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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.
  • 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.
Needs["VectorAnalysis`"]
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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