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Differential Equations Project - Summer 2016
This is a group project. You are expected to work in
groups of two. The goal is to take a problem from some application area
that can be modeled in terms of an ordinary differential equation and
solved numerically. If solutions are available, then numerical solutions
should be compared to known exact solutions or other models. Graphical
solutions are expected including the varying of parameters in the model.
You will report your group composition July 5th and
proposed problem on July 6th. A
detailed progress report on your work to date is due July 12th. The final
full report will be due July 19th.
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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. This is a report and thus you will use proper sentence and
paragraph formatting. 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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Structure
A suggested outline of the final report would be: Title
page (including Title, Names, Abstract), Introduction to Problem
(Statement and Background). Formulation of Model and Method of Solution
(Discussion of Simulink Model),
Solution Results (Analytical, Numerical, Plots of Solutions),
Discussion/Results (Summary and Discussion of Solution), Bibliography.
The first source of topics can be found in Chapter 3 of
the text and other ideas may be found in
the Simulink notes. Examples:
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Free fall - beyond simple free fall - add air
resistance, etc. See problems in Chapter 3.
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Projectile motion - golf balls, soccer balls, etc.
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Oscillations - masses on springs, circuits
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Population models
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Kinetics models
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Mixing models
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Other ideas or
Check here - This might give some ideas, but may need to discuss
with Dr. H. to see if doable with a little help.
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Additional Information You can
also use
Maple, MATLAB, or some of the other packages discussed in class.
However, the main model should use Simulink.
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