- 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 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 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

--- In Hyacinthos@yahoogroups.com, "Francois Rideau"

<francois.rideau@...> wrote:>

with

> 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

> components:

d1(f))

> (A2 . d3(f) - A3 . d2(f), A3 . d1(f) - A1 . d3(f), A1 . d2(f) - A2 .

> 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]

>