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{\bf Math 325, Spring 2001}
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  {\bf Tips for Studying for the Midterm}
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 The midterm is Wednesday, March 8.  It will
cover everything we have done so far, so Sections 4.1-4.4, 8.1, 8.3,
8.5,
 Chapter 7, and Sections 9.1-9.2 (up to \emph{The Oscillating
   Pendulum}
on p.\ 473) in Boyce and DiPrima and
Chapters 5, 7, 8, and 12
of {\it Differential Equations with Maple}.
You may bring a summary (one side of an  $8\frac 12'' \times 11''\/$
sheet of paper, with notes in your writing) to the midterm.


Since you are allowed to bring in notes,
I am not testing your ability
to memorize formulas, algorithms, rules, etc.  
As you know by now, it is easy to get a computer to solve many ODE and
systems of ODE, often explicitly, and almost always numerically.  That
means that the ability to do computations by hand is much less
important. An understanding of the theory, an ability to
tell whether computer output is reasonable, and the ability  to interpret the
output
is very important.  


What should you expect the exam to look like?
It will have four problems, some with several parts, each worth 20-30
points. 

At least two of the problems will involve computing solutions.
What kind of problems have you learned how to compute solutions for
this semester?  Higher order constant coefficient
 linear equations and first order 
constant coefficient systems.  I won't ask you to compute a numerical
solution---that is best done by computer.   


Since you have done a fair amount of work with Maple, I will want
to test your ability to write simple Maple code.  The simplest way
for me to do that is to add a part to a computational problem
which asks you to write Maple code to solve the problem (either
explicitly or numerically), to plot the solution and/or 
to evaluate the solution at a specific time.  This means that the
problem will have to be an initial value problem.  So, while you are
reviewing how to solve such problems by hand, you might also want
to try them with Maple.

You're probably thinking, ``But when I do a Maple problem for
homework,
if my Maple code doesn't work, I can tell and correct it.''
Unfortunately,
I have no way to let you do that during the exam, so I'll do the next
best thing.  The last sheet of the exam will be a bonus problem for
you to remove from the rest of the exam, take with you, and turn in
no later than the start of class on Friday, March 9.
The problem will be to write down your solution from the exam and try
it on a computer to see if it works.  If not, figure out what is wrong
and correct it.


How can I test your ability  to
tell whether computer output is reasonable and if so, to interpret it?
 You have had some lengthy Maple problems from Problem Set C and
Problem Set F.
I will guarantee at least one problem (and at most two)
 in which you are
shown a Maple worksheet which has the Maple input and output but no
comments.  The worksheet will have some relationship to one of the
lengthy Maple problems.  You will  be asked various questions connected with
the worksheet.  How can you study for such problems?  Make sure you 
understand how to answer \emph{all} the questions you were asked
on the Maple problems from Problem Sets C and F.  If you were 
just shown the Maple input and output, would you be able to answer
all the questions?  Would you be able to tell what the point of 
the Maple worksheet was?  You might look at the solution of \#3 on Problem 
Set C at the back of the Maple book (without looking at the actual
problem).  Cover up all the explanations and just
 look at the input and
output.  See how much you can figure out about what the problem was
and what information is contained in the Maple output.  Now go back 
and look at the problem. Answer any questions you haven't already
answered.

While some of the problems may require an understanding of theory,
or be a lot easier if you do understand some theory, I won't test
that understanding very directly.  By that, I mean
there will be no problems of the type that often cause you the most 
trouble in homework---none involving reading abstract mathematical
statements or doing proofs.

 
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