: change in the value of a quantity (as temperature, pressure, or concentration) with change in a given variable and especially per unit on a linear scale
: a graded difference in physiological activity along an axis (as of the body or an embryonic field)
: change in response with distance from the stimulus
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 . Thus, the gradient of a function f, written grad f, or f, is f = if + jf + kf where f, f, and f 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), f is the direction of the heat-flow vector in the field.