MAT 537 Spring 2013

PROJECTS

1.
Background * *

Each student will do one unique project where they apply the tools learned in
class to a linear partial differential equation. The
PDE can be from one of the sections in the book, or one based on your research. The
goal of the project is different than that of homework problems because it is a
research assignment that has a general goal, but may not have a clear answer.
You are supposed to use the knowledge acquired in class, to think about the
problem for several days, to ask new questions and to try to answer them, to
stir your imagination, and to search for suitable references. Start as soon as
possible, and let your subconscious work for you. Solutions will come to you at
the strangest times!

2.
Written progress
report: * *

This will be a short report on your progress. Include any unexpected problems
and how you have resolved or are planning to resolve them. This report
does not need to be any longer than one (typed) page.

3.
Oral presentation: * *

Presentations should be 20 minutes long. The presentation
should follow this outline

I.
Problem
description. This should take 1-2 slides and your goal should be to motivate
why one would want to study this problem. For example, justify the
equations, describe what type of phenomena they describe and outline the
questions you intend to answer or explore in your project.

II.
Approach. Do not
spend a lot of time going through the math but outline the approaches or
methods you used from class (or outside of class) to study your problem.
This should take 1-2 slides.

III. Results. You may want to show graphs or tables at this
point but make sure there is a summary slide which
lists your conclusions about the graphs or tables. Do not show a
table or graph unless it explains a point you want to make or one of your conclusions.

Some
general suggestions:

§
Make the
presentation simple, and do not include too many details. If someone is
interested in your work, they can read the full report.

§
Realize that your
audience is the other members of the class.

§
Do not put up a slide
with very complicated drawings or millions of numbers. Less is more.

§
Begin with a
slide containing the title of the project, and the names of the people in the
group.

§ Use a large font, or write large enough so people can
see in the back of the room. I would use no more than 12 lines per slide.

4.
Written report:

The
final research paper should include an introduction, methods, results, and
discussion section accompanied by tables and graphs illustrating your
results. Follow the basic instructions I gave above for the oral
presentation. In addition, use complete sentences, good grammar and
correct punctuation in your mix of equations, formulas and prose. Your report
should be written in such a way that it can be read
and understood by anyone who knows the material in this course. You will be
graded on your written presentation as well as the mathematical
content.

A one-page executive summary or abstract
should also be included at the beginning of the report. Write this in
non-technical language for the reader who has an interest in the research
question but does not have any technical training. It must state briefly: (1)
the research question and why it is important; (2) the methods used to study
the question; (3) the findings and what they mean; and (4) what action you
recommend on the basis of your findings.