Mathematics 3113-005 - Introduction to ODE - Spring 2002
Information about the Final Examination
The Final Exam will be in the usual classroom on May 8, 2002, from 1:30 to 3:45. Notice that
you will have an extra 15 minutes to work, if you need it, so there should be no need to hurry
through the exam, and there should be time to check your work for careless errors.
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.
You will be given a list of formulas for the Laplace transform, identical to the one you
received with Exam III (you can view it here).
The exam will be worth 77 points, and will cover the sections shown in the table below, which
gives the approximate point breakdown by section of the text:
| 1.3 | 3
|
| 1.4 | 3
|
| 1.5 | 7
|
| 3.2 | 9
|
| 3.3 | 2
|
| 3.5 | 8
|
| 3.8 | 6
|
| 4.1 | 4
|
| 4.2 | 5
|
| 7.2 | 8
|
| 7.3 | 3
|
| 7.5 | 6
|
| 7.6 | 3
|
| 8.1 | 10
|
| Total | 77
|
The following topics will definitely be covered (of course, the exam is not limited to
these topics):
| 1.
| The theory of linear differential equations.
|
| 2
| Solving first-order equations using an integrating factor.
|
| 3.
| 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).
|
| 4.
| Variation of parameters.
|
| 5.
| Finding eigenvalues and eigenfunctions for boundary value problems.
|
| 6.
|
Writing a higher-order equation or system of higher-order equations as a system of first-order
equations.
|
| 7.
|
Calculating transforms and inverse transforms,
and using the transform to solve equations and systems of equations.
|
| 8.
|
Analytic functions, and power series methods from section 8.1.
|
You should know basic trigonometric identities, Cramer's rule, power series for e^x, sin(x),
cos(x), and the general formula for the Taylor series of a function f(x) at x=a.
You do not need to review slope fields, Bernoulli equations, vibrations, over- and
under-damping, partial fractions. phase-angle form, the Wronskian or the Amazing Theorem.
You can see two sets of exams that I wrote for this course in previous semesters, on the website for the Spring,
2001 course.