Home page for the course

This page will change throughout the semester.

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.

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.

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

Postscript copy of the third exam
PDF copy of the third exam
Third exam answers, page 1
Third exam answers, page 2

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

Postscript copy of the fourth exam
PDF copy of the fourth exam
Fourth exam answers, page 1
Fourth exam answers, page 2

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.