Exam III will cover sections 15.7, 16.1-16.9, and the surface area of the graph of a function, but only the material that we discussed in class, and obviously not every single item can be covered in depth. About 3/4 of the exam is Chapter 16, the rest is section 15.7. The current and probably final draft has 60 points possible.

To ensure that there is sufficient time for you to try all the problems, most of the exam will be in the usual classroom on Monday, November 14, but the part on section 15.7 will be during the first portion of the problem session on Tuesday, November 15.

Be sure you follow the instructions of each problem, and give the answers requested, without spending time on anything that is not needed. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others. Many of the questions will have rather short solutions, if you know how to do them, so if you find yourself doing something lengthy and unusually complicated on a problem, it might be best to move on to other problems and come back later to it later if you have time.

Calculators are not needed, although you may, if you really want to, use a non-graphics simple arithmetic calculator without even trig functions or log and exponential, but no mechanical or electronic device more sophisticated that this (including iPods, earpieces, etc.). Blank paper will be provided, so all you will need is something to write with. Please write your solutions on the blank paper. You may have as many sheets as you need, and may put the problems in any order. Please put your name on your exam paper and all pages of your solutions, and hand them all in together, although without any pages of scratch work that is not to be graded.

Most of the exam problems will be very similar to homework problems, while others will draw upon the material presented in the lectures. Definitions of important concepts are perfectly reasonable questions, and although you do not need to know them word-for-word, you should be able to write down a coherent and accurate definition of any major concept or term.

The following topics are very likely to appear, although the exam is not limited to them:

1. Critical points of functions of two variables, setting up optimization problems, finding extreme values of a function on a domain using critical points and examination of the function on the boundary.
2. Supplying limits for integrals on planar domains, in Euclidean and polar coordinates. Interchanging the order of integration.
3. Applications of double and triple integrals to mass and centers of mass. Use of integrals to find surface area of the graph of a function.
4. Triple integrals, supplying limits of integration.
5. Spherical coordinates. This is important and will be emphasized.
6. Change of variables for two-dimensional domains. The Jacobian, its computation, its geometric meaning, and its use in change of variables.

It is not necessary to memorize many formulas, for example the formulas relating Euclidean and spherical coordinates will be given. Riemann sums will not appear. Cylindrical coordinates as such are not covered--- they are just ordinary coordinates but using polars in one planar direction, so present no serious complications once you know polar coordinates. Topics that we did not cover in class, such as moment of inertia, are not covered, but note that the surface area element dS = \sqrt{1 + f_x^2 + f_y^2} dR is covered, as it is conceptually important for what we do later.

The exams from all my classes since 2000 are available at their course web pages, linked at the course pages page. Some of those classes met twice a week, so their exams were geared to a 75-minute time period.