Math 251-502 — Final Exam Review
General Information. The final exam will be on Monday,
5/5/08. Please bring an 8½×11 bluebook. To get some idea
of what the test will be like, look at the
final exam on the math department's 251 web page and
the final
on my web page. Be aware that that you will not be given any
formulas. Also, these cover a somewhat different selection of topics
and are definitely not the same as what your test
will be. Reviews at the ends of chapter 12, 13, and 14 contain a good
collection of practice problems.
Extra office hours. Here are my office hours this week: Tuesday
(4/29), 11:30-12:30; Wednesday (4/30), 11:30-12:30; Thursday (5/1),
9:30-10:30; and Friday (5/2), 10:30-12:30 — other times, by
appointment only.
Material covered. First of all, the material in chapter 11 and
sections 12.1-12.3 will be covered to the extent that it arises in
connection with the material below.
- Chapter 12, sections 12.4-12.7.
- Chapter 13, sections 13.2-13.6, 13.8-13.11. We are skipping 13.1
and 13.7. You need to know and be able to use polar, cylindrical, and
spherical coordinates, as well as cartesian coordinates. In addition,
you need to know the area or volume elements for each of these
coordinate systems. In the case of 13.11, be able to do simple 2D
changes of coordinates.
- Chapter 14, sections 14.1-14.9. You should be able to parameterize
curves — circles, lines (in 2D and 3D), ellipses, spirals, and
functions of the form y = f(x). You should know the pararemtrizations
for spheres, cylinders, planes, surfaces of rotation, spiral ramps,
and surfaces of the form z = f(x,y). For these surfaces, you should
know and be able to derive standard and unit normals and
surface area elements. Here are some suggested problems for 14.8-14.9:
- 14.8: 2, 5, 7, 11(a)
- 14.9: 2, 11, 13, 18
Calculators. You may use calculators that do scientific
calculations -- sines, cosines, logs, arithmetic, etc. --, although
you will not need them. You may not use any calculator that
has the capability of doing algebra, calculus, graphing, or of storing
material.
Other devices. You may not use cell phones, computers,
or any other device capable of storing, sending, or receiving
information.
Structure. There will be 9 to 12 questions, some of which will
be fill-in-the-blank questions or questions involving setting up
double or triple integrals as iterated integrals, but not calculating
them. The problems will be similar to ones done for homework, or done
as examples in class or in the text. It's a good idea to review
integration formulas for the test. You should also know how to
calculate charge, mass, moments, center of mass, and moments of
inertia, and flux. The split between old material split and material
from 13.11 and chapter 14 will be roughly 40% and 60%.
Updated 4/29/08 (fjn)