gradient vector

См. также в других словарях:

• 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

• Gradient descent — For the analytical method called steepest descent see Method of steepest descent. Gradient descent is an optimization algorithm. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the… …   Wikipedia

• Gradient conjecture — In mathematics, the gradient conjecture, due to René Thom, was proved in 2000 by K. Kurdyka, T. Mostowski and A. Parusinski. It states that given an analytic function f in R n and a trajectory x ( t ) of the gradient vector field of f having a… …   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 — [grā′dē ənt] adj. [L gradiens (gen. gradientis), prp. of gradi, to step: see GRADE] ascending or descending with a uniform slope n. 1. a) a slope, as of a road or railroad b) the degree of such slope 2. Biol. a gradation in rate of growth,… …   English World dictionary

• 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 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

• 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

• gradient — /gray dee euhnt/, n. 1. the degree of inclination, or the rate of ascent or descent, in a highway, railroad, etc. 2. an inclined surface; grade; ramp. 3. Physics. a. the rate of change with respect to distance of a variable quantity, as… …   Universalium

• Vector potential — In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential , which is a scalar field whose negative gradient is a given vector field.Formally, given a vector field v, a… …   Wikipedia