The Gradient of a Scalar Field Flashcards
1
Q
Define ∇, del.
A
2
Q
What is the symbol for del.
A
∇
3
Q
What does ∇ stand for?
A
del or nabla
4
Q
Define _∇_f
A
5
Q
What is the symbol for gradient or grad f?
A
_∇_f
6
Q
What does _∇_f stand for?
A
Gradient or grad f
7
Q
What components does the vector field grad f have?
A
8
Q
In what direction does _∇_f go for lines of constant f?
A
Normal to them
9
Q
What are three properties of scalar fields?
A
10
Q
Prove the following when n=2.
A
11
Q
Prove the following when n=2.
A
12
Q
Prove the following in n dimensions.
A
13
Q
If we use arc length s as the parameter then how does the following change?
A
14
Q
Define the directional derivative of f in the direction ñ.
A
15
Q
In which direction does _∇_f point in?
A
The direction where f increases fastest.
16
Q
Prove that _∇_f points in the direction where f increases fastest.
A
