JacobianDeterminant

As of version 9.0, vector analysis functionality is built into Mathematica

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


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

DetailsDetails

  • To use , you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
  • is equivalent to Det[JacobianMatrix[pt, coordsys]].
  • 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]:=
Click for copyable input

Jacobian determinant for transformation from cylindrical to Cartesian coordinates:

In[2]:=
Click for copyable input
Out[2]=

Use the Jacobian determinant to change variables in a multiple integral:

In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
Out[4]=
New to Mathematica? Find your learning path »
Have a question? Ask support »