What is the Divergence? is it only the Partial derivatives?
Lets say I have a vector field:, the divergence is
?
And if it is, than what is the gradient?(Thinking)
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What is the Divergence? is it only the Partial derivatives?
Lets say I have a vector field:
And if it is, than what is the gradient?(Thinking)
You can only take the gradient of a scalar field. You can take the curl of F if you want .....Quote:
Originally Posted by asi123
http://img.photobucket.com/albums/v4...e2143a3-21.jpgQuote:
Originally Posted by asi123What is the Divergence? is it only the Partial derivatives?
Lets say I have a vector field:
And if it is, than what is the gradient?(Thinking)
Does this clarify things?
--Chris
Mr. F, when you take the divergence of a field, you're left with a scalar value...it should be 2x+2y+2z, not 2xi+2yj+2zk...Quote:
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...
--Chris
Quote:
Originally Posted by Chris L T521
So one is like the dot product and the other is the cross product?
But still, isnt the gradient already define the partial derivative? why do I need the Divergence?
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:
Originally Posted by asi123
Yes, the gradient consists of partial derivatives, but note the difference between the values of the gradient and divergence: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.
Quote:
Originally Posted by Chris L T521
Yeah man, that makes a lot of sense.
thanks a lot.
My mistake. I didn't look closely enough and so saw what I expected to see ......Quote:
Originally Posted by Chris L T521