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.


gives the Jacobian matrix of the transformation from the coordinate system coordsys to the Cartesian coordinate system at the point pt.

更多信息更多信息

  • To use , 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.

范例范例打开所有单元关闭所有单元

基本范例  (1)基本范例  (1)

In[1]:=
Click for copyable input

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]=