Differential Equations -- Fall 2016
Information about the final exam
The final exam will occur on
Tuesday, 12/13 11:20AM - 1:50PM in our normal classroom. Between
75% and 80% of the exam will cover the material we have considered
since the previous exam. The remaining material will cover the
course as a whole. In the information below, these will be
discussed separately, but on the exam itself they will not be presented
as separate sections.
Portfolios will be evaluated at the final exam, and a numerical score
will be assigned. If you intend to have a portfolio contribute to
your final grade, remember to bring your portfolio to the exam and to
collect it before you leave.
For the part of the exam covering the last third of the course, you are
responsible for the following material: sections 3.6, 3.7, 5.1, 5.2,
4.1, 4.2, 4.3, and the handout
on the annihilator method. This part of the exam will be
similar to the prior two exams: you should be able to demonstrate
understanding and proper use of
concepts, definitions, theorems, notation, terminology, and the various
kinds of graphs we have used. And of course you should be able to
use established procedures to solve problems. This part of the
final will also be similar in length to the other exams.
For the part of the final covering the course as a whole, you might
asked some questions from prior exams. These items, if any, will
be identical to what has already appeared on an earlier exam. In
addition, you may
be asked to show what you have learned about ideas, concepts, and themes that have
repeatedly over the semester. Expect a few questions about these
ideas, possibly as
essay questions, multiple choice, fill-in-the-blank, or other question
are some examples of the kinds of concepts I am referring to:
You might be asked to comment on
one or two of these in depth in an essay question, or there might be
questions covering most or all of them in a short answer, T/F, or
multiple choice format.
- Modeling: How differential
equations are formulated to model real systems or phenomena, what sorts
of analyses are undertaken in such applications, and how the results
are used and interpreted. This includes the use of parameters
within differential equations, qualitative analyses, and consideration
of the sensitivity of results to small variations in the parameters.
- Analytic, numerical,
graphical, and qualitative approaches to studying differential
equations. What are they, when are they applicable, how are these
different? What kinds of information can they
provide? How do they complement each other?
- Qualitative Analysis.
What is it? Why is it useful? What are some examples we
have seen? What are some important concepts associated with
qualitative analysis (for example bifurcations)?
- Linearity. What's the
difference between linear and nonlinear differential equations and
systems? What are the special properties of linear equations and
systems that make them particularly useful or tractible?
- Autonomy. What's the
difference between autonomous and nonautonomous equations or
systems? What are the special properties of autonomous equations
or systems that we have used repeatedly?
- Existence and
Uniqueness. In general terms, what do existence and uniqueness
results tell us? Why are these important? How have we used
I am not providing a sample exam
for the final. Procedural questions will be similar to those
assigned in homework. Questions that are more conceptual or that
your knowledge of terminology, definitions, and theorems will be
similar in nature to what has appeared on prior exams. For this
of question study the text and your class notes. Although I
planning to hold a review session on the last day of class, I am not
preparing specific material
to go over at the review. It is important that students bring
own questions about homework or prior exam problems, concepts, or
methods that arise in their preparation for the final.