VectorAnalysis`
VectorAnalysis`

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)

Jacobian determinant for transformation from cylindrical to Cartesian coordinates:

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