Re: Vector Analysis

• To: mathgroup at smc.vnet.net
• Subject: [mg15656] Re: Vector Analysis
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Sat, 30 Jan 1999 04:28:50 -0500 (EST)
• Organization: University of Western Australia
• References: <78pcue\$d5h@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```adam.smith at hillsdale.edu 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

http://www.pd.uwa.edu.au/Physics/Courses/Second_Year/ElectroMagnetism.html

> 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

There may be a better way.  Have a look at

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

Cheers,
Paul

____________________________________________________________________
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 physics.uwa.edu.au  AUSTRALIA
http://www.physics.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

• Prev by Date: RE: How to construct all possible orderings
• Next by Date: Re: speed
• Previous by thread: Vector Analysis
• Next by thread: error messages in mathematica