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Imaginary calculus

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.

Imaginary calculus

Imaginary Im*ag"i*na*ry, a. [L. imaginarius: cf. F. imaginaire.] Existing only in imagination or fancy; not real; fancied; visionary; ideal. Wilt thou add to all the griefs I suffer Imaginary ills and fancied tortures? --Addison. Imaginary calculus See under Calculus. Imaginary expression or quantity (Alg.), an algebraic expression which involves the impossible operation of taking the square root of a negative quantity; as, [root]-9, a + b [root]-1. Imaginary points, lines, surfaces, etc. (Geom.), points, lines, surfaces, etc., imagined to exist, although by reason of certain changes of a figure they have in fact ceased to have a real existence. Syn: Ideal; fanciful; chimerical; visionary; fancied; unreal; illusive.

Imaginary Im*ag"i*na*ry, a. [L. imaginarius: cf. F. imaginaire.] Existing only in imagination or fancy; not real; fancied; visionary; ideal. Wilt thou add to all the griefs I suffer Imaginary ills and fancied tortures? --Addison. Imaginary calculus See under Calculus. Imaginary expression or quantity (Alg.), an algebraic expression which involves the impossible operation of taking the square root of a negative quantity; as, [root]-9, a + b [root]-1. Imaginary points, lines, surfaces, etc. (Geom.), points, lines, surfaces, etc., imagined to exist, although by reason of certain changes of a figure they have in fact ceased to have a real existence. Syn: Ideal; fanciful; chimerical; visionary; fancied; unreal; illusive.

- called the impedance. This approach is called phasor calculus. In electrical engineering, the imaginary unit is denoted by j, to avoid confusion with I, which...

- Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number...

- In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector...

- context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis...

- e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine...

- writing definitions for existing ones. This glossary of calculus is a list of definitions about calculus, its sub-disciplines, and related fields. Contents: ...

- of the terms into real and imaginary parts is justified by the absolute convergence of the series. The real and imaginary parts of the above expression...

- rational. Imaginary numbers: Numbers that equal the product of a real number and the square root of −1. The number 0 is both real and imaginary. Complex...

- In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a result that relates the flux of a vector field...

- function itself for any bounded continuous function on (0,∞), using the calculus of finite differences. Specifically, one has the following theorem, due...

- Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number...

- In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector...

- context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis...

- e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine...

- writing definitions for existing ones. This glossary of calculus is a list of definitions about calculus, its sub-disciplines, and related fields. Contents: ...

- of the terms into real and imaginary parts is justified by the absolute convergence of the series. The real and imaginary parts of the above expression...

- rational. Imaginary numbers: Numbers that equal the product of a real number and the square root of −1. The number 0 is both real and imaginary. Complex...

- In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a result that relates the flux of a vector field...

- function itself for any bounded continuous function on (0,∞), using the calculus of finite differences. Specifically, one has the following theorem, due...

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