Del operator?

1. Dec 9, 2007

okay

hello every one,
i am working on vector analysis and i have come across this definition of del operator.i dont understand where does it come from but it works great to determine rotation curl gradient or other stuff of a vector field.can anyone tell me how we are getting this magical operator is there a proof about this? in 2-D i ve found great deal of explanation about vectors but in 3-D it is really complicated.
i am looking forward to seeing your helps.

Last edited: Dec 9, 2007
2. Dec 9, 2007

cristo

Staff Emeritus
The "del" operator is just defined in 3 dimensional, cartesian coordinates as $$\nabla=\bold{i}\frac{\partial}{\partial x}+\bold{j}\frac{\partial}{\partial y}+\bold{k}\frac{\partial}{\partial z}$$

I don't really understand what proof you are looking for; could you expand on your question?

3. Dec 9, 2007

okay

i just want to know is it something special that this three partial derivatives working great to reveal these gradiant curl ..etc .or is it some thing good looking thing that appear in these equations as we try to determine curl, rotation.. so on?

4. Dec 9, 2007

Defennder

In my opinion, you are probably asking what does del mean physically. It can't possibly appear from thin air, and all the mathematical results follow from it. I suggest this would help you:

http://en.wikipedia.org/wiki/Del

The above should clear your confusion up a little. It's simply a mathematical convention which has a lot of mathematical implications.

Last edited by a moderator: Apr 23, 2017
5. Dec 9, 2007

okay

thank u defennnder