Jacobian

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Jacobian

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
ams2001glos-Je1
sometimes also written
ams2001glos-Je2
The geostrophic advection of any scalar ψ may be written
ams2001glos-Je3
where g is the acceleration of gravity, f the Coriolis parameter, and z the isobaric contour height.