“Gradient”的概念、定义、习题解题方法及翻译-数学辞典

单词

Gradient

释义

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)

For general Curvilinear Coordinates, the gradient is given by

(2)

which simplifies to

(3)

in Cartesian Coordinates.

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)

be the Line Element in principal form. Then

(5)

For a Matrix

(6)

For expressions giving the gradient in particular coordinate systems, see Curvilinear Coordinates.

See also Convective Derivative, Curl, Divergence, Laplacian, Vector Derivative

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.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。