Math 2210
Review Topics for Opportunity #4
Chapter 16
Here is a list of topics that you should expect to see for our second opportunity. Please look for
problems in the book and through your homework to verify the types of problems you can expect to
see.
1. Evaluate line Integrals
a. Along a given path (recall this is independent of its parameterization)
b.
In a vector field:
2. Be able to use The fundamental theorem for Line Integrals
a. Show that a vector field F is conservative or not
b. What does a conservative vector field look like? What can you say about a line integral
around any closed path in a conservative vector field?
c. If it is known that a vector field is conservative what does this mean about the path C taken
to as curve goes from a to b ?
d. Find a potential function f such that f  F
3. Green’s Theorem
a. Know the requirements to use Green’s Theorem
b. Use Green’s Theorem to evaluate a line Integral
4. Curl and Divergence
a. Calculate the Curl of a vector field, what does this say about a vector field being
conservative or not?
b. Calculate the Divergence of a vector field, what does it mean to have a positive or negative
Divergence?
5. Parametric Surfaces
a. Find a Tangent Plane to a parametric surface
b. Determine the area of a parametric surface
c. Determine the area given an explicit surface
6. Surface Integrals
a. Evaluate a Surface Integral
b. Evaluate a Surface Integral over a vector field
7. Stokes Theorem
a. Evaluate a Line Integral using Stokes Theorem
8. The Divergence Theorem
a. Evaluate a flux integral over a region E
I am arranging the test so that the longest problem is on the last page. However, when you get it read
the whole test to see which ones might be easiest and fastest for you first !!! Please show all your work
on the test as I do award partial credit. I will grade the problems on a scale of 10 pts each. The
problems I select for the test will be similar to problems we have looked at in class or from your
homework. Thus please make sure your homework is complete before the test.
Remember: All work is due the day of the test and not accepted afterwards !!!!
Useful Formulas to know
 F  dr   f  dr  f  r  b    f  r  a  
C
C
A   ru  rv dA
D
A  
D
 z   z 
1       dA
 x   x 
2
2
 Q P 
Pdx

Qdy

C
D  x  y  dA
 F  dS   F   r  r  dA
u
S
 F  dS  
S
v
D
P, Q, R   g x ,  g y ,1 dA
D
 F  dr   curlF  dS
C
S
 F  dS   div( F ) dV    F dV
S
E
E