Vector operator

A vector operator is a type of differential operator used in vector calculus. Vector operators are defined in terms of del, and include the gradient, divergence, and curl:

$\operatorname{grad} \equiv \nabla$

$\operatorname{div} \ \equiv \nabla \cdot$

$\operatorname{curl} \equiv \nabla \times$

$\nabla^2 \equiv \operatorname{div}\ \operatorname{grad} \equiv \nabla \cdot \nabla$

Vector operators must always come right before the scalar field or vector field on which they operate, in order to produce a result. E.g.

$\nabla f$

yields the gradient of f, but

$f \nabla$

is just another vector operator, which is not operating on anything.

A vector operator can operate on another vector operator, to produce a compound vector operator, as seen above in the case of the Laplacian.

[edit] See also

H. M. Schey (1996) Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, ISBN 0-393-96997-5.

This page was last modified 02:56, 6 October 2006 by Wikipedia user Oleg Alexandrov. Based on work by Wikipedia user(s) SmackBot, Mathbot, Charles Matthews and AugPi and Anonymous user(s) of Wikipedia.
All text is available under the terms of the GNU Free Documentation License. (See Copyrights for details.)
Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a US-registered 501(c)(3) tax-deductible nonprofit charity.
About Wikipedia
Disclaimers