Due Monday, August 29, 11:59pm
Category: Assignment Instructions (Page 5 of 5)
Due on the OpenLab Monday, December 12
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 necessarily taken a Differential Equations course.
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.
Your work will be scored using this rubric.
Suggested topics
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
Format
Your final report can take any form you like. Here are some suggestions:
- a written essay that’s around 1 to 2 pages long (500 to 1000 words; 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)
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
- 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.
Academic integrity
No plagiarism is allowed! Your work must be your own and you must cite any sources you use.
First steps
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
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.
Due Sunday, September 6, 11:59pm
Ideas
Section 1.2 and 1.3 of your text cover some elementary but fundamental ideas that you’ll carry with you for the rest of the course. In Section 1.2, you learn:
- what a differential equation is, what its order is, ordinary versus partial differential equations,
- what a solution to a differential equation is,
- how to check that a function is a solution of a particular differential equation.
Section 1.3 focuses on differential equations of the form $\frac{dy}{dx} = f(x,y)$ because we can draw pictures representing these equations and their solutions: direction fields (sometimes called slope fields) and integral or solution curves.
None of these topics are actually new to you, but we’re putting them together slightly differently than you would have in your calculus classes.
Instructions
There is no WeBWorK set corresponding to Sections 1.2 and 1.3.
- Instead, you will each pick one exercise from the textbook homework from these sections listed in the schedule:
- p.14: 1, 2(a-c,e-h), 4(a-f), 5, 6, 9 and p. 21: 1-11.
- Solve the problem completely, clearly showing each of the steps.
- Then, share your work as a new post on the OpenLab. Title your post by the section and problem number so we know which one you are completing. Select the category Sections 1.2 & 1.3 under “Document” on the right-hand-side of the screen before publishing your post.
- You may upload a photo of your solution to place in your post or, if you are ready, you can try typing it using LaTeX (see the other OpenLab assignment you have this week for instructions here).
- Try to choose a question that your classmates haven’t already posted. Try to make sure solutions for all the questions (from Section 1.2 especially) are posted. The idea of this assignment is that you as a class are crowdsourcing the solution guides for these sections.
- After you’ve posted your solution, check your classmates’ work and leave them a comment if you think you’ve found an error or have a question about something they wrote (or if you just want to congratulate them for producing some nice work).
You will receive participation credit for this post whether your solution is correct or not.
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