Description
This is a group (2 people) assignment. You will investigate the
applications
below. For each application the groups should do the following:
- Pick an application area of interest to your group. No two
groups can work on the same models. Get approval for your project from Dr.
Herman.
- Develop a model that results in a linear system of equations.
- Study the system using the techniques from the class including matrix
methods, qualitative analysis and phase portraits.
- Discuss the various behaviors encountered in terms of the parameters
of your systems. If there are no parameters, then introduce some.
- How can one generalize/vary the model leading to other interesting
behavior? Provide some of these variations of your model with some
solutions.
- All reports should include figures, solution plots, and other
results from computer computations.
- Write up a report according to the guidelines.
Possible Application Fields/Models:
-
Spring-Mass Systems: Two masses with two
springs.
-
Electric Networks: Combinations of resistors,
inductor and capacitors. Do not do the standard series RLC circuit.
-
Two Compartment Models: Two tank model, drugs in
two compartments (membranes)
-
Predator-Prey Models: Models of competing
species number two to three species.
-
Love Affairs: Investigate the typical Romeo and
Juliet problem.
-
Chemical Kinetics: There are many models of
chemical reactions leading to systems of equations. Study some leading to
linear systems.
-
Other Applications: There are plenty of other
applications in physics, biology, etc. which might be of interest to your
group.
All work should be typed with double-spacing and 12 pt font.
[You may also use the LaTeX article style with 12 pt format.]
You will be expected to use correct English grammar and punctuation. You
will be graded on the evidence of work, mathematical detail and
understanding, proper exposition and neatness. Your work should also be
supported with properly labeled and embedded plots. Any references
used should be cited as well. These reports will count towards
the project component of your grade.
Timetable/Deadlines
-
Feb
9 Let Dr.
Herman know who is in the group and what problem you will work on.
-
Feb 11 Progress Report 1:
Submit a synopsis of your problem. Include title, the linear system and
its modeling, and possible directions you plan to go with the research.
-
Feb 18 Progress
Report 1: Submit a detailed progress report indicating how far you have gone
towards the goals provided in the last report showing considerable progress.
It is best to aim fo a draft of the final project report.
-
Feb
25 Final
Report: Submit completed final report.
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