## Questions concerning the del operator.

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• Hey, I was looking for certain vector identities involving the del operator, gradient, curl and divergence when I saw the identity of del operator X ( A X B )
Message 1 of 4 , Oct 29, 2006
Hey,

I was looking for certain vector identities involving the del operator, gradient, curl and divergence when I saw the identity of del operator X ( A X B ) or in other words, the curl of A cross B. http://mathworld.wolfram.com/VectorDerivative.html
If you look at Equation number 3 from the following link you get a term, on the right hand side of the equations, that contains A dot del. I understand that del dot A is the divergence but I am not familiar with how A dot del is defined. I also came accross questions containing terms like A cross del as opposed to del cross A(which is the curl). if anybody could tell me what A dot del and A cross del it would be greatly appreciated.

Fred

Send instant messages to your online friends http://uk.messenger.yahoo.com

[Non-text portions of this message have been removed]
• I suppose (A.del) is a differential operator acting on the vector field B. And this differential operator is the scalar product of the vector field A with the
Message 2 of 4 , Oct 30, 2006
I suppose (A.del) is a differential operator acting on the vector field B.
And this differential operator is the scalar product of the vector field A
with the del operator
If A has components (A1, A2, A3) and del components (d1, d2, d3)
Then A.del is the operator : A1 . d1 + A2 . d2 + A3 . d3
Here d1 is the partial derivative wrt the first variable ( usually called x)
and similarly for d2 and d3.
So the operator A.del acts on a function f by:
(A.del)f = A1.d1(f) + A2.d2(f) + A3.d3(f)
So the symbol (A.del)B is the vector field with components:
( (A.del)B1, (A.del)B2, (A.del)B3)
where (B1, B2, B3) are the components of the vector field B.
Friendly
Francois

On 10/30/06, Fred <fkbd2002@...> wrote:
>
> Hey,
>
> I was looking for certain vector identities involving the del operator,
> gradient, curl and divergence when I saw the identity of del operator X ( A
> X B ) or in other words, the curl of A cross B.
> http://mathworld.wolfram.com/VectorDerivative.html
> If you look at Equation number 3 from the following link you get a term,
> on the right hand side of the equations, that contains A dot del. I
> understand that del dot A is the divergence but I am not familiar with how A
> dot del is defined. I also came accross questions containing terms like A
> cross del as opposed to del cross A(which is the curl). if anybody could
> tell me what A dot del and A cross del it would be greatly appreciated.
>
> Fred
>
>
> Send instant messages to your online friends http://uk.messenger.yahoo.com
>
> [Non-text portions of this message have been removed]
>
>
>

[Non-text portions of this message have been removed]
• I see I forget the (A x del) operator. I think that is the operator with components: (A2 . d3 - A3 . d2, A3 . d1 - A1 . d3, A1 . d2 - A2 . d1) with the same
Message 3 of 4 , Oct 30, 2006
I see I forget the (A x del) operator.
I think that is the operator with components:
(A2 . d3 - A3 . d2, A3 . d1 - A1 . d3, A1 . d2 - A2 . d1)
with the same notations of my previous post.
So acting on a function f, the symbol (A x del)f is the vector field with
components:
(A2 . d3(f) - A3 . d2(f), A3 . d1(f) - A1 . d3(f), A1 . d2(f) - A2 . d1(f))
Friendly
François
All these formulas are only mnemonic!
I think to know the basic rules of differential calculus is far better!

[Non-text portions of this message have been removed]
• Thanks, That helped a lot. I broke it into component form and it checks out. Fred ... with ... d1(f))
Message 4 of 4 , Oct 31, 2006
Thanks,
That helped a lot. I broke it into component form and it checks out.

Fred
--- In Hyacinthos@yahoogroups.com, "Francois Rideau"
<francois.rideau@...> wrote:
>
> I see I forget the (A x del) operator.
> I think that is the operator with components:
> (A2 . d3 - A3 . d2, A3 . d1 - A1 . d3, A1 . d2 - A2 . d1)
> with the same notations of my previous post.
> So acting on a function f, the symbol (A x del)f is the vector field
with
> components:
> (A2 . d3(f) - A3 . d2(f), A3 . d1(f) - A1 . d3(f), A1 . d2(f) - A2 .
d1(f))
> Friendly
> François
> All these formulas are only mnemonic!
> I think to know the basic rules of differential calculus is far better!
>
>
> [Non-text portions of this message have been removed]
>
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