The following is a chapter by chapter guide intended to help you organize the material we have covered in class as you study for your exam. It is only intended to serve as a guidline, and may not explicitly mention everything that you need to study. The exam will focus on chapters covered since the last midterm, but some of these chapters do rely on older material, so it is important that you remember the material from earlier chapters as well. It is also still important that you are comfortable with the basics of differention and integration (as covered in Calculus I and Calculus II classes).
Please review all homework, quiz and workshop problems for the chapters given below. I have also compiled a list of additional practice problems.
14.6: You should be able to carry out the chain rule in general (either using the method in the textbook, or using matrices, as discussed in class). You should also be able to use the chain rule for differentiating implicit functions.
14.7: Know how to identify and classify critical points of a function, and how to find global maxima and minima. You do not need to know the proof of the second derivative test or Theorem 4 of this chapter.
14.8: Know how to use Lagrange multipliers to optimize a function subject to one or more constraint equations. Note that the methods in this section can also be used to find the maximum and minimum values of a function on the boundary of a closed, bounded domain.
15.1 & 15.2: These sections cover double integrals over rectangles and more general domains in ℝ2. Make sure you know how to find the limits of integration and how to find the double integral by calculating the iterated integral. Also know how to switch limits of integration. In addition, you should be able to find the average value of a function of two variables over a given domain.
15.3: This section is analogous to the previous one. You should once again be able to find limits of integration, and to find the triple integral by calculating the iterated integral. You should also be able to switch limits of integration. Finally, you should know how to find the average of a three variable function, including how to find the centroid and center of mass of a given three dimensional domain.
12.7: You should know how to convert between the various co-ordinate systems given in this section, including how to describe sets of points or functions given in one system in terms of one of the others.
15.4: You must know how to convert integrals in rectangular co-ordinates to integrals in one of the other co-ordinate systems, both in terms of finding the new limits, and knowing the correct expansion factor by which you need to multiply the integrand. Practising problems here will help you become more comfortable with identifying the most efficient co-ordinate system to use for a given problem.
15.5: Practise finding the appropriate change of co-ordinates to simplify your integral, by either simplifying the domain or the function. Know how to find the Jacobian determinant and use it to calculate (or approixmate) the change in area of a domain. Finally, make sure you know the change of variables formula for double and triple integrals.
Maintained by ynaqvi and last modified 11/01/11