Chapter 1 Exercises
1.1 (a)
Direction of maximum rate of change is along the gradient vector.
Find the gradient vector and plug in the point to find the direction of most rapid rate of change at that point.
Direction cosine:
The elements of a basis are usually chosen to be unit vectors. Every vector in the space may be written as a linear combination of unit vectors, with the components of each being given by direction cosines
1.1 (b)
To find the maximum rate of change, find the magnitude of the gradient vector
1.2 (a)
Divergence theorem: