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 be slightly weighted towards chapters covered since the last midterm, but this exam is cumulative, 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.
16.1: This section deals with the basics of vector fields, and what they represent. It is really important to understand this section since all subsequent sections build on this material.
16.2 This section generalizes arc length integrals from Section 13.3. You should be able to find the line integral of a scalar function and of a vector field over a given space curve. You should also be able to interpret the vector line integrals physically and geometrically.
16.2 You must know the Fundamental Theorem for Conservative Vector Fields, and how to identify when a given vector field is conservative. You should also know how to find a potential function for such vector fields, and be able to identify situations where this is useful for evaluating an integral.
16.4: Make sure you practice finding parametrizations of surfaces, especially for cones, cylinders and spheres, along with their parametrization domains and normal vectors. You should also know how to find the surface integral of a scalar valued function.
16.5: You should know how to integrate vector fields over a surface, and how to interpret this physically and geometrically. You will not be explicitly examined on the examples of fluid flow and electromagnetic induction, but these examples are useful for understanding this physical and geometric interpretation.
17.1-17.3: You must know the statement of Green's Theorem, Stokes' Theorem, and the Divergence Theorem, and be able to use them to obtain the value of a given integral. (In particular, you should be able to see how these theorems give analogues to the Fundamental Theorem of Calculus.) Make sure you know how to identify the boundary of a given surface or volume, and how to determine its orientation. You should also be comfortable with finding the curl and divergence of vector fields and know how to use the ideas of curl and divergence to get vector potentials.
Maintained by ynaqvi and last modified 12/10/13