Due on the OpenLab Friday, December 18 (updated deadline)
You will have a lot more freedom for Project #4 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 taken a Differential Equations course.
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.
You have complete freedom in terms of the topic you choose. You were already introduced to some in Chapter 1 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
- Preditor-prey model
- Black-Scholes equation (finance)
- Navier-Stokes equation (this has an interesting cultural component as a Clay Millennium problem)
- More ideas available here
Your final report can take any form you like. Here are some suggestions:
- a written essay that’s around 1 to 2 pages long (may include video links)
- a video you record that’s around 5 minutes long
- a sequence of Tik Tok videos
- a poster (a scientific-style poster or one with more graphic-design flair)
- something more creative (here is a really cool idea)
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
- Okay, 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.
No plagiarism is allowed! Your work must be your own and you must cite any sources you use.
Comment below with the topic you are interested and whether you want to work alone or if you’re looking for a group. Reply to your classmate’s comment if you’d like to join their group and establish a way to be in contact.
Submitting your work
Post your report (or a link to your report if it’s not in a written format) on the OpenLab with the title Project #4 [topic]. Select the category Project #4 before publishing. Don’t forget to include everyone’s names!
The point of this assignment is just to learn something new and to have fun doing it! Whatever form your assignment takes, there must be mathematical content, but you don’t need to stress too much if you don’t develop a deep understanding of it. Just tell us what you learned. Remember, your report should be understandable by someone who has taken Calculus II but not Differential Equations.