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Practice Problems for the Final Exam

Note: This is not really a practice test as it is not by any means inclusive. However, being able to do these problems will certainly benefit you when you are taking the final exam.

1.
(Vector Fields)
(a)
Page 964, #13.
(b)
Page 964, #14.
(c)
Page 964, #15.
(d)
Page 964, #17.
2.
(Line Integrals)
(a)
Page 1018, #3.
(b)
Page 1019, #5.
(c)
Page 1019, #9.
(d)
Page 1019, #10.

3.
(Independence of Path)
(a)
Page 1019, #6. Find a potential function and use the fundamental theorem of calculus to evaluate the integral when A=(0,0,1) and B=(1,2,3).
(b)
Page 1019, #7. (Use any method.)

4.
(Green's Theorem)
(a)
Page 1019, #11.

5.
(Surface Integrals, Stokes' Theorem, and Divergence Theorem)
(a)
Page 1019, #17. Use Stokes' Theorem to check your answer.
(b)
Page 1019, #19. Use the divergence theorem to check your answer.

Other things you should know include what flux and circulation (what I called rotation in class) of fluid mean, how they relate to divergence and curl, and how to relate them to a graph.


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Joshua Holden
12/9/1999