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JacobianMatrix

JacobianMatrix[pt]
gives the Jacobian matrix of the transformation from the default coordinate system to the Cartesian coordinate system at the point pt.
JacobianMatrix[pt, coordsys]
gives the Jacobian matrix of the transformation from the coordinate system coordsys to the Cartesian coordinate system at the point pt.
  • The Jacobian matrix consists of the elements mi, j=PartialDujri where r1, r2, r3 are the Cartesian coordinates x, y, z and u1, u2, u3 are the coordinates of the coordinate system coordsys, if specified, or the default coordinate system otherwise.
  • 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 matrix for transformation from cylindrical to Cartesian coordinates:
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Out[2]//MatrixForm=
Determinant for this transformation:
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Out[3]=
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Out[4]=