What is the Divergence? is it only the Partial derivatives?

Lets say I have a vector field: $\displaystyle F=x^2i+y^2j+z^2k$, the divergence is $\displaystyle F=2xi+2yj+2zk$?

And if it is, than what is the gradient?(Thinking)

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- Jul 27th 2008, 08:51 PMasi123Divergence
What is the Divergence? is it only the Partial derivatives?

Lets say I have a vector field: $\displaystyle F=x^2i+y^2j+z^2k$, the divergence is $\displaystyle F=2xi+2yj+2zk$?

And if it is, than what is the gradient?(Thinking) - Jul 27th 2008, 08:57 PMmr fantastic
- Jul 27th 2008, 09:06 PMChris L T521
http://img.photobucket.com/albums/v4...e2143a3-21.jpg

Does this clarify things?

--Chris - Jul 27th 2008, 09:22 PMChris L T521Quote:

Originally Posted by asi123

What is the Divergence? is it only the Partial derivatives?

Lets say I have a vector field: F=x^2i+y^2j+z^2k, the divergence is F=2xi+2yj+2zk? Mr F says: Yes. Chris says: Not quite. This would be your**gradient**, but not your**divergence**...

**i**+2y**j**+2z**k**...

--Chris - Jul 27th 2008, 09:23 PMasi123
- Jul 27th 2008, 09:33 PMChris L T521
This is the proper way of writing it in vector notation. Yes, one is a dot product, and the other is a cross product. Divergence and Curl are important in the study of fluids [this is where the names originated]. Divergence tells you how the fluid flows towards or away from a point; Curl tells you the rotational properties of the fluid. It would make sense that divergence is a scalar, and curl would be a vector.

Quote:

But still, isnt the gradient already define the partial derivative?

http://img.photobucket.com/albums/v4...e2143a3-22.jpg

Does this make a little more sense now?

--Chris

EDIT: I should have made this a little clearer by noting that the gradient can only be applied to scalar fields, as Mr. Fantastic had mentioned earlier. - Jul 27th 2008, 09:37 PMasi123
- Jul 27th 2008, 09:40 PMmr fantastic