calculus of tensors

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• Intermediate treatment of tensors — In mathematics and physics, a tensor is an idealized geometric or physical quantity whose numerical description, relative to a particular frame of reference, consists of a multiple indexed array of numbers. A vector, for example, is a tensor with …   Wikipedia

• Matrix calculus — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

• Classical treatment of tensors — A tensor is a generalization of the concepts of vectors and matrices. Tensors allow one to express physical laws in a form that applies to any coordinate system. For this reason, they are used extensively in continuum mechanics and the theory of… …   Wikipedia

• Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …   Wikipedia

• tensor analysis — the branch of mathematics dealing with the calculus of tensors, esp. the study of properties that are unaffected by a change of coordinate system. * * * Branch of mathematics concerned with relations or laws that remain valid regardless of the… …   Universalium

• Levi-Civita, Tullio — ▪ Italian mathematician born March 29, 1873, Padua, Italy died December 29, 1941, Rome       Italian mathematician known for his work in differential calculus and relativity theory (relativity). At the University of Padua (1891–95), he studied… …   Universalium

• tensor analysis — the branch of mathematics dealing with the calculus of tensors, esp. the study of properties that are unaffected by a change of coordinate system …   Useful english dictionary

• Tensor — For other uses, see Tensor (disambiguation). Note that in common usage, the term tensor is also used to refer to a tensor field. Stress, a second order tensor. The tensor s components, in a three dimensional Cartesian coordinate system, form the… …   Wikipedia

• Mathematics of general relativity — For a generally accessible and less technical introduction to the topic, see Introduction to mathematics of general relativity. General relativity Introduction Mathematical formulation Resources …   Wikipedia

• Curvilinear coordinates — Curvilinear, affine, and Cartesian coordinates in two dimensional space Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian… …   Wikipedia

• Exterior algebra — In mathematics, the exterior product or wedge product of vectors is an algebraic construction generalizing certain features of the cross product to higher dimensions. Like the cross product, and the scalar triple product, the exterior product of… …   Wikipedia