# JacobianDeterminant

As of Version 9.0, vector analysis functionality is built into the Wolfram Language

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.

# Details

• 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

## Basic Examples(1)

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Jacobian determinant for transformation from cylindrical to Cartesian coordinates:

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

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