VectorAnalysis`
VectorAnalysis`

JacobianMatrix

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

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.

Details

  • To use JacobianMatrix, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
  • The Jacobian matrix consists of the elements where , , are the Cartesian coordinates and , , are the variables 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.

Examples

Basic Examples  (1)

Jacobian matrix for transformation from cylindrical to Cartesian coordinates:

Determinant for this transformation: