Exam III will be held in the usual room at the usual time: 12:30-1:20 on Monday Nov. 19. It will start promptly at 12:30, so make sure you're on time. The test will cover sections 14.8, 15.1 - 15.4, 15.7 - 15.9.

The test will have four problems, possibly with several parts each. Calculators or other mechanical assistance are not needed and are not to be used.

The following topics are likely to be covered, though the exam is not limited to these topics:

• solving optimization problems using Lagrange multipliers
• Riemann sums for double and triple integrals
• average value of a function of 2 or 3 variables
• integrating over 2- and 3-dimensional regions using iterated integrals in x, y, z
• describing regions and integrating over them using polar coordinates, cylindrical coordinates, and spherical coordinates
• finding volumes and areas using integrals
• conversions between different coordinate systems

We did not cover "two constraints" on p. 985 or moments, center of mass, moment of inertia, or centroid mentioned on p. 1047.

Advice: I recommend first reviewing homework problems from each section, perhaps doing a few odd-numbered ones and checking your answers. If you get one wrong, don't skip ahead, but tackle it right away and find out how it works. There may be a similar example worked out in the section, or among one of our graded problems, or you can try getting help. I also recommend the "Concept Check" questions at the end of each chapter as a way of finding out where to focus your efforts. There are extra problems there too that are worth trying out.

When it comes time for the test itself, relax and do the best you can. Because you have studied, you know which topics you know best, and can get those problems out of the way quickly. Then you'll have plenty of time to spend on the remaining ones.

Here is a past exam from Calc 4 which covers much of the same material. You might want to try it under realistic conditions (with a time limit, etc). The solutions are here.