Mathematics 3113-005 - Introduction to ODE - Fall 2003
Information about the Final Examination
The Final Exam will be in the usual classroom on December 15, 2003, 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, similar to the one you received with Exam
III.
The exam will be worth 76 points, and will cover the sections shown in the
table below, which gives the approximate point breakdown by section of the
text:
| 1.4 | 4
|
| 1.5 | 4
|
| 3.2 | 6
|
| 3.3 | 4
|
| 3.8 | 8
|
| 4.1 | 2
|
| 4.2 | 5
|
| 7.1 | 4
|
| 7.2 | 8
|
| 7.3 | 3
|
| 7.4 | 3
|
| 7.5 | 4
|
| 7.6 | 5
|
| 8.1 | 12
|
| 8.2 | 4
|
| Total | 76
|
The following topics will definitely be covered (of course, the exam is not limited to
these topics):
| 1.
| The theory of linear differential equations, including definitions.
|
| 2
| Solving first-order equations using an integrating factor.
|
| 3.
| Finding eigenvalues and eigenfunctions for boundary value problems.
|
| 4.
| Writing a higher-order equation or system of higher-order
equations as a system of first-order equations.
|
| 5.
| Differential operators.
|
| 6.
| Calculating transforms and inverse transforms,
and using the transform to solve equations and systems of equations.
|
| 7.
| Power series methods from section 8.1, singular points as discussed in
section 8.2.
|
You should know Cramer's rule, the method of partial fractions, and the
power series for e^x, sin(x), cos(x), ln(1+x), sinh(x), cosh(x).
The test does not cover slope fields, word problems, Bernoulli equations,
vibrations, over- and under-damping, phase-angle form, the Wronskian or the
Amazing Theorem, the the method of undeterined coefficients,
or variation of parameters.
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.