OBSOLETE VECTOR ANALYSIS PACKAGE SYMBOL

# 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.

## DetailsDetails

• 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.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

 In[1]:=

Jacobian matrix for transformation from cylindrical to Cartesian coordinates:

 In[2]:=
 Out[2]//MatrixForm=

Determinant for this transformation:

 In[3]:=
 Out[3]=
 In[4]:=
 Out[4]=