| ||||||||||||
![]() The gradient is a vector operator denoted
For general curvilinear coordinates, the gradient is given by
which simplifies to
The direction of In tensor notation, let
be the line element in principal form. Then
For a matrix
For expressions giving the gradient in particular coordinate systems, see curvilinear coordinates.
Arfken, G. "Gradient, Kaplan, W. "The Gradient Field." §3.3 in Advanced Calculus, 4th ed. Reading, MA: Addison-Wesley, pp. 183-185, 1991. Morse, P. M. and Feshbach, H. "The Gradient." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 31-32, 1953. Schey, H. M. Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, 3rd ed. New York: W. W. Norton, 1997. ![]() CITE THIS AS: Eric W. Weisstein. "Gradient." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Gradient.html ![]() |
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