http://interval.louisiana.edu/courses/350/fall-2004-math-350_exam_hints.html

### Math. 350-02, Fall, 2004 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 and PDF formats.  Postscript format, that can be printed with a Postscript printer, and can  be viewed and printed with Ghostscript and GSview.  PDF files can be viewed and printed with Adobe Acrobat Reader.

The first exam:
The exam will be on Friday, September 17.  It will be closed book.  For studying, concentrate on the following:

• Be able to classify differential equations as linear or nonlinear, and be able to explain why. Be able to state the order of a differential equation, and be able to identify the independent and dependent variables.
• Be able to solve, by hand, first order linear initial value problems, as well as separable equations.
• Be able to formulate, solve, and answer questions about mathematical models involving first-order differential equations, as we discussed in class and as in §2.3 of the text.
• Be able to state intervals in which particular initial value problems have unique solutions, or else be able to show that a solution either doesn't exist or is not unique.  Along these lines, you should memorize Theorem 2.4.1 and Theorem 2.4.2 of the text.
Be sure to bring your student ID to the first exam.
Postscript copy of the first exam
PDF copy of the first exam

The second exam:
The exam will be on Wednesday, October 13.  It will be closed book.  For studying, concentrate on the following:

• This exam will focus on the manual solution of linear constant coefficient second order ODE's.  Be sure to be able to do the following:
• Write down the characteristic equation to solve a constant coefficient linear homogeneous ODE, when the roots of the characteristic equation are distinct.
• Know how to handle multiple roots of the characteristic equation.
• Know how to handle complex roots of the characteristic equation.
• Know how to write down the general solution to a non-homogeneous constant coefficient linear differential equation, if the forcing term is of a particular form, whether or not the forcing term is a solution of the corresponding homogeneous ODE.
• Know how to solve corresponding initial value problems.
• Know how to compute the Wronskian to determine whether two solutions to a linear (not necessarily constant coefficient) homogeneous ODE are linearly independent (i.e. whether they form a fundamental set).
• Given a fundamental set for a non-constant coefficient homogeneous linear ODE, solve a corresponding initial value problem.
Postscript copy of the second exam
PDF copy of the second exam

The third exam:
The third exam was on Wednesday, November 3.

The fourth exam:
The third exam was on Wednesday, November 17.

The final exam

The following will be on the final exam:

• a problem solving an initial value problem by writing down the characteristic equation.
• a problem solving an initial value problem by Laplace transforms.
• a problem using series to solve an initial value problem.
• a problem solving an initial value problem by converting to a system and using and computing eigenvalues and eigenvectors. In this problem, be prepared to do computations with complex eigenvalues and eigenvectors.
Postscript copy of the final exam
PDF copy of the final exam