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Vector Analysis

  • To: mathgroup at
  • Subject: [mg15605] Vector Analysis
  • From: adam.smith at
  • Date: Thu, 28 Jan 1999 04:23:33 -0500 (EST)
  • Organization: Deja News - The Leader in Internet Discussion
  • Sender: owner-wri-mathgroup at

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.

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.  I have used
the brute force method below:

a = {x,2 y, 3 z}
b = {3 y, -2 x,0}

adotdelb = {(a[[1]]*D[b[[1]],x] + a[[2]]*D[b[[1]],y] +
	    (a[[1]]*D[b[[2]],x] + a[[2]]*D[b[[2]],y] + a[[3]]*D[b[[2]],z]),
	    (a[[1]]*D[b[[3]],x] + a[[2]]*D[b[[3]],y] + a[[3]]*D[b[[3]],z])}

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

Adam Smith

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