JacobianDeterminant

JacobianDeterminant[pt]
gives the determinant of the Jacobian matrix of the transformation from the default coordinate system to the Cartesian coordinate system at the point pt.

JacobianDeterminant[pt, coordsys]
gives the determinant of the Jacobian matrix of the transformation from the coordinate system coordsys to the Cartesian coordinate system at the point pt.

MORE INFORMATION

To use JacobianDeterminant, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].

JacobianDeterminant[pt, coordsys] is equivalent to Det[JacobianMatrix[pt, coordsys]].

The coordinates of pt should be given in the coordinate system coordsys, if specified, or the default coordinate system otherwise.

If pt is not given, the default coordinate variables for coordsys are used.

EXAMPLES

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Basic Examples (1)

Needs["VectorAnalysis`"]

Jacobian determinant for transformation from cylindrical to Cartesian coordinates:

In[2]:=

Out[2]=

Use the Jacobian determinant to change variables in a multiple integral: