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Preparing for the final
I recommend the following strategy to prepare for the final exam. The
material discussed below is all on the Web, and almost all of it can
be reached using links from this page.
Please review the two exams given already this semester. These exams,
with answers and comments, are included here. You should also review
the three quizzes we gave this semester. They, along with answers, are
included here. There is also a review sheet for the final exam. Look
over this material. If I thought it was important before, I probably
still believe it's important. The final exam is cumulative, with
somewhat heavier emphasis on the material covered since the last exam
("vector calculus"). If you insist on having even more
questions to look at, consider glancing at the Web pages for the Math
251 course I taught last semester. I don't think that's necessary and
don't recommend it. What I've suggested is already enough to prepare
for the exam thoroughly and well.
Time and place of the final exam Thursday, May 8, 1997,
from 12:00 PM - 3:00 PM, in SEC-117. Please note that this is not the
same as was listed on the syllabus for the course.
Additional office hours; review session I'll have office hours
in Hill 542 on Monday, May 5, from 1 to 4 PM, and on Tuesday, May 6,
from 10 AM to Noon. I also am teaching Math 152, so there may be
competition for my time. There will be a review session on Wednesday
evening, May 7, from 7:30 to 9:30 PM in SEC 203.
The final exam itself is now
(5/20/97) available here. Two minor misprints have been corrected, and
the formatting has been rearranged to make the exam shown more compact.
Housekeeping
Here's the
syllabus and textbook problem assignments as initially distributed.
There have been some changes in the
timing of the second exam and the syllabus.
Workshops & Quizzes
The
first "workshop" was
designed to be a diagnostic exam. The questions
asked were about material which will be used frequently in Math 251.
Solutions of workshop problems won't usually be given, but since
these problems were to be done in a limited time in the classroom, here are solutions
The second workshop
was a more standard model with problems about lines and planes. We
want students to hand in problem 3. A few extra problems were
written on the way but weren't given to students.
The third workshop was about
curves. One problem dealt with tangent lines to the twisted cubic. The
second problem, which we wish students to hand in, is a more
qualitative question on curvature.
The fourth workshop had
two problems, one about a linear approximation where one variable of a
several variable function was perturbed, and one about graphs of
functions. We'd like students to hand in the first problem.
During the next period we gave a quiz about some "elementary"
computations of two-variable limits, partial derivatives, and the
chain rule. Here are some
solutions to one version of this quiz.
The next workshop had two
problems, one about the best-fitting straight line to ex on
[0,1], and the other a geometrically pleasing but analytically
slightly intricate Lagrange multiplier problem. Both of the problems
could certainly benefit from Maple's help. We'd like students
to hand in solutions to the first problem.
Vacation begins in only a few days. Here to celebrate are the beginning of the integration
problems. The first one, very carefully written, asks readers to
discover which iterated integrals compute geometric volumes. One of
the parts of this problem is very tricky. The next two problems deal
with simple improper two-dimensional integrals, and the last problem
asks students to closely consider the signs of the functions and signs
of their integrals. We'd like students to hand in the second and
fourth problems of this set.
In this workshop we give a
"simple" double integral to be evaluated three different ways, and a
problem about center of mass, and a problem about surface area. The
engineering students and everyone else should hand in the problem
about center of mass.
Here is a sample workshop
solution , with a companion
Maple worksheet . Students may find it useful to examine
the style of this sample.
During the next period we gave
another quiz to help students review for the next exam which will
be given on April 15. The quiz included a question about critical
points, and some additional questions about double and triple
integrals. Here are some
solutions to these questions.
Maple
Introductory material similar to what was done last semester was
distributed. Then a first lab on
curvature computations was handed out. This lab included some
background expository material and was rather different from what was
given out last semester.
The second Maple lab was about
surfaces defined by second-degree polynomial equations. It was a
simpler version of last semester's second lab.
The third Maple lab was about
discovering maximum and minimum values of functions of two
variables. It was a simplified and changed version of last semester's
third lab.
The last Maple lab is
optional and should be handed in sometime before the end of the
semester to be considered for credit.
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