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 functions on a Banach space which have vectorial values, is the Jacobian. Interpretations of the gradient Consider a room in which the temperature is given by a scalar field T, so at each point (x,y,z) the temperature is T(x,y,z) (we will assume that the… (More on Gradient)