Return to Other Sample Exams.
THIRD HOUR EXAM, MATH 223
Instructor: Kris Green, December 5, 19967
- 1.
- Multiple Choice (5 points each):
- (a)
- The divergence of the vector field at the point (1,1,-1) is:
a. -2 |
b. |
c. |
d. 2xy + 2yz + 2xz |
- (b)
- The curl of is:
- (c)
- Choose the expression that best describes the vector field shown
below:
(include vector field)
- (d)
- Consider the following line integral:
Over which of the following parameterized paths can Green's Theorem be
applied to this integral?
- 2.
- Short answer (10 points each):
- (a)
- Give 3 characterizations of a conservative vector field. If you name
more than 3 correctly, then extra credit will be given. (Hint: One of
these can be the definition of a conservative vector field.)
- (b)
- State Stokes' Theorem and describe the conditions under which it can
be applied.
- 3.
- (10 points) Compute the line integral for the vector field
along the path y=x2 from (1,1) to (2,4).
- 4.
- (10 points) Compute the line integral for the vector field
along the path for .
- 5.
- (10 points) Compute the line integral for the vector field
along the square with vertices (2,2), (-2,2), (-2,-2), and (2,-2) in the
counterclockwise direction.
- 6.
- (10 points) Find the flux of over the portion of
the surface z = 16 - x2 - y2 that lies above the disk .
- 7.
- Let . Compute the flux of through the sphere of radius 4
centered at (1,-1,0).
- 8.
- Find the circulation of around the triangle in the plane z = y with vertices
(3,0,0), (0,2,2) and (0,0,0) oriented in this order.
Vector Calculus
8/20/1998