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Re: Vector Analysis

  • To: mathgroup at
  • Subject: [mg15656] Re: Vector Analysis
  • From: Paul Abbott <paul at>
  • Date: Sat, 30 Jan 1999 04:28:50 -0500 (EST)
  • Organization: University of Western Australia
  • References: <78pcue$>
  • Sender: owner-wri-mathgroup at

adam.smith at wrote:

> I am using Mathematica Ver. 3 and am teaching a course in
> Electromagnetism which relies heavily on the del operator.  The use of
> the <<Calculus`VectorAnalysis` package has been quite useful as far as
> Grad[],Div [],Curl[], etc.

I'd be interested to hear more about your course.  I too teach a course
on Electromagnetism.  My course notes are available at

> However, in trying to confirm some often cited identities (see any book
> on Electromagnetism) such as:
> Grad[A.B] = Cross[A,Curl[B]] + Cross[B,Curl[A]] + (A.Del)B + (B.Del)A
> where A and B are vectors with 3 components that are functions of
> Cartesian components x, y and z.
> I have not been able to come up with an elegant method for representing
> things with the form of the last 2 terms, i.e. (A.Del)B.  

There is no real easy way to represent operator algebra in Mathematica.
Why not formally use A.Grad[B] (since Mathematica will differentiate
each component of the vector B).

> Can anyone tell me a way of defining a function that I can input any 2
> vectors and do this.  What I have in mind is something like
> AdotDelB[a,b].

There may be a better way.  Have a look at 

which is slated to appear in the forthcoming issue of the Mathematica


Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul at  AUSTRALIA              

            God IS a weakly left-handed dice player

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