Final Exam Information for Fall 2009 Math 208

As you know, the final exam is a unit exam, meaning that all students of Math 208 take it at the same time, and comprehensive, meaning that anything in the common syllabus is fair game. You should also know that the preparation of the exam is a collective effort by all instructors of 208, so you shouldn't expect it to look like two hour exams from your own section folded together. As a matter of fact, anything's fair game, and I cannot offer any clues or hints as to what is specifically on the final exam you'll be taking. However, I can do my best to help you prepare for the final. It is your responsibility to determine the topics on which you need to get help from me.

"Anything's fair game" is a mouthful for this course. So what should you study? An easy answer is "what's on the final." As a matter of fact, that isn't as facetious as it sounds. You can pick up some pretty good clues as to what's expected of you by looking at old finals. Towards the end of the semester it is even possible to obtain a copy of several old unit finals from the University Book Store for a small price, compliments of the math department. You should hustle over and buy copies as soon as they become available.

In the interests of helping you sort out priorities, I did a little research on some old unit finals of which I happen to have copies. Since these are a matter of public record, I can provide information for you about their contents. These are the Fall '92, '93, '97, '01, '02, '03, '04, '05, '06, '07 and '08, along with the Spring '01, '03, '04, '05, '07, '08 and '09 exams. Below is a an outline of the sections of the text (formerly Smith and Minton, Weir and Thomas since 2007) that we cover in Math 208, together with a classification of all the problems that I found on these unit exams according to which section they belong. I listed both the frequency of questions on this topic in parentheses and the topic. Some problems could fit into two sections. In such cases I chose the predominant section unless it was very evenly split, in which case I split the question. This should give you a pretty good idea of what's important. Note that since we have switched texts and changed the syllabus, the problems from Chapter 11 are no longer relevant to Math 208 since this chapter is covered in Math 107. Also note that I'm counting the number of problems, not the total points per question, though these numbers correlate reasonably well. ¹

Chapter 10: Vectors and the Geometry of Space (27 problems)

10.1: Three-dimensional Coordinate Systems

10.2: Vectors

10.3: Dot Product

10.4: Cross Product

10.5: Lines and planes in space

10.6: Cylinders and Quadratic Surfaces

Chapter 11: Vector-Valued Functions (10 problems)

11.1: Vector-valued Functions

11.2: Calculus of Vector-valued Functions

11.3: Motion in Space

Chapter 12: Partial Derivatives (83 problems)

12.1: Functions of Several Variables

12.2: Limits and Continuity in Higher Dimensions

12.3: Partial Derivatives

12.4: The Chain Rule

12.5: Directional Derivatives and Gradient Vectors

12.6: Tangent Planes and Differentials

12.7: Extreme Values and Saddle Points

12.8: Lagrange multipliers

Chapter 13: Multiple integrals (65 problems)

13.1: Double and Iterated Integrals over Rectangles

13.2: Double Integrals over General Regions

13.3: Area by Double Integration

13.4: Double Integrals in Polar Form

13.5: Triple integrals in Rectangular Coordinates

13.6: Moments and Center of Mass

13.7: Triple Integrals in Cylindrical and Spherical Coordinates

Chapter 14: Vector Calculus (90 problems)

14.1: Vector fields

14.2: Line integrals

14.3: Independence of path and conservative vector fields

14.4: Green's Theorem

14.5: Curl and divergence

14.6: Surface integrals

14.7: Stokes' Theorem

14.8: Divergence Theorem and Unification