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 gradient is Perpendicular to the Level Curve through if and Perpendicular to the level surface 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.

© 1996-9

1999-05-25