Mathematics 3113-001 - Introduction to ODE - Fall 2003
Information about Exam II
Exam II will be in the usual classroom on October 23, 2003.
Only a basic, non-graphing calculator may be used. Actually, there is no
need to use a calculator. Scratch paper will be available, so all you will
need is something to write with.
The exam will be worth 56 points (not including the 4-point bonus problem),
and will cover sections 3.3-3.5, 3.8 and 4.1-4.2. The approximate point
breakdown by section of the text is as follows:
| 3.3 | 8
|
| 3.4 | 5
|
| 3.5 | 18
|
| 3.8 | 14
|
| 4.1 | 5
|
| 4.2 | 6
|
| Total | 56
|
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, and how to apply the formula to specific equations).
|
| 3.
| The method of variation of parameters. You will be given
the formulas y_1 u_1' + y_2 u_2'=0, y_1' u_1' +
y_1' u_1' = f(x).
|
| 4.
| Finding eigenvalues and eigenfunctions for boundary value problems.
|
| 5.
| Writing A cos(wx) + B sin(wx) in phase-angle form.
|
You will not need to know about pendulums, critical damping, or
pseudoperiods, nor about beam deflections and whirling strings. For this
exam, you will not need to know about trajectories, or about the Existence
and Uniqueness Theorem for Linear System.
Remember that you can find exams that I wrote for this course in previous
semesters, on the Course Pages From Previous Semesters page. For some
students, these are a useful study aid. But the lectures, homework, and
above description are your best guide to what is likely to be on our exam
this semester.