http://interval.louisiana.edu/courses/350/fall2002math350_exam_hints.html
Math. 35001, Fall, 2002 Hints for the Exams
Instructor: R.
Baker Kearfott, Department
of Mathematics, University of Louisiana
at Lafayette
Office hours
and telephone, Email: rbk@louisiana.edu.
Home
page for the course
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 exam will be closedbook, but you will be using the computer for
some of the problems. Here are the hints:

Be able to distinguish between linear and nonlinear differential equations,
and be able to state the order of a differential equation.

Know how to solve an initial value problem involving a linear firstorder
differential equation involving nonconstant coefficients.

Know how to plot direction fields, how to recognize equilibrium points
on a direction field, and how to recognize whether the equilibrium point
is stable or unstable.

Know how to find equilibrium points and determine whether they are asymptotically
stable, unstable, or simply stable.

A problem from §2.5, pp. 8489 of Boyce and diPrima (seventh edition)
will be used as an example for the preceeding two aspects.
Postscript
copy of the first exam
PDF
copy of the first exam
The second exam: Tuesday,
November 5
The exam will be openbook, oncomputer. You should

be able to solve by hand any kind of initial value problem involving constantcoefficient
second order homogeneous ordinary differential equations (whether there
are two real roots, one real root, or complex roots of the characteristic
equation);

be able to solve by hand an initial value problem involving any constantcoefficient
second order nonhomogeneous ordinary differential equation (using either
undetermined coefficients or variation of parameters);

be able to check the solutions for items 1 and 2 above using DSolvefrom
Mathematica;

understand the concepts of amplitude, frequency and quasifrequency, and
critical values in mechanical systems (damped spring systems) and in linear
electrical circuits involving inductance, capacitance, and resistance.
There will be a somewhat nonroutine word problem involving this.
Postscript
copy of the second exam
PDF
copy of the second exam
The third exam:
Postscript
copy of the third exam
PDF
copy of the third exam
Third
exam answers, page 1
Third
exam answers, page 2
Third
exam answers, page 3
Third
exam answers, Mathematica notebook
The final exam:
Postscript
copy of the final exam
PDF
copy of the final exam
Final
exam answers, page 1
Final
exam answers, page 2
Final
exam answers, page 3
Final
exam answers, Mathematica notebook with problem 5 and checking the other
problems