Jacobian: Difference between revisions
From Glossary of Meteorology
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{{Term | |||
|Display title=Jacobian | |||
{{ | |Definitions={{Definition | ||
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|Meaning=The determinant formed by the ''n''<sup>2</sup> partial derivatives of ''n'' functions of ''n'' variables, when the derivatives of each function occupy one row of the determinant. | |||
|Explanation=For the case of two functions ''f''(''x'', ''y'') and ''g''(''x'', ''y''), the Jacobian ''J''(''f'', ''g'') is <blockquote>[[File:ams2001glos-Je1.gif|link=|center|ams2001glos-Je1]]</blockquote>sometimes also written <blockquote>[[File:ams2001glos-Je2.gif|link=|center|ams2001glos-Je2]]</blockquote> The [[geostrophic advection]] of any [[scalar]] ψ may be written <blockquote>[[File:ams2001glos-Je3.gif|link=|center|ams2001glos-Je3]]</blockquote> where ''g'' is the [[acceleration of gravity]], ''f'' the [[Coriolis parameter]], and ''z'' the [[isobaric]] contour height. | |||
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Latest revision as of 07:48, 26 March 2024
The determinant formed by the n2 partial derivatives of n functions of n variables, when the derivatives of each function occupy one row of the determinant.
For the case of two functions f(x, y) and g(x, y), the Jacobian J(f, g) is
sometimes also written
The geostrophic advection of any scalar ψ may be written
where g is the acceleration of gravity, f the Coriolis parameter, and z the isobaric contour height.
