- #1
Cyrus
- 3,238
- 16
A couple of quickies on the interpertation of the partial derivative I want to clear up with myself.
If we have a parametric function:
r(u,v)= x(u,v)i + y(u,v)j+z(u,v)k
then the partial derivative W.R.T u or v is regarded as the tangent vector, and we can think of it as the speed, or velocity vector at the point (u,v) along the curve.
Now for a function defined by,
xi + yj + z=f(x,y)k
When we take the partial derivative with respect to x or y, can we still regard it as the speed or velocty vector at the point (x,y)?
I don't see any reason not to call it that, they are both legitamite vectors tangent at the point (x,y) or (u,v).
If we have a parametric function:
r(u,v)= x(u,v)i + y(u,v)j+z(u,v)k
then the partial derivative W.R.T u or v is regarded as the tangent vector, and we can think of it as the speed, or velocity vector at the point (u,v) along the curve.
Now for a function defined by,
xi + yj + z=f(x,y)k
When we take the partial derivative with respect to x or y, can we still regard it as the speed or velocty vector at the point (x,y)?
I don't see any reason not to call it that, they are both legitamite vectors tangent at the point (x,y) or (u,v).