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 guideline, 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, WeBWorK and worksheet problems for the chapters given below. I have also compiled a list of additional practice problems.
14.5: Know how to find the gradient of a function and the directional derivative with respect to a given vector. (You should also know their geometric interpretations.) Also make sure you know how to use gradients to find the derivative of a function defined along a space curve (via the chain rule for paths).
14.6: You should be able to carry out the chain rule in general. 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 constraint equation. (You do not need to know how to use Lagrange multipliers with several constraints at the same time.) 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, and be able to identify situations in which the integral can only be solved analytically by switching these limits.
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. Once again, you should be able to switch limits of integration.
11.3 & 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. For this exam, you may use this pdf of conversion tables.
Maintained by ynaqvi and last modified 03/30/15