Gradient

The gradient is a Vector operator denoted and sometimes also called Del or Nabla.It is most often applied to a real function of three variables , and may be denoted

(1)

(2)

(3)

The direction of is the orientation in which the Directional Derivative has the largest value and is the value of that Directional Derivative. Furthermore, if , then the gradientis Perpendicular to the Level Curve through if and Perpendicular to the levelsurface through if .

In Tensor notation, let

(4)

(5)

(6)

References

Arfken, G. ``Gradient, '' and ``Successive Applications of .'' §1.6 and 1.9 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 33-37 and 47-51, 1985.

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