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Topic: Jacobian Determinant in Mathematica 5.2
Replies: 3   Last Post: Mar 6, 2007 8:59 AM

 Messages: [ Previous | Next ]
 Paul Abbott Posts: 1,437 Registered: 12/7/04
Re: Jacobian Determinant in Mathematica 5.2
Posted: Mar 5, 2007 10:08 PM

"logan" <logan946@gmail.com> wrote:

> I was seeking information on how to go about computing the Jacobian
> determinant in Mathematica 5.2:
>
> T (x,y,z) >> (x(u,v,w),y(u,v,w),z(u,v,w))
>
> in other words the:
>
> |(dxdydz)/(dudvdw)|

The Jacobian can be computed using D (see the documentation for D).

For example, entering

D[ {r Cos[t], r Sin[t]}, {{r, t}} ]

yields the matrix

Cos[t] -r Sin[t]

Sin[t] r Cos[t]

> I know how to compute it by hand but I am dealing with a troublesome
> function and needed Mathematica to check my work, but I don't know
> exact syntax for such a function or how to enter the matrix in one
> whole line.
>
> For those, so inclined, here is the function:
>
> T: R3 > R3, T(u,v,w) = (u*cos(v)*cos(w), u*sin(v)*cos(w), u*sin(w))

Det[D[{u Cos[v] Cos[w], u Cos[w] Sin[v], u Sin[w]}, {{u, v, w}}]] //
Simplify

u^2 Cos[w]

Note that the Mathematica newsgroup, comp.soft-sys.math.mathematica is a

Cheers,
Paul

_______________________________________________________________________
Paul Abbott Phone: 61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
The University of Western Australia (CRICOS Provider No 00126G)
AUSTRALIA http://physics.uwa.edu.au/~paul

Date Subject Author
3/5/07 logan
3/5/07 [Mr.] Lynn Kurtz
3/5/07 Paul Abbott
3/6/07 Dana DeLouis