Meaning of GRADIENT in English


In mathematics, a differential operator applied to a three-dimensional vector-valued function to yield a vector whose three components are the partial derivatives of the function with respect to its three variables.

The symbol for gradient is 2207; . Thus, the gradient of a function f , written grad f , or 2207; f , is 2207; f = i f x + j f y + k f z where f x , f y , and f z are the first partial derivatives of f and the vectors i , j , and k are the unit vectors of the vector space . If in physics, for example, f is a temperature field (giving the temperature at every point in a space), 2207; f is the direction of the heat-flow vector in the field.

Britannica Concise Encyclopedia.      Краткая энциклопедия Британика.