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gradient of vector field

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  • Vector field — In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a (locally) Euclidean space.Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid… …   Wikipedia

  • Complex lamellar vector field — In vector calculus, a complex lamellar vector field is a vector field in three dimensions which is orthogonal to its own curl. That is, Complex lamellar vector fields are precisely those that are normal to a family of surfaces. A special case are …   Wikipedia

  • Conservative vector field — In vector calculus a conservative vector field is a vector field which is the gradient of a function, known in this context as a scalar potential. Conservative vector fields have the property that the line integral from one point to another is… …   Wikipedia

  • Killing vector field — In mathematics, a Killing vector field, named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is,… …   Wikipedia

  • Lamellar vector field — In vector analysis and in fluid dynamics, a lamellar vector field is a vector field with no rotational component. That is, if the field is denoted as v, then : abla imes mathbf{v} = 0 .A lamellar field is practically synonymous with an… …   Wikipedia

  • Laplacian vector field — In vector calculus, a Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v, then it is described by the following differential equations:: abla imes mathbf{v} = 0, : abla cdot… …   Wikipedia

  • Gradient (disambiguation) — Gradient may refer to:* Gradient, in vector calculus, a vector field representing the maximum rate of increase of the scalar field direction of the maximum change. * Slope or grade, referring to the inclination of a road or other geographic… …   Wikipedia

  • Gradient — In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change.A generalization of the gradient for… …   Wikipedia

  • Vector 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

  • Vector calculus identities — The following identities are important in vector calculus:ingle operators (summary)This section explicitly lists what some symbols mean for clarity.DivergenceDivergence of a vector fieldFor a vector field mathbf{v} , divergence is generally… …   Wikipedia

  • Vector Laplacian — In mathematics and physics, the vector Laplace operator, denoted by scriptstyle abla^2, named after Pierre Simon Laplace, is a differential operator defined over a vector field. The vector Laplacian is similar to the scalar Laplacian. Whereas the …   Wikipedia

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