
Re: Jacobian Determinant in Mathematica 5.2
Posted:
Mar 5, 2007 10:08 PM


In article <1173141467.532199.76910@h3g2000cwc.googlegroups.com>, "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.softsys.math.mathematica is a good place to ask questions about Mathematica.
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

