Does anyone know some links (exclude wiki) that explain the "Directional derivative of a vector field". I've been googling but found none, and i have a task that deals with it but have no literature.

Printable View

- Feb 1st 2008, 07:36 AMPinskyDirectional derivative of a vector field
Does anyone know some links (exclude wiki) that explain the "Directional derivative of a vector field". I've been googling but found none, and i have a task that deals with it but have no literature.

- Feb 1st 2008, 08:31 AMtopsquark
- Feb 1st 2008, 08:52 AMPlato
These may help you. They are from a text by Keisler (it is free to download from his website at the Unuversity of Wisconsin).

- Feb 1st 2008, 12:54 PMPinsky
Determine the derivate of a vector field

in the direction of vector

Any chance somebody can solve this with a step-by-step explanation what is done and why? - Feb 1st 2008, 01:41 PMPlato
It seems to me as you may have confused two different concepts.

First, you began this thread by asking about directional derivatives. They apply to functionals: functions from a vector space to the reals.

Then you now appear to be asking vector value functions or vector fields.

There is the concept of the*divergence*in the field. But we don’t find divergence in a particular direction.

Rather divergence is direction at a particular point in the field.

So what exactly are you asking? As put the current question is meaningless.

If is a vector field, do you mean to ask for the divergence at**the point** - Feb 1st 2008, 04:17 PMPinsky
I have the solution of the task, but i don't know what it means. Perhaps it's divergence and i messed things up. Here it is, maybe you can figure out something out of it.

The text goes:

Find the derivate of a vector field in direction of the vector in the point .

Solution:

- Feb 1st 2008, 06:20 PMtopsquark
Ah! If I'm right it's something akin to what I have come to call a "vector gradient." (With all due apologies, I don't know what the actual name of it is.)

When the gradient of a scalar function is taken it returns a vector. But you can define a version of this that acts on a vector as operating on each component of the vector individually. .

I've seen it mentioned in my Electrodynamics text, but have never actually used the thing.

-Dan