http://interval.louisiana.edu/courses/350/spring2000math350_exam_hints.html
Math. 35001, Spring, 2000 Hints for the Exams
Instructor: R.
Baker Kearfott, Department
of Mathematics, University of Louisiana
at Lafayette
Office hours
and telephone, Email: rbk@louisiana.edu.
This page will change throughout the semester.
/ The first exam /
The
second exam / The third exam /The
final exam /
Note: Previously given exams are available below
in Postscript format, that can be printed with a Postscript printer.
The files can also be viewed and printed with Ghostscript
and GSview.
The first exam:
The first exam will be openbook, opennotes, computeron. You
should know how to do the following.

Solve a firstorder linear initial value problem by hand by computing an
integrating factor.

Solve a firstorder equation by hand with separation of variables.

Use Mathematica to plot a family of solutions to a differential equation
corresponding to different initial values.

Be able to print your Mathematica notebooks.

Know how to compare your manually derived solutions to solutions obtained
with Mathematica. (Be prepared to write down a short discussion paragraph.)
Answers,
page 1 (GIF)
Answers,
page 2 (Mathematica notebook)
Answers,
page 3 (GIF)
Answers,
page 4 (Mathematica notebook)
Postscript
copy of the exam
The second exam:
The exam will be openbook, opennotes, computeron. Be sure to bring
your student ID card, since I (Prof. Kearfott) will not be proctoring the
exam.

You will determine the equilibrium solutions of a firstorder differential
equation. You will use PlotVectorField with ScaleFunction
>(1&) and AspectRatio > 1 to plot the vector field
for the differential equation, to explain which of the equilibrium solutions
are stable and which are unstable.

You will need to solve two differential equations either by hand or using
DSolve,
then plot the two solutions. These two differential equations are mathematical
models of a somewhat familiar phenomenon. You will need to discuss, based
on the graphs of the solutions, which model you think is most appropriate.
Postscript
copy of the second exam
Answers,
page 1 (Mathematica notebook)
Answers,
page 2 (Mathematica notebook)
The third exam:
The exam will be openbook, opennotes, computeron. Be sure to prepare
well, since you will be short of time otherwise.

You will need to solve by hand a homogeneous secondorder constant coefficient
ODE and a nonhomogeneous secondorder constant coefficient ODE.
You should be familiar with how to handle multiple roots of the characteristic
equation. You will check your solutions with Mathematica.
Given physical data, you will write down the differential equation
governing a damped spring system. Be sure you understand the physical
units, both in the English system and the metric system. You will
need to state the critical damping value, as well as the frequency of vibration.
You will use Mathematica to produce graphs of the solution, for various
values of the damping parameter.
Postscript
copy of the third exam
Answers,
page 1 (GIF)
Answers,
page 2 (GIF)
Answers,
page 3 (Mathematica notebook)
The final exam:
As with the exams during the semester, the exam will be openbook,
opennotes, computeron. Here is a study guide.

Be able to solve a simple initial value problem with Laplace transforms.
You may use the table in the book, or you may use Mathematica's <<Calculus`LaplaceTransform`
with LaplaceTransform and InverseLaplaceTransform.
Be sure you write down all of your steps, or hand in your notebook. You
will also need to solve the problem by another method, and show that the
answers that you get are equivalent.

Be able to compute the first few terms of the Taylor series to the solution
of an initial value problem that does not have constant coefficients.

Be able to solve a higherorder (that is, higher order than 2) constant
coefficient differential equation by writing down the characteristic equation
and by using undetermined coefficients. Also, be able to show that
your solution is equivalent to a solution that you obtain another way.

Be able to solve an initial value problem for a differential equation that
is an Euler equation, or else for a differential equation that has a regular
singular point. Understand that the solutions to such problems are
not necessarily unique.
Postscript
copy of the final exam
Answers,
page 1 (GIF)
Answers,
page 2 (GIF)
Answers,
page 3 (GIF)
Answers,
page 3b (Mathematica notebook)
Answers,
page 4 GIF)