Tensor calculus definition of Tensor calculus in the Free Online Encyclopedia.

tensor, in mathematics, quantity that depends linearly on several vector U [−3,1] and V [5,2], one can add their corresponding components to find the resultant vector R [2,3], or one can graph U and V on a set of coordinate axes and complete the parallelogram formed with U and V
..... Click the link for more information. variables and that varies covariantly with respect to some variables and contravariantly with respect to others when the coordinate axes are rotated (see Cartesian coordinates Cartesian coordinates (kärtē`zhən)
..... Click the link for more information. ). Tensors appear throughout mathematics, though they were first treated systematically in the calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit —the notion of tending toward, or approaching, an ultimate value.
..... Click the link for more information. of differential forms and in differential geometry r moves along a curve at arc length s from some fixed point, then t = dr/ds is a unit tangent vector to the curve at r. The normal vector n
..... Click the link for more information. . They play an important role in mathematical physics, particularly in the theory of relativity relativity, physical theory, introduced by Albert Einstein, that discards the concept of absolute motion and instead treats only relative motion between two systems or frames of reference.
..... Click the link for more information. . Tensors are also important in the theory of elasticity, where they are used to describe stress and strain. The study of tensors was formerly known as the absolute differential calculus but is now called simply tensor analysis.

Bibliography

See R. Abraham et al., Manifolds, Tensor Analysis, and Applications (1988).

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Bibliography

tensor
(redirected from Tensor calculus)