Math 311-101 — Final Exam Review — Summer
I, 2012
General Information
The final exam (Monday, July 2, 10:30-12:30) will have 7 to 10
questions, some with multiple parts. The topics that the test will
cover are listed below. Problems will be similar to ones done for
homework and as examples in class. I will have extra office hours on
Monday morning, 8:30-10:00 am.
-
Calculators. You may use scientific calculators to do numerical
calculations — logs, exponentials, and so on. You
may not use any calculator that has the capability of doing
algebra or calculus, or of storing course material.
-
Other devices. You may not use cell phones, computers, or any
other device capable of storing, sending, or receiving information.
Topics Covered
Topics from Tests 1 & 2
- Test 1. We will cover the material listed in
the
review sheet for Test 1, starting with subspaces of vector
spaces (Leon, chapter 3, 3.2-3.4, 3.6). You will need to know the
material from chapters 1 and 2, and section 3.1 in Leon to the extent
that it is needed to do problems from later sections.
- Test 2. We will cover the material listed in
the
review sheet for Test 2, except for the material on
similarity (Leon, section 4.3), and computing eA. You will
still need to know how to deal with coordinate vectors. However, I
will not give you any problem explicitly involving changing bases.
Vector analysis
- Be able to compute line integrals directly or via Green's theorem
(Colley, sections 6.1 and 6.2).
- Parameterized surfaces (Colley, section 7.1)
- Given a parameterization for a surface, be able to find these
quantities: standard normal N, unit normal n, vector
area element dS, and the scalar area element dS.
- Know parameterizations for spheres, cylinders, and planes. For
each of these, know and be able
to derive N, n, dS, dS.
- Surface integrals
- Be able to compute both scalar and vector surface integrals,
either directly (Colley, section 7.2), or via Stokes's
Theorem or Gauss's Theorem (Colley, section 7.3).
- Questions over vector analysis will make up 30% to 35% of the
test.
Updated: 6/28/2012 (fjn)