Exam II will be held in the usual room at the usual time: 10:30-11:20 on Wednesday Mar. 12. It will start promptly at 10:30, so make sure you're on time. The test will cover sections 13.3, 14.1, and 14.3 - 14.8.

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:

• computing arc length and curvature of a parametrized curve; finding normal and binormal vectors along the curve
• level curves of a two-variable function; level surfaces for a 3-variable function; visualizing the graph z = f(x,y) from level curves
• partial derivatives (definition, meaning in terms of slope of a line); second partial derivatives; Clairaut's theorem
• finding the tangent plane to z=f(x,y) at a point; using the tangent plane to estimate f nearby; the linear approximation L(x,y); differentials, using them to estimate errors
• the multivariable chain rule
• directional derivatives, gradient vector, relation between them; geometric meaning of the gradient vector
• finding local maxima and minima, classifying critical points using the second derivatives test; finding absolute maxima and minima, by considering also the boundary of the region
• Finding maxima and minima subject to a constraint, using the method of Lagrange multipliers (two or three variables)

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 I recommend 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.