University Mathematics Handbook (2015)
IX. Vector Analysis
Chapter 7. Scalar Field Gradient
a. The function given in every point of body , defined a scalar field.
b. Through every point , just one level surface passes (see VII.2.2).
c. The change rate of a differentiable scalar field at in the direction of vector is directional derivative (see VII.7).
d. Vector is called gradient of function , and is denoted or when operator (Nabla) is
operating on function , following the rule
e. A gradient of scalar field at is in the direction of the normal to the level surface passing through (or a level curve, if the field is planar).
f. Maximum change rate of scalar fiend is in the direction of vector .
g. The maximum value of the directional derivative of function on is