Mach wave: Difference between revisions

Revision as of 23:00, 27 February 2014

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-A '''vector operator''' is a [[differential operator]] used in [[vector calculus]].  Vector operators are defined in terms of [[del]], and include the [[gradient]], [[divergence]], and [[Curl (mathematics)|curl]]:
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-:<math> \operatorname{grad} \equiv \nabla </math>
-:<math> \operatorname{div} \ \equiv \nabla \cdot </math>
-:<math> \operatorname{curl} \equiv \nabla \times </math>
-The [[Laplacian]] is
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-:<math> \nabla^2 \equiv \operatorname{div}\ \operatorname{grad} \equiv \nabla \cdot \nabla </math>
-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.
-:<math> \nabla f </math>
-yields the gradient of ''f'', but
-:<math> f \nabla </math>
-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.
-==See also==
-* [[del]]
-* [[D'Alembertian operator]]
-* [http://modis.ispras.ru/wikipedia/pic/Vector_calculus.html Related articles on a diagram]
-==Further reading==
-* H. M. Schey (1996) ''Div, Grad, Curl, and All That: An Informal Text on Vector Calculus'', ISBN 0-393-96997-5.
-[[Category:Vector calculus]]

Mach wave: Difference between revisions

Revision as of 23:00, 27 February 2014

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