Description
This is a group (2 people) assignment. You will investigate an application
that can be modeled using systems of differential equations. For each application the groups should do the following:
- Pick an application area of interest to your group from the
suggestions below.
- Develop a model that results in a linear system of first order
differential equations.
- Solve the system, plot solutions in Maple or MATLAB.
- 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 physical model leading to other interesting
behavior?
Add some of these variations of your model and find 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:
The model you pick can be based upon an application described in Chapter 3.
Starting points might be suggested by problems 11 (three springs), 12 and 13
(LRC circuits), 14 (tanks), 16 (chemical reactions), or 17 (epidemic 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. Try a
parallel combination.
-
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.
Timetable/Deadlines
-
Feb 10 Let Dr.
Herman know who is in the group and what problem you will work on.
-
Feb
17 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
24 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.
-
Mar 2 Final
Report: Submit completed final report.
Format
All work should be typed with double-spacing and 12 pt
font. 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 and equations. Any references
used should be cited as well. These reports will count towards
the project component of your grade.
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