tensor derivative

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• Tensor derivative (continuum mechanics) — The derivatives of scalars, vectors, and second order tensors with respect to second order tensors are of considerable use in continuum mechanics. These derivatives are used in the theories of nonlinear elasticity and plasticity, particularly in… …   Wikipedia

• 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

• Derivative (generalizations) — Derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, and geometry. Derivatives in analysis In real, complex, and functional… …   Wikipedia

• Tensor field — In mathematics, physics and engineering, a tensor field is a very general concept of variable geometric quantity. It is used in differential geometry and the theory of manifolds, in algebraic geometry, in general relativity, in the analysis of… …   Wikipedia

• Tensor-Diagramm-Notation — Die penrosesche graphische Notation – auch als penrosesche diagrammatische Notation, Tensor Diagramm Notation oder auch einfach Penrose Notation bezeichnet – ist eine von Roger Penrose vorgeschlagene Notation in der Physik und Mathematik, um eine …   Deutsch Wikipedia

• Tensor contraction — In multilinear algebra, a tensor contraction is an operation on one or more tensors that arises from the natural pairing of a finite dimensional vector space and its dual. In components, it is expressed as a sum of products of scalar components… …   Wikipedia

• Tensor density — A tensor density transforms as a tensor, except that it is additionally multiplied or weighted by a power of the Jacobian determinant.For example, a rank 3 tensor density of weight W transforms as::A {ijk}^prime =egin{vmatrix} alpha… …   Wikipedia

• Tensor product — In mathematics, the tensor product, denoted by otimes, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules. In each case the significance of the symbol is the same:… …   Wikipedia

• Covariant derivative — In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… …   Wikipedia

• Directional derivative — In mathematics, the directional derivative of a multivariate differentiable function along a given vector V at a given point P intuitively represents the instantaneous rate of change of the function, moving through P in the direction of V. It… …   Wikipedia

• Material derivative — The material derivative[1][2] is a derivative taken along a path moving with velocity v, and is often used in fluid mechanics and classical mechanics. It describes the time rate of change of some quantity (such as heat or momentum) by following… …   Wikipedia