The Final Exam will be held in the usual room on Monday May 5, 8:00-10:00 am. It will start promptly at 8:00, so make sure you're on time. The test will cover the same material that was covered in exams I - III, as well as sections 16.3 - 16.10. Some extra emphasis will be given to the newer material; probably half or more will be on chapter 16.

You are permitted to bring a 4x6 index card with notes on both sides. Think carefully about what to put on your card! Calculators or other mechanical assistance are not needed and are not to be used.

See first exam, second exam, and third exam for topics to be covered from the first three exams. For the newer material, the following topics are likely to be covered, though the exam is not limited to these topics:

• conservative vector fields and their properties
• testing for conservativity
• the fundamental theorem of line integrals
• Green's theorem, applications (eg. area)
• surface integrals, using a parametrization
• Stokes' Theorem, divergence theorem

You do not need to know the 2-dimensional version of the divergence theorem, or how to compute the line integral that appears in that theorem.

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.