The final exam is cumulative, that is, it covers all the material from the first
day of class onwards. Approximately 25-35% will cover material since the second exam. This is
Sections 16.4, 16.5, 17.1 -- 17.4, and Chapter 18. It is recommended that you go over the homework
problems as well as your class notes. Many of the problems and questions we discuss in
class are excellent examples of test questions. I have also listed some sample problems
from the Chapter 16, 17 and 18 Reviews and Check Your Understanding Sections below.
For problems from the earlier chapters see the previous Exam Review sheets.
Note that these problems are a SAMPLE selection.
Certain topics are covered in the reviews better than others.
The odd answers are in the back of the book
while the evens are listed here. The exam will be designed to take 2 hours although you
will have the full 3 hour exam period.
Note: You will be allowed one "cheat sheet" 8.5 x 11 piece of paper,
front and back, full of whatever formulas, graphs, etc. you wish. Creating this
reference paper will be an excellent opportunity to review topics for the exam.
EXAM REVIEW SESSION: Sunday, May 8, 2:00 - 4:00 pm in SWORDS 359. Please come prepared
with specific questions.
List of Topics By Chapter
Chapter 16 Review, pp. 777 - 779
The answers to the evens are:
Chapter 16 Check Your Understanding, pp. 780 - 781
The answers to the evens are:
Chapter 17 Review, pp. 819 - 822
The answers to the evens are:
Chapter 17 Check Your Understanding, pp. 822 - 823
The answers to the evens are:
Chapter 18 Review, pp. 857 - 860
The answers to the evens are:
Chapter 18 Check Your Understanding, pp. 860 - 861
The answers to the evens are:
Problems: 1, 3, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 17, 18, 19, 21, 23, 24, 25, 27, 33, 35, 41
6. 0 <= r <= 3, 0 <= z <= 2, 0 <= theta <= 2Pi
8. 0 <= rho <= 5, 0 <= phi <= Pi, 0 <= theta <= Pi/2
10. 85/12
12. 10(e-2)
16. 7Pi/3
18. Pi(3 - 2 Ln 2)
24. positive
Problems: 1, 3, 5, 7, 11, 15, 19, 21, 23, 25, 27, 28
28. True
Problems: 1, 3, 5, 7, 9, 10, 11, 13, 15, 17, 22, 25
10. x = 3 - 2t, y = -2 + t, z = t
22. (a) First show x^2 + y^2 = R^2. Radius = R, ccw motion, period = 2Pi/omega.
(b) velocity is perpendicular to position r, speed = R omega.
(c) acceleration a = -omega^2 r, ||a|| = omega^2 R
Problems: 1, 3, 5, 7, 9, 15, 17, 19, 21, 23, 25, 30, 31
30. False
Problems: 1, 3, 5, 7, 9, 10, 11, 12, 13, 17, 19, 21, 23
10. (ii) and (iv)
12. Path-independent since F = grad f where f = y^2/2
Problems: 1, 5, 6, 7, 9, 13, 15, 19, 23, 27, 29, 31, 39
6. False