The final exam is cumulative, that is, it covers all the material from the first day of class onwards. Approximately 40-50% will cover the material from Chapters 9 and 10. This is sections 9.1, 9.2, 9.3, 10.1 and 10.2. You should go over homework problems, class notes and past quizzes and exams.

The exam will be designed for 2 hours (twice the length of the mid semester exams) so you should have plenty of time to complete it in the alloted 3 hour time slot. You will be expected to use a calculator on the exam. You are NOT allowed to use your calculator to store formulas, do symbolic or numerical integration or use any graphing capabilities it may have. Any such use will be considered a violation of the honor code for this course.

**FINAL EXAM REVIEW:** Wednesday, May 1, in SWORDS 359 from 1:00 - 3:00 pm. Please come prepared
with specific questions from the chapter reviews, past exams, homework problems, etc.

** List of Topics By Chapter **

- Chapter 6: Integration, anti-derivatives, basic rules of integration (constants pull out, power rule, etc.), u-substitution, finding the area under a curve, Riemann sums (left-end points, right-end points, midpoints), the Fundamental Theorem of Calculus, average value, area between two curves
- Chapter 7: Integration by parts, integration using tables of integrals, numerical integration (Trapezoid rule, Simpson's rule), improper integrals
- Chapter 8: Multivariable Calculus, functions of several variables, domain and range, level curves (contour plots), partial differentiation, first and second-order partial derivatives, maxima and minima of functions of two variables, second-derivative test, constrained max and min problems (Lagrange multiplier method), double integrals, volume under a graph, average value
- Chapter 9: Differential Equations (D.E.'s), showing a given function satisfies a D.E., general versus particular solutions, finding a particular solution to a D.E., solving a separable differential equation, applications of separable D.E.'s (population growth, Newton's law of cooling, etc.)
- Chapter 10: Probability, discrete and continuous random variables, probability density function (PDF), computing probabilities given a PDF, expected value or mean of a continuous random variable, variance, standard deviation

Some sample problems from Chapter 9 and 10 are given below. Note that this is only a partial list. In many cases, the homework problems more accurately reflect the material covered in class. For problems from the other Chapters, see the review sheets from past Exams and quizzes.

**Chapter 9 review, pp. 724-725**

Problems: 2, 3, 4, 9, 10, 21, 24

**Answers to even problems:**

2. Show that y satisfies the D.E.

4. Show that y satisfies the D.E., c = -1

10. y = 1 - 3e^[-(1/3)x^3]

24. 105 words per minute

**Chapter 10 review, pp. 770-771**

Problems: 1, 5, 9, 11, 13, 15, 23