Mathematics 3113-005 - Introduction to ODE - Spring 2002
Information about Exam I
Exam I will be in the usual classroom on February 12, 2002. Rather than taking your usual
seat, you will need to sit so that there is no one on either side of you.
Only a basic, non-graphing calculator may be used. Actually, there is no need to use a
calculator. Scratch paper will be provided, so all you will need is something to write with.
The exam will be worth 50 points, and will cover sections 1.1-1.6 and 3.1. In addition to the
50 points, there will be a 4-point bonus problem. The approximate point breakdown by section
of the text is as follows:
| 1.2 | 4
|
| 1.3 | 6
|
| 1.4 | 8
|
| 1.5 | 9
|
| 1.6 | 6
|
| 3.1 | 17
|
| (bonus) | 4
|
| Total | 54
|
The following topics will definitely be covered (of course, the exam is not limited to
these topics):
| 1.
| initial value problems, the existence and uniqueness theorem for IVP's
|
| 2.
| separation of variables, solving first-order linear equations using
an integrating factor
|
| 3.
| solving second-order linear equations with constant coefficients and
with initial conditions of the form y(a)=b_0, y'(a)=b_1
|
| 4.
| the theory of second order linear equations summarized on the handout
|
There are no word problems on the exam. You will need to know the integrating factor method
for first-order linear equations from memory. If there is an equation of Bernoulli type to
solve, you will be given the formula v=y^{1-r}. If there is an equation that can be put in the
form y' = F(y/x), you will need to know to use the substitution v = y/x.
You can see two sets of exams that I wrote for this course in previous semesters, on the website for the Spring,
2001 course. Our exam may be a bit longer than those, since those courses had 50-minute
classes.