Math 340: Differential Equations (Fall 2015)

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Course Project

A printable version of the Course Project handout is available.
The rubrics for evauation of the Oral Presentation and Project Papers are available.
The forms for Individuals and Groups To evaluate their Project Participation are also availale.

Differential Equations Course Project

In this course, you are being asked to complete a course project. This handout details the
information you need to complete the project successfully. The goals of this project are to have
you extend your knowledge of differential equations according to your own personal interest and to
practice your new ODE skills and enhance both your technical writing and communication skills.
The project is worth 20% of your final course grade.
Please prepare for it with the appropriate resources necessary to do a satisfactory job.

Project Description: The idea behind the project in differential equations is to provide you with the opportunity to present your understanding of a topic in differential equations that you find interesting or compelling.

OPTION 1:  Choose a topic from one that we will not cover in ourr class

Some potential ideas of topics to choose from that we will not discuss in class are:

  1. Using differential equations in biological systems (modified predator-prey, HIV or SIR models, etc)
  2. Series solutions of diferential equations (i.e. Method of Frobenius)
  3. Solution methods for Bernouilli Equations
  4. Damping (overdamped, underdamped) systems of linear 2nd order ODEs with forcing terms
  5. Numerical methods for solving ODEs (i.e. Runge-Kutta, Modified Euler, etc)
  6. Boundary value problems (as opposed to initial value probleme) and their applications
  7. Difference Equations and Finite-Difference Methods for Numerical Approximations of ODEs
  8. Chaos and strange attractors
  9. More complicated examples of bifurcations (Cusp vifurcations, Hopf-Adroponov, etc)
  10. Definition of special functions that involve ODEs (Bessel's functions, Legendre functions, Laguerre functions, hypergeometric functions, elliptics functions, Jacobi functions, etc)
OPTION 2: Choose an application of differential equations that show up in another field or discipline and discuss what concepts from the class are used in order to understand or explain that context.

The project may be done as a trio or pairs (or in very rare cases as an individual)
but in all cases groups get a single grade assigned to them, with members and
myself having input into how the credit should be allotted.

Project Timeline: Your project will have several deadlines associated with it. Although
the majority of your project grade will be based on the final paper and presentation, failure
to fully complete a step by the deadline will result in a 5 point deduction off your final grade.

The project is worth a total of 300 points

1. Project Proposal: Friday, October 2nd. 50 points] On this day you will turn in
a project proposal that is no less than one page typed and double spaced. It should explain
whether you are choosing option 1 or option 2, your project topic and how the topic is connected
to differential equations. It should include any references you already have that you plan to
be using. If you are choosing option 1, please attach one copy of your primary paper (you can
consult many papers, but only attach the “main” one) as well as an idea of references you may
still need to find. It should also include a detailed plan to complete your project and what you
want your punch line to be that is, you should have an understanding of why your project is cool
and important. If you are proposing a group project, you should also detail how each member
plans to contribute. You only need to include one copy of the proposal, signed by all members.

It is strongly encouraged that you contact me (either in person or by e-mail) to discuss your
proposed Project topic prior to submitting your proposal.

2. Rough Draft: Friday November 13th:  50 points] One component of your final project will
include a formal write up of your work. You should turn in a rough draft of your project paper
by Friday, November 13th at 5 p.m. It is fine to turn in your rough draft early. Drafts should
be submitted by hard copy and not electronically. The length of the paper will vary between
projects, but it is anticipated that no project will be adequately described in less than 5 pages.
You should also include an outline of the paper with your rough draft. This is a technical paper
and should include an abstract, an introduction, a paper body, a conclusion, and appendices.
Figures and relevant data should be included and properly labeled. You should also make sure
to cite any references you have used. A single sourced paper is an unconvincing and uninteresting paper.
One of the key ideas of the paper is to try and connect the ideas you are discussing to other mathematical
ideas and concepts in differential equations (both ones that we have discussed in class and hopefuly some that we have not discussed).

3. Final Paper: Wednesday December 2nd: [100 points] All groups will turn in their final paper
on Wednesday December 2nd by 5 p.m. EXTRA CREDIT OPPORTUNITY:  Choosing an Early Oral Presentation Slot (Mon 11/17/14).

4. Oral Presentations: Monday November 23rd, Monday November 30th and Wednesday, December 2nd [100 points]
Oral presentations will be done in class during the last week. Each project group should plan on speaking
for 12 minutes if the group consists of two people or 8 minutes if solo and 15 minutes if the
group is a trio. This is not a long time to explain the amount of work you have been doing,
so your presentations will have to be well prepared and practiced. Your presentation should be
done with the use of a computer projector in a medium such as power point. A properly timed
presentation will be within a minute of the allotted time. Speaking for a substantially (i.e. 2-3 minutes) shorter
or longer length of time will affect your oral presentation project grade by at least 5 points.
EXTRA CREDIT OPPORTUNITY: Oral Presentation on Monday November 23rd


Here is checklist for how to evaluate your Course Project Paper. Also, here is the grading rubric I will use

Does this paper:

¨      have an Introduction, Conclusion and Thesis Statement (which I would prefer that you write in bold)?

¨      provide a paragraph (100-200 word abstract) at the top which summarizes the salient details of the project?

¨      include ALL and appropriate (I expect at least 5) references and citations (in a consistent style) to sources used to complete the project?

¨      give a precise and well-organized explanation of both the problem and its answer?

¨      clearly label diagrams, tables, graphs, or other visual representations of the math?

¨      define all variables, terminology, and notation used?

¨      use correct spelling, grammar, and punctuation?

¨      contain correct mathematics?

¨      is spell-checked, free of grammar-errors and of a reasonable duration?

¨     contain a cover page with the signatures of all the members of the group?

  Here are the presentation slots for the 2015 edition of Math 341: Differential Equations

Time Slot

Time Limit

Group

Title

MON NOV 23 #1* (extra credit)

15 minutes

Niko Lachman, Kaleb Mitchell and Matt Mulvehill

Various Applications of the Hopf Bifurcation

MON NOV 23
#2* (extra credit)

15 minutes

Brian Okimoto, Yifan Shen and Jonah Taylor The Double Pendulum
MON NOV 23
#3* (extra credit)
15 minutes Noor Ahmed, Gloria Mayorga-Garcia and Erin Kim Chaos Theory

MON NOV 30 #1

12 minutes

Trevor Nash and Peter Renn An Orderly Approach To Chaos
(link)

MON NOV 30 #2

12 minutes

 Riley James and Thayer Fisher Stiff Differential Equations

MON NOV 30 #3

12  minutes

Will Bergman and Mike Ma Harmonic Oscillators

WED DEC 2 #1 

15 minutes

Zack Conrad, Michal Nowicki and Eddie Perezic The Magnus Effect

WED DEC 2 #2

12  minutes

Stephen Heim and Ellie O'Brien Three Dimensional Systems of Linear ODEs

WED DEC 2 #3

15 minutes

Jake Chambers, Courtney Hutton and Evan Lubin Nonlinear Systems in Three Dimensions

Here are the project groups for the 2015 edition of Math 340: Differential Equations

Group

Members

Time Limit

1 Zack Conrad, Michal Nowicki and Eddie Perezic
15
2 Stephen Heim and Ellie O'Brien
12
3 Niko Lachman, Kaleb Mitchell and Matt Mulvehill
15
4 Noor Ahmed, Gloria Mayorga-Garcia and Erin Kim
15
5 Trevor Nash and Peter Renn
12
6  Jake Chambers, Courtney Hutton and Evan Lubin
15
7  Riley James and Thayer Fisher
12
8 Brian Okimoto, Yifan Shen and Jonah Taylor
15
9
 Will Bergman and Mike Ma
12