Gradient Function

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A Gradient Function is a differentiable scalar field function that returns a Vector that points in the direction of the greatest rate of increase in the scalar field.




    • Suppose we have a scalar function that depends on three space coordinates, x, y and z. Let's call it T. For example it could be the temperature in the room you're in now.

      Since T depends on those three variables we can ask the question: how does T change when we change one or more of those variables?

      And as always, the answer is found by differentiating the function. In this case, because the function depends on more than one variable, we're talking partial differentiation. (Have a look at the MathHelp notebook on Partial Differentiation if you're not sure about this.)

      Now if we differentiate T with respect to x, that tells us the change of T in the x-direction. That is therefore the i-component of the gradient of T.