• Proposal: comment on this post by Monday, May 1
  • First draft: post by Monday, May 8 (title: Project #3 Draft – [subject], category: Project #3 Draft)
  • Final draft: post by Monday, May 22 (title: Project #3 Final – [subject], category: Project #3 Final)
Bart Simpson sitting at the kitchen table saying, "Well, um, I'm doing a school project on, uh,"

You will have a lot more freedom for Project #3 than you have had for previous projects. This is a research project. You get to decide the topic and whether you’d like to work in a group or work alone.

The main goal of the project is to convince other students to learn differential equations. Your report should be understandable by someone who has completed a Calculus II course but who hasn’t necessarily taken a Differential Equations course.

You have two choices for your approach: Option A and Option B (see below).

Details

Content requirements

For this research project, choose one application of differential equations and teach us about it. Your project may be as detailed as you like.

  • It must include a description of the real-world problem as well as a description of which differential equations are involved and how they are used to solve the problem.
  • For a particular equation, explain what the solution represents and what the other components of the equation represent.
  • Depending on the application you choose, you may or may not want to include a solution of the differential equation. For example, if your application involves a system of partial differential equations, you should not solve it! But if your application involves an ordinary differential equation of the type we’ve seen in this class, then you should include its solution.

Suggested topics

You have complete freedom in terms of the topic you choose. You were already introduced to some in Chapter 1, Chapter 4, and Chapter 6 of your textbook. Here are some more ideas, though you are welcome to choose another one; just clear it with me first.

  • Epidemic spread SIR model (this would be an interesting choice during a pandemic, but don’t choose this one if it would be too traumatic for you)
  • Population growth with food supply
  • Hurricane forecasting
  • Tacoma Narrows bridge collapse
  • Fluid dynamics
  • Three-body problem
  • Predator-prey model
  • Black-Scholes equation (finance)
  • Navier-Stokes equation (this has an interesting cultural component as a Clay Millennium problem)
  • More ideas available here

Format

Your final report can take any form you like. Here are some suggestions:

  • traditional: a written essay that’s around 2 pages long (around 1000 words)
  • a video you record that’s around 5 minutes long
  • a sequence of Tik Tok videos you record
  • a poster (a scientific-style poster or one with more graphic-design flair)
  • a PowerPoint/Google slide presentation
  • something more creative (here is a really cool idea)

Resources

As usual, the internet is sort of the wild west when it comes to looking for useful information. There is some good stuff, but it can be hard to find. Here are some possible starting points:

  • your textbook or another differential equations textbook
  • online notes from a differential equations class at a university
  • SIMIODE
  • Wikipedia
    • Wikipedia is not always super reliable! You are probably not allowed to use it as a source for your other research projects, but you may use it here if it’s not your only source. Some Wikipedia articles provide about the right level of detail for a project like this. You can always scroll to the references at the bottom of the page for more resources.

Academic integrity

No plagiarism is allowed! Your work must be your own and you must cite any sources you use (but see separate rules for Option B below).

Option A

The first option is the straightforward one.

  1. Submit your proposal as a comment on this post. Your proposal must include your topic and your partner’s name (if you are working with a partner).
  2. Submit your first draft as a post on the OpenLab BUT DO NOT REVEAL THAT YOU WROTE THE PROJECT YOURSELF!(We will play a game later.)
  3. Use your peers’ feedback to rewrite your draft before you submit your final draft as a new post on the OpenLab. Your

Your work will be scored using this rubric.

Option B

Interested in having an AI like ChatGPT complete your project? Okay, but there are some rules!

  1. Submit your proposal as a comment on this post. Your proposal must include your topic and your partner’s name (if you are working with a partner).
  2. Submit your prompt to your chosen AI and have it generate your first draft. You may have to go back and forth with it a few times to adjust its output to match the requirements. Copy and paste its final output as a new post on the OpenLab BUT DO NOT REVEAL THAT YOU USED AN AI TO GENERATE YOUR PROJECT! (We will play a game later.)
  3. At this point in time the widely available AIs make a number of false claims. Your final draft will have two parts; submit the two parts as a single post on the OpenLab:
    • First, copy-paste the conversation you had with your AI to get it to generate your first draft. Include which AI you used and describe anything else you did to arrive at its output.
    • Next, annotate the AI’s final output. You will fact check EVERY CLAIM that the AI made to verify whether it was correct or not (this will involve a lot of work because you need to check every single sentence). Your annotation for each claim will include a discussion of whether the claim is correct or incorrect as well the source you used to check it. Here are some suggestions for submitting an annotated version:
      • Copy-paste the AI’s final output into a Google Doc and use the comment tool to highlight each individual claim and comment with your discussion/source. Include the link to the Google Doc in your OpenLab post (don’t just copy-paste the URL; use the “share” feature in Google).
      • If you have a tablet, import a PDF of the AI’s final output use a note-taking app like Notability to highlight each individual claim and hand write your discussion/source. Upload the annotated PDF directly to the OpenLab or share a link to in in your post.
      • Use the OpenLab’s built-in annotation features to annotate the AI’s final output right in your OpenLab post (I am not as familiar with these, but if you can get something to work, that’s great).

Your work will be scored using a modification of this rubric.