Re: operators
- To: mathgroup <mathgroup at yoda.physics.unc.edu>
- Subject: Re: operators
- From: Ronald D. Notestine <ronald at sccs.chukyo-u.ac.jp>
- Date: Tue, 09 Nov 93 03:17:03 +0900
Yes. A good exposition is in a book by Dimitri
VVedensky, just published by Addison-Wesley,
titled "Partial Differential Equations with
Mathematica". I take the following from the
introduction:
u := {r,theta,phi}
h := {1,r,r Sin[theta]}
Where the entries must be in the same order.
The Jacobian, J, is
J = h[[[1]]h[[2]]h[[3]]
and the gradient is given by
Grad[f_] := Table[D[f,u[[i]]]/h[[i]],{i,3}]
and the divergence by
Div[f_] := (1/J)Sum[D[(J f[[i]])/h[[i]],
u[[i]],{i,3}]
I have not used these myself, and retyped them by
hand. But, they certainly look correct.
Incidentally, I have just noticed that there
is also a package "Calculus`VectorAnalysis`"
that has all of this and a lot more premade.
The package is desscribed in the technical
report "guide to Standard Mathematica Packages".
We get a copy in every MMA box we get for
the Macintosh.
Hope this helps. Good luck.
Ronald D. Notestine
Faculty of Management
Chukyo University
Nagoya, Japan
ronald at sccs.chukyo-u.ac.jp
fax: 81-52-835-7196