The final exam is CUMULATIVE, that is, it covers all the material from the first day of class onwards. Approximately 15 - 20% will cover material from Chapter 7 on Differential Equations. This is Sections 7.1 - 7.4. You should go over homework problems, the midterm exams and your class notes. Many of the problems and questions we discuss in class are excellent examples of test questions.

I have listed some sample problems from the Chapter 7 Review below. The odd answers are in the back of the book while the evens are listed here. For questions from other chapters, see the previous exam review sheets: Exam 1 (Chapters 1, 2) , Exam 2 (Chapters 3, 4, 5.1 - 5.6) , Exam 3 (Chapters 5.7, 5.10, 6, 8) Note that some sections are poorly covered by the problems in the Chapter Review Exercises (eg. trig. substitution is missing in Ch. 5.) The Concept-Check and True-False Quiz at the end of each chapter (before the exercises) are also a good source for questions.

The exam will be designed to take two hours (twice the length of a midterm) although you will have the full 3 hours to complete the exam. Click here for a sample final exam (PDF File).

**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 Thursday, Dec. 7, 1:30 - 3:00 pm
in Swords 359. Please come prepared with specific questions.

**Office Hours for this week: **

Wednesday, Dec. 6th: 2:30 - 4:00 pm

Thursday, Dec. 7th: 3:00 - 4:15 pm

Friday, Dec. 8th: 2:00 - 3:30 pm

**Chapter 7 review, pp. 551-553**

Problems: 1, 3, 4, 5, 7, 8, 16

The answers to the evens are:

4. (a) 1.08, (b) 1.1292, (c) y(x) = 1/(1-x^2) and y(0.4) = 25/21 = 1.190476.

8. y(x) = ln( (3 - cos x)/(1 + cos x) ).

16. (a) 46.666 degrees Celsius, (b) 1.35 hours or 81.3 minutes.