am i right in saying the following
where is some scalar field?
Im equating
and wondering if this is the same as
To be honest im really just looking for the difference between
and
if there is any difference. I thought they would equate to the same thing?
I fixed my original post as well as i had a small but significant mistake in the formula
No, they are not the same thing. They are not even the same "kind" of thing.
is the vector function .
is not a function at all but rather a "vector operator". If f is a real valued function then .
If is a vector valued function, say then
We could also write