The final exam is CUMULATIVE, that is, it covers all the material from the first day of class onwards. Approximately 20% will cover material from Chapter 11 on Differential Equations. This is Sections 11.1 - 11.5. You should go over homework problems as well as your class notes. Many of the problems and questions we discussed in class are excellent examples of test questions.

I have listed some sample problems from the Chapter 11 Review below. For questions from other chapters, see the previous exam review sheets: Exam 1 (Chapters 1, 2, 3) , Exam 2 (Chapters 4, 5, 6, 7) , Exam 3 (Chapters 8, 9, 10) For some good conceptual questions to work on. I have listed some sample problems from each Chapter's "Check Your Understanding" section. It is also a good idea to go over your previous exams and the chapter topic review sheets. These review sheets make an excellent studying tool allowing you to identify particular areas you may have struggled with during the semester.

The exam will be designed to take two hours (twice the length of a midterm) although you will have the full 3 hours.

**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. You will be given a
scientific calculator for the exam which does NOT have graphing
capabilities so be prepared to answer questions without your personal
calculator or computer. The only numerical computations required will be the kind
a scientific calculator can perform.

**Exam Review:** We will review for the exam Friday, Dec. 10, 1:00 - 2:30 pm
in Swords 359. Please come prepared with specific questions.

**Chapter 1 "Check Your Understanding", pp. 52 - 53**

Problems: 3, 5, 6, 7, 8, 9, 13, 15, 18, 19, 24, 25, 36, 39

The answers to the evens are:

6. FALSE

8. TRUE

18. FALSE

24. TRUE

36. FALSE

**Chapter 2 "Check Your Understanding", pp. 103**

Problems: 7, 8, 10, 11, 16, 17, 21, 22, 23

The answers to the evens are:

8. TRUE

10. FALSE

16. TRUE

22. TRUE

**Chapter 3 "Check Your Understanding", pp. 162**

Problems: 1, 3, 7, 9, 11, 13, 14, 15

The answers to the evens are:

14. FALSE

**Chapter 4 "Check Your Understanding", pp. 216 - 217**

Problems: 1, 3, 5, 6, 7, 11, 20, 21, 23, 24, 25

The answers to the evens are:

6. TRUE

20. f(x) = e^x works

24. Impossible

**Chapter 5 "Check Your Understanding", pp. 257**

Problems: 1, 3, 6, 7, 9, 11, 12, 13

The answers to the evens are:

6. TRUE

12. FALSE

**Chapter 6 "Check Your Understanding", pp. 287 - 288**

Problems: 3, 5, 6, 7, 9, 11, 12, 13, 14, 15

The answers to the evens are:

6. FALSE

12. TRUE

14. TRUE

**Chapter 7 "Check Your Understanding", pp. 342**

Problems: 1, 3, 5, 7, 11, 17, 18, 19, 20

The answers to the evens are:

18. TRUE

20. FALSE

**Chapter 8 "Check Your Understanding", pp. 401**

Problems: 1, 3, 5, 8, 9, 10, 12

The answers to the evens are:

8. FALSE

10. FALSE

12. FALSE

**Chapter 9 "Check Your Understanding", pp. 431**

Problems: 3, 4, 6, 7, 9, 11, 18, 22, 23, 24

The answers to the evens are:

4. FALSE

6. FALSE

18. TRUE

22. TRUE

24. FALSE

**Chapter 10 "Check Your Understanding", pp. 473-474**

Problems: 1, 3, 5, 7, 8, 9, 13, 19

The answers to the evens are:

8. TRUE

**Chapter 11 "Check Your Understanding", pp. 555-556**

Problems: 3, 5, 8, 9, 34, 37

The answers to the evens are:

8. FALSE

34. dy/dx = f(x), with f(x) a positive, increasing, differentiable function

**Chapter 11 review, pp. 552-555**

Problems: 3, 5, 9, 11, 15, 19, 21, 30, 31, 35, 39

The answers to the evens are:

30. y = -2 is unstable, y = 0 is stable, y = 4 is unstable