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 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, WeBWorK and worksheet problems for the chapters given below. I have also compiled a list of additional practice problems.
Note that you may bring one sheet (standard letter size, front and back) of handwritten notes to the exam. You will be required to hand this in with your final.
15.4: You must know how to convert integrals in rectangular co-ordinates to integrals in one of the other (polar) 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.
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 as the work done by a force in moving something along an oriented curve.
16.3 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 as the flux across a surface.
17.1-17.3: You will be given the statement of Green's Theorem, Stokes's Theorem, and the Divergence Theorem. You should 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 that a vector field with a divergence of 0 must be the curl of some other vector field.
Maintained by ynaqvi and last modified 04/27/15