Mathematics 3113-005 - Introduction to ODE - Spring 2002
Information about Exam II
Exam II will be in the usual classroom on March 14, 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 53 points, and will cover sections 3.2-3.5 and 3.8. The approximate
point breakdown by section of the text is as follows:
| 3.2 | 9
|
| 3.3 | 6
|
| 3.4 | 8
|
| 3.5 | 20
|
| 3.8 | 10
|
| Total | 53
|
The following topics will definitely be covered (of course, the exam is not limited to
these topics):
| 1.
| The recipe for writing down the general solution of a linear
homogeneous DE, using the characteristic equation.
|
| 2.
| The method of undetermined coefficients --- writing trial solutions and
using them to find a particular solution. The formula
x^s ( (A_0+A_1 x+...+A_n x^n) e^{rx} cos(kx)
+ (B_0+B_1 x+...+B_n x^n) e^{rx} sin(kx) )
will be given, but without any further explanation (that is, you need to know what s, n, r,
and k mean).
|
| 3.
| The theory of nth-order linear equations, as summarized on the handout
sheet.
|
| 4.
| The method of variation of parameters.
|
| 5.
| Finding eigenvalues and eigenfunctions for boundary value problems.
|
| 6.
| Writing A cos(wx)+B sin(wx) in phase-angle form.
|
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.