Choose one of the questions from Test #2 that you did not receive full credit for and re-solve the problem. Submit your complete solution (a photo of your written work or typed using LaTeX) as an OpenLab post with title Test #2 Solutions and the type of equation you are solving and with category Test #2 Solutions.

There were different versions of the test with similar questions. Try to choose a problem whose solution a classmate has not already posted.

Step 2

As part of your OpenLab post, write the story of your solution. That is, pretend you got stuck on the first step. Then write a step-by-step instruction manual for how to complete the solution, without actually doing any of the calculations.

Step 3

Read your classmates’ solutions and find one for another question on your version of Test #2. Submit a comment on their post describing how you approached that question similarly or differently or any questions or suggestions you have.

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)

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)

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

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.

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).

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.)

Use your peers’ feedback to rewrite your draft before you submit your final draft as a new post on the OpenLab. Your

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

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).

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.)

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.

Part 1 due Monday, April 17, Part 2 due Monday, April 24

Summary

Project #2 will be similar to Project #1. For Project #2, you will see how the techniques you’ve learned for solving second-order differential equations apply to certain real-world examples. In groups, you will put together a full lesson for your classmates on these applications. Project #2 has two parts:

In pairs, you will complete an assigned homework problem from the text and post your full solution on the OpenLab, along with a video describing your solution step by step.

As a group, you will submit a single OpenLab post with

a short lesson to your topic, and

links to the pairs’ posts from Part 1 as examples .

Part 1: partners

Post due on the OpenLab by Monday, April 17, 11:59pm

Sign up for a homework question using the sign-up sheet here (you should work with a partner, but you may work alone).

Read the corresponding section and complete your homework question.

Contact your partner to compare your solutions (you may direct message them on the OpenLab). If your solutions differ, discuss them until you agree.

Decide which of you will record a video explaining the solution step by step. (Suggestion: record a Zoom meeting together with your partner where you present your solution together.)

Decide which of you will post your solution on the OpenLab.

The post must include both partners’ names.

Your video will serve as an example for your group’s lesson; it should contain as much detail and explanation as is necessary for your classmates to understand. It will include english sentences and connecting words, not just math notation. Read Professor Francis Su’s handout on writing mathematics well.

You may include photos of written work in your post, or type your work directly into the post using LaTeX (LaTeX instructions from your previous assignment are here).

Title your post with “Project #2” and the textbook section and problem number. Select the category Project #2 pairs before you publish your post.

Post due on the OpenLab by Monday, April 24, 11:59pm

For the group component of Project #2, your group will need a secretary. The secretary will be the one who will submit the group’s OpenLab post by the deadline. To submit this post they will copy-paste the group’s work from Part 2 and include links to the pairs’ video posts from Part 1. Volunteer to serve as your group’s secretary in the sign-up sheet here. If more than one person volunteers, the group will elect a secretary.

The group post is a lesson on the textbook section that the whole class will read. It has three components:

Lesson (this will be the longest part of the post).

Two to four paragraphs describing the real-world example that anyone can understand. What type of problem is the section trying to solve?

A description of the differential equations/equations that are used to solve the problem. What type of equations are they and what techniques can be used to solve them? What do the individual variables represent?

Links to examples.

Include a list with a link to each of the pairs video posts from Part 1.

Some of the textbook sections have more than one type of application or equation, so your lesson may need to have a few different subsections. Make sure the appropriate examples are grouped together and linked to the appropriate paragraph description.

Title the post “Project #2” and the title of the textbook section. Select the category Project #2 groups before you publish your post.

Grading

Half of your Project #2 grade will come from Part 1 and half will come from Part 2. here are the questions to consider:

Part 1

Does the post have the correct title and category?

Does the video provide a clear and organized solution?

Does the video use the correct language?

Is the solution complete and correct? How does it answer the original question?

Part 2

Does the post have the correct title and category?

Is the lesson easy for someone to read? Is the description of the relevant equations complete and clear?

Are the examples linked to the relevant written description?

WeBWorK

Choose ONE of the following WeBWorK sets to complete by Monday, April 17:

Applications of Second Order Equations-Springs Undamped

Applications of Second Order Equations-Springs Damped

Applications of Second Order Equations-RLC Circuit

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