http://interval.louisiana.edu/courses/350/fall-2002-math-350_exam_hints.html

### Math. 350-01, 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.

/ 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 closed-book, but you will be using the computer for some of the problems.  Here are the hints:

1. Be able to distinguish between linear and nonlinear differential equations, and be able to state the order of a differential equation.
2. Know how to solve an initial value problem involving a linear first-order differential equation involving non-constant coefficients.
3. 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.
4. Know how to find equilibrium points and determine whether they are asymptotically stable, unstable, or simply stable.
5. A problem from §2.5, pp. 84--89 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 open-book, on-computer.  You should

1. be able to solve by hand any kind of initial value problem involving constant-coefficient second order homogeneous ordinary differential equations (whether there are two real roots, one real root, or complex roots of the characteristic equation);
2. be able to solve by hand an initial value problem involving any constant-coefficient second order non-homogeneous ordinary differential equation (using either undetermined coefficients or variation of parameters);
3. be able to check the solutions for items 1 and 2 above using DSolvefrom Mathematica;
4. understand the concepts of amplitude, frequency and quasi-frequency, and critical values in mechanical systems (damped spring systems) and in linear electrical circuits involving inductance, capacitance, and resistance. There will be a somewhat non-routine word problem involving this.
Postscript copy of the second exam
PDF copy of the second exam