Strengthen your understanding of the theory and application of differential equations, introduce you to undergraduate level research in mathematics, practice unpacking and understanding mathematics writing and explaining mathematical content to your peers.
Working in groups of 2-3,
Choose an “application of differential equations” paper from either the Rose-Hulman Undergraduate Mathematics Journal (https://scholar.rose-hulman.edu/rhumj/), Mathematics Magazine (https://www.tandfonline.com/toc/umma20/current), or The College Mathematics Journal (https://www.tandfonline.com/toc/ucmj20/current). Make sure the paper involves only ordinary differential equations (no partial differential equations).
Read and fully understand the paper.
Present the paper to the class (∼10 minutes).
You must submit two suggested papers by Friday, September 13 for approval. The papers you submit should be already at least 80% understandable.
You will sign up to present your chosen paper on one of the following days: Sept 23, 25, and 30
The paper presentation grade will be based on three factors, each equally weighted.
(a) Accuracy and depth of understanding demonstrated
(b) Clarity of exposition, including the presentation slides.
(c) Completeness of presentation (e.g. sufficient background)
Strengthen your understanding of the theory and application of differential equations, your numerical simulation and programming skills, your creative problem-solving, and your ability to conduct independent research.
Working in groups of 2-3,
You can either
Option 1: Take part in the 2024 SCUDEM - SIMIODE Challenge Using Differential Equations Modeling,
- Challenge Period is Saturday 19 October - Tuesday 12 November, 2024.
or Option 2: Model a new (to you) physical system or apply/extend a model that was presented in class.
Analyze your model in the following ways:
- Analytic solutions, if applicable.
- Numerical simulations of solutions to your model.
- Qualitative analysis (phase transitions, bifurcations, etc) using numerical simulations.
Present your work in a 10-minute video presentation
Option 1:
Form a group and meet with me by Wednesday, October 9
Register as a group of 3 by Wednesday, October 16
Take part in the SCUDEM challenge October 19-November 12
Option 2:
Form a group and meet with me to have your Differential Equation Model approved by Friday, November 1
Submit preliminary numerical results and analysis by Friday, November 15
Submit video presentation by Wednesday, November 27
The final project grade will be based on:
(a) Ambitiousness
(b) Accuracy & Completeness:
Have you
analyzed the strengths and weaknesses of your model? thought about the story it tells algebraically and explained where it comes from and why it models the described situation? determined the limitations of the model, or fully thought out all the relevant variables
made connections to class concepts when possible
solved your model equation either analytically or numerically, and included a discussion of the method used?
analyzed the results in the context of the model to determine if they make sense?
provided necessary scientific or other background as appropriate?
(c) Clarity of presentation of project.
Are all variables defined?
Is the scenario clearly described?
Are your slides or other visual aids easy to read and engaging?
Is your presentation clear and well-articulated?
First and foremost: Fully understand the material you are presenting. It should make perfect sense to you in order to explain it clearly.
Suggestions:
• Define all variables and notation used.
• Understand and be able to explain derivation of all equations - even if they are well known
• Highlight what is interesting/novel about the model. Provide motivation for the material. What is the point of the material presented?
• Tie-in to class concepts / content when applicable Give necessary background to provide context for the material presented
• Engage the audience. Ask questions (even if it is rhetorical), ask audience to justify steps of proof, etc. Don’t read notes. You can use them for reference but then put them down before continuing with the presentation.
• Carry out illustrative examples to reinforce the theory presented. Do not try to do or show explicit computations. If you wish to show a solution to an equation, it is better to give the equation, indicate briefly (in words) the method of solution and then give the solution.
• You must cite your sources.
A good presentation relies on BOTH the presenter and the audience. For the audience, this means being engaged in the presentation; i.e. really thinking about what is presented, not just following along. And being engaged in a presentation usually leads to follow-up questions. Therefore, in addition to your two presentation grades, your full assignment grade will require at least one (interesting and insightful) follow-up questions from each student throughout the other presentations.