From ayong@uiuc.edu Wed Dec 10 10:48:21 2008
Date: Wed, 10 Dec 2008 10:48:20 -0600 (CST)
From: Alexander Yong
To: ayong@illinois.edu
Subject: Final class notes (fwd)
Some questions and answers
Q. How will the course be graded?
A. I will compute the raw score based on your exams and quizzes.
Then I will make a comparison with all students in the class. What
I like to do is start with the highest grade and assign A+ or A,
depending on circumstances. Then all students with "almost" the same
raw score will receive the same grade. Then the next group receives
the next grade etc. Usually this means that more than half of the class
receives a B-. I will also give any group that has a raw score above
90% an A, 80% a B etc, as stated in the syllabus.
Q. Will there be definitions and statements of theorems on the exam?
A. Not explicitly. You will be expected to state theorems and
definitions clearly if you use them, in order to ensure full credit.
Q. Is the exam comprehensive?
A. Yes.
Q. What material will the exam emphasize?
A. The exam will emphasize that subset of the textbook we discuss
in class, and in particular those parts which I've emphasized as
important in class.
In terms of specific types of "technique questions" a bias towards questions
that were not asked on the tests. One example is that of a mechanical systems
question. Material previously tested
will tend to arise inside questions that involve multiple techniques
(e.g., solving a mechanical system with initial data by constructing
a system of differential equations).
In terms of "theory questions" I will ask questions that test your
_basic_ understanding of the principles behind the techniques. The
tests I,II and III give examples of the level of these types of
questions.
Q. What are some of the "basic principles"?
A. If we ignore specific techniques, many of which are a consequence of the
principles, there are surprisingly few actually: here's a reasonable
list, you may add others:
1. Idea of slope fields
2. Theory of linear differential equations
3. Theory of systems of linear questions, matrices, determinants and
inverses
4. Fourier theory, including convergence theorems
5. The idea of separation of variables to solve certain partial
DE's (such as the heat equation).
6. Sturm Liouville theory (as a more general Fourier theory).
_Some_ examples of topics which are important, but which aren't
"basic principles", but rather applications include:
a. Mechanical systems
b. Endpoint problems
c. systems of DE.
Q. How can I study for this exam?
A. Do problems with an emphasis on understanding _every_ implication
you write down. For example, on test 3, many people wrote down the
endpoint conditions X(0)=X(L)=0 without explanation. Know the reason
this is true! The tests and assignments are meant to give you a list of useful
problems to work on.
Q. Will there be proofs?
A. Yes, both in the sense that every solution you write down, even
for a technique question is a "proof" of your solution, as well as in
the sense that I will ask you to prove things in the abstract, testing
your understanding of basic principles. Your textbook has a number of
proof problems for practice.
Q. How hard will the test be?
A. This is difficult to judge in advance! However, my goal is to
make the test about the same difficulty as Test 3.
Q. I thought Test 3 was hard, why make the exam so hard?
A. My goal is to make the test tough but fair. In answer to this
question, there are a few notes. I wanted to make the tests gradually
more difficult so that one could ease into the level of hardness. The
desire after all is to make you stronger mathematically than you were
when you entered in September, both from a technical point of view,
and as a problem solver. So Test 1 was intentionally "softer" to help
build your self confidence.
Also a tough test allows everyone to improve their standing more. An
easy exam, for example, where everyone scores 100% will not improve
_anyone's_ final grade.
Finally, we (and I do mean you and I) want solid standards for our
institution!
Q. Will there be extra office hours?
A. Yes, I will be have extended office hours 1-4pm next Monday and Tuesday.
Q. When will the exam be?
A. Hence our final is 1:30-4:30PM on December 17th, 2008.
Q. Where will the exam be?
A. It depends on th FIRST LETTER of your LAST NAME. If it is A-K
inclusive, go to 229 NHB (Natural History Building). If it is
L-Z inclusive, go to 161 Noyes Lab.
Q. What if I go to the wrong room?
A. Your exam will be confiscated and you will receive a score of 0.
Q. Why take such a tough stand?
A. I _hate_ to! The fact is that for a large class such as ours, one
needs to have firm admistrative guidelines to ensure things run smoothly.