I have not included calculus of variations problems in the sample
final problems, because I have realized there were quite a few of them
already on the last homework. Some topics which were extensively
covered by the first and second midterm sample problems, such as
solving the geodesic equations explicitly, are not on the sample
final, but are likely to show up on the real final. Watch out!
The Final Exam is coming May 14, 4-6 pm, in the regular class
room VinH 301. The final covers what we have studied in class
during the term and Sections 1.1-3, 1.5, 2.1-2.4, 3.1, 3.2, 3.3
(through p. 101), 3.4, 3.5, 4.1, 4.2 (skipping the proof of Theorem
2.2), 4.3, 4.5, 5.1, 5.2 (through p. 159, Example 2.1), 5.5, 6.2, 6.3,
6.5, 6.6, 8.1, 8.2 (pp. 264-266), and 8.5 (pp. 287-289) of the
textbook. It will be a closed-book, closed-notes exam. The formulas
for K and H on p. 91, the first and the second fundamental forms for a
surface of revolution from p. 100, and the geodesic equations from
p. 156 will be provided on the exam. Remember that the final is 45%
worth your grade in class. This means you need a lot of study and good
luck!
Before the final, which will be Tuesday, May 14, 4-6 p.m. in our
regular classroom VinH 301: Monday, May 13, there will be a
Review Session (VinH 211) 3-4 p.m., and office hours
(VinH 324) 2-3 and 4-5 p.m. I am going to post a collection of review
problems for the final later this week.
The mean on the second midterm was 27 out of 40. This is very good,
especially if you compare it to the first exam!
I have made a correction in Problem 3 of the original version of
Sample Test II problem set: changed s to s^2 in s = u^2 + 1. Sorry.
There will be no homework due during the test week (May 1). I will
just post a collection of sample test problems within today or
tomorrow. A Problem Session before Hour Test II will be on
Monday, April 29 from 5 to 6 p.m. in VinH 301.
Hour Test II is coming May 1, during the regular class
meeting. The test covers what we have studied in class since the
first test and Sections 3.1, 3.3 (through p. 101), 3.4, 3.5, 4.1,
4.2 (skipping the proof of Theorem 2.2), 4.3, 4.5, 5.1, 5.2 (through
p. 159, Example 2.1), 5.5, 6.2, 6.3, 6.5, and 6.6 of the textbook. It
will be a closed-book, closed-notes exam. Although the problems will
be not oriented on what we studied before Hour Test I, knowledge of
the previous material is absolutely necessary to solving many problems
on surfaces. The formulas for K and H on p. 91 will be provided on the
test, if needed. There will be more computational problems on this
test, as compared to the previous one.
Sunday: 5:15 pm: I have changed Problem 3 to a different problem since
the original posting. Please, make sure to download a correct copy:
Problem 3 should be about the surface x^2 + y^4 + z^6 = 1.
You should ignore the questions about geodesics in Problems 5.5.2 and
5.5.4 from Problem Set 10. In the second part of Problem 5.5.10, the
book has a misprint. It is supposed to be: Show that v(u) = 2 arctan
exp (a+bu) -pi/2 and show that such curve has a straight line as its
I-image.
I will be out of town Monday, April 15 through Thursday, April 18
participating in a workshop in Berkeley, CA. The Monday class will be
taken over by Professor Scot Adams. The Wednesday, April 17, class
will be rescheduled as a review/problem session before Hour Test II
which is coming on May 1. The homework will be due Friday, April
19. The week of April 15-19, I will hold only my Friday office
hours 2:30-3:30 p.m. You are very welcome to make an appointment with
me for some other time or just stop by.
I will be out of town Tuesday, April 2, through the morning of
Wednesday, April 3. My office hours, 2:30-3:30 p.m. Tuesday and 10-11
a.m. Wednesday, will be canceled. You are very welcome to make an
appointment with me for (or just stop by) Monday or see me Wednesday
from about 12:30 p.m. before the class.
I will be out of town Friday, March 29. Prof. Scot Adams is going to
substitute for me in class. My office hours, 2:30-3:30 p.m. that day,
will be canceled.
The mean on Hour Test I was 15 out of 40. Oh, well, who said the test
was too simple?
I have changed a hint in Problem Set
7. Hit "Reload" when accessing it.
Although it is called an Hour Test, it will be a 50-minute test. An
hour means an academic hour, which equals 50 minutes. Also, I believe,
a 60-minute test would be unfair, because this will cause some of you
to be late for other classes and even other tests. The good news is
that there will be only four problems.
I have removed Problem 5 from the sample test, because I did not
realize how long the computations involved will be. Sorry about
that. See a newly posted copy of the sample test.
Problem Session (Makeup class For February 1): will be held
Monday, March 4, 4:30 pm in VinH 6.
Hour Test I is coming March 6, during the regular class
meeting. The test coverage is Sections 1.1-3, 1.5, 2.1-2.4, 3.1
(through Exercise 1.5), and 3.2. It will be a closed-book,
closed-notes exam. Come on, it is the IT, and we are serious
here. However, you do not need to memorize formulas for K and H on
p. 91 - they will be provided during the test.
Summer Research Experiences for Undergraduates (REU): If you
are seriously interested mathematics, you may wish to try yourself at
mathematical research during the summer. There are REU summer programs running at several excellent
national research universities, including Minnesota. One of the best
REU programs is the one at Penn State; you can request a flyer from
me.
I may be late for my office hours 10-11 a.m. Wednesday, February
6, having a doctor's appointment at 9:15 a.m. Please, wait, I will
be in my office, though. I apologize for the inconvenience.
I added a hint to Exercise 1.1.4 in Problem Set 1.
Friday, January 25 - today's office hours canceled, due to a family
emergency.
Friday, February 1 - class and office hours canceled. I will be in
Washington, D.C., doing an important government job. The class will be
rescheduled as a problem solving session before the first test March
6.