-the-art (in 1900) of the theory of calculus of variations, with...

- properties of continuous functions on closed and bounded intervals. Weierstr**** also made significant advancements in the field of calculus of variations. Using...

- differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus...

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