You should know how to access the Web, my
homepage, and the relevant pages for
this class which you will find through my homepage. In particular,
homework
assignments and announcements will be posted there.
You will find frequent references in the
textbook to computer algebra systems, and in particular MAPLE. While
we do not REQUIRE that you use MAPLE in this course, we will from time
to time suggest that you look at a problem that will require some
computer software. Use whatever system you know. If your MAPLE skills
are rusty, or if you would like to learn how to use MAPLE for these
problems, you may ask me for help or a MAPLE reference OR you may go
to the
go to the MAPLE tutorial developed
by the Los Alamos National Laboratory.
It is CRUCIAL that you learn to
do problems "by hand" as
well as using the computer. There is a good reason for this
statement. Computer systems are not infallible; there is NO
software system of any complication, and certainly MAPLE is one such
system,
which does not have bugs. With any such software system when used
systematically, human intervention is frequently necessary. This
means you need to:
- (a)
- Understand the theory and the methods of
computation well enough to make intelligent choices about what to
tell a machine to do.
- (b)
- Develop sufficient intuition so as to be able to tell
whether an answer displayed by the machine is a reasonable answer.
- (c)
- Be able to check, in basic situations, what a correct
answer is, so as to be able to work independently from the machine
when necessary.
In order to earn a "C" grade in this class you MUST be able to
compute with paper and pencil both quickly and accurately.
There are certain skills that you learned
in your first calculus
classes that will be used many times in M342.
You may find it worthwhile to review these topics. Just as you
cannot successfully complete a calculus course without knowing basic
algebra, you cannot successfully complete M342 without being
PROFICIENT at:
- (a)
- using the chain rule, especially in change-of-variable
problems ;
- (b)
- using the Fundamental Theorem of the Calculus;
- (c)
- being able to compute easily both derivatives and integrals involving
the basic functions introduced in M242 and M243. In particular, to be proficient
with the method of integration by parts, partial differentiation, and
basic vector computations;
- (d)
- being able to compute quantities such as the arc length of a curve,
centroids, and volumes of solids of revolution.
- (e)
- being able to use the method of partial fraction decomposition
Examinations in this course are designed
to find out three
things:
- (a)
- Can you compute quickly and accurately by hand?
- (b)
- Are you able to analyze basic "word problems" which often
illustrate applications that you will find useful in OTHER classes?
- (c)
- Do you have a sufficient command of the ideas of this
course to solve problems that you have NOT MET BEFORE? This is,
after all, the aim of any course: to develop ability to use the
skills you learn!
Experience has shown that to pass this course
you should devote
two hours outside of class for every hour in class. Note that this
requires you to spend a total of nine hours (minimum) each week on
M342. This amount of time is a little more than one full working day
per week of a routine nine-to-five job!