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\centerline{Mathematics 304 -- Ordinary Differential Equations}
\centerline{Review Sheet -- Exam 2}
\centerline{November 8, 2000}
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{\it General Information}
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The second midterm exam this semester will be given in class on 
Thursday, November 16, as announced in the class last week.  This 
will be an {\it open-book} exam, and you may use calculators at
any point.  The reason for this is the relatively complicated
forms of particular solutions for inhomogeneous second order linear
ODE from section 4.8.  {\it Be well prepared on that and the other
topics below, though.  You will not have enough time to complete the 
exam if you need to look everything up in the text!}

The exam will cover the material from Chapters 4 and 5 of the text
that we have studied since the first midterm (see specific
topics and review problems below).  

If there is interest, I would be happy to arrange a late afternoon
or evening review session for the exam.  Tuesday, November 14 is probably
the best day to aim for.
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{\it Topics To Be Included}
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\item{1)}  The theory of second order linear ODE:
the existence and uniqueness theorem
for solutions, fundamental sets of solutions for homogeneous equations,
the Wronskian and Abel's identity, general solutions of inhomogeneous equations.
\item{2)}  The constant coefficient case -- the auxiliary equation,
forms for solutions when the roots are real or complex.
\item{3)}  Superposition and the method of undetermined coefficients
for inhomogeneous equations.
\item{4)}  First order systems -- critical points and their classification,
the phase plane, trajectories and integral curves.
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\noindent
{\it Suggested Review Problems}
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\item{} From \S 4.2: 1-10, 19-22
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\item{} From \S 4.3: 7-13, 15, 19, 26
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\item{} From \S 4.5: problems like 13-20, 39-42,
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\item{} From \S 4.6: problems like 21-28
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\item{} From \S 4.7: 13, 14
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\item{} From \S 4.8: problems like 25-32, 58, 59
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\item{} From \S 4.10: 3-6
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\item{} From \S 4.12: 3, 5
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\item{} From \S 5.2: problems like 1 - 24, 29, 35a,b,c
\bye