MA330: Assignment 5
Required Reading.
• Read Chapter 4, § 41
• Read Chapter 5, § 43 & 44
To be turned in April 19th at the start of class.
1. Suppose f , g, u, and v have the following properties:
∇f = hx, y, zi
∇g = h1, 1, 1i

sin x −z 2
0
∇u =  0
0
−2xz
f (0) = 1
g(0) = 2
u(0) = 0

1
1
0

1
∇v = 0
0
y
x
0

yz
xz 
xy
v(0) = h0, 0, 1i
(a) Compute ∆f at r = 0.
(b) Compute ∇ · u at r = 0.
(c) Compute ∇ × v at r = 0.
(d) Compute ∇(f g) at r = 0.
(e) Compute ∇ · (f u) at r = 0.
(f) Compute ∇ × (gv) at r = 0.
2. Textbook, page 113, #1
3. Textbook, page 113, #3
4. Textbook, page 113, #6
5. A particle in 2D at location r experiences the force F =
point (1, 0) to the point (0, 1),
−r
krk .
Compute the work done to move the particle from the
(a) along a circular path, centered at the origin,
(b) and along a straight line.
(c) By comparing the two values from the previous parts, form a hypothesis about the nature of this field. Prove
your hypothesis.
1