In vector calculus, the gradient of a scalar field's a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude's the greatest rate of change. A generalization of the gradient for functions on a Euclidean space which have values in another Euclidean space's the Jacobian. A further generalization for a function from one Banach space to another's the Fréchet derivative. Interpretations of the gradient For instance, consider a room… (More on Gradient)