This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

JacobianMatrix

JacobianMatrix[pt]
gives the Jacobian matrix of the transformation from the default coordinate system to the Cartesian coordinate system at the point pt.

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 where are the Cartesian coordinates and 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.
Jacobian matrix for transformation from cylindrical to Cartesian coordinates:
Determinant for this transformation:
Needs["VectorAnalysis`"]
Jacobian matrix for transformation from cylindrical to Cartesian coordinates:
In[2]:=
Click for copyable input
Out[2]//MatrixForm=
Determinant for this transformation:
In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
Out[4]=