Quote:

Originally Posted by **zylo** z = f(x,y)
1) $\displaystyle dz = f_{x}dx + f_{y}dy = \bigtriangledown f\cdot$ d**r**
2) $\displaystyle dz/ds = \bigtriangledown f\cdot$ **n**
3) $\displaystyle f_{x}dx + f_{y}dy - dz = N\cdot$ d**r** = 0
1) Gradient. $\displaystyle \bigtriangledown f$ points in dir of max increase of z; see Eq 2).
2) Directional derivative in dir of unit vector n. **n**=d**r**/ds, ds=|d**r**|
3) Equation of tangent to surface. N is normal to surface.
d**r** is defined by respective Eq. |

dz is not normal to the surface. See 1)

N is normal to the surface. See 3)