This is an individual component of the group project. You may consult with your group members
regarding your answers, but you must write this paper on your own. All computations must be done
by you and in your own words. If group members submit papers that are identical or if portions of the
papers are identical, no credit will be given.
If you do not feel like a paper is the best way to present your work, please get in touch with me to
discuss other options, such as a video, podcast, or artwork.
Make sure you only present your own work. Read about academic honesty policies here.
I suggest that use any feedback you received on the Application Project discussion board to amend
your research paper before you submit it.
1. Include a title page with the following information:
1. the title of your project
2. your full name
3. your group members’ full names
2. Include an introduction to your project. Make sure to include the following information:
an abstract (at least 50 words)
a brief history of the problem (at least 50 words)
When did researchers become interested in this type of problem?
What strategies were first used to solve this type of problem?
How was the strategy that you are using developed?
the field in which you are applying methods of differential equations to
an explanation of the importance of the problem and why you are particularly interested in it
(at least 50 words)
3. Summary of how you used differential equations to solve your chosen problem (at least 50 words)
Include the names of all methods and theorems used. These names should be consistent with
the terminology used in this course
4. Present the solution to your problem (approximately 2 handwritten pages). Make sure to include:
A statement preceding each computation explaining why the computation is necessary and
where each piece of the computation comes from. Students should be able to read this
statement and then understand how to replicate this computation for a similar exercise.
A concluding statement following each computation that interprets the result in context
All steps for solving equations. Do not use software to solve equations.
All steps necessary for graphing by hand
Graphs and diagrams, if relevant
5. Include a conclusion (at least 50 words). Include the following information
Summarize the answer of your problem
Any insights you may have had while working on the project
An unanswered question (or questions) related to your problem that you leave for the reader
6. Works Cited
For full credit, make sure you either write mathematical expressions by hand and submit photos of
your work or use a math-typesetting program (such as LaTex). Points will be taken away if
mathematical expressions not clearly represented. For example, your paper should not include “x^2”
but rather . For this reason, you may hand-write your work for item 4. Type your work for items 1-3
and 5-6. You do not need to follow any particular formatting, such as MLA or APA.
View the rubric below to understand how this assignment will be graded. There are a few items I’d
like to give you some tips on.
Authenticity of Topic
Most of the word problems in your textbook are contrived so that they are easy to solve. These are
great exercises to practice to get familiar with the material. For this project, however, I am asking that
you try to come up with a problem to solve that uses differential equations in a way similar to how a
professional (in any field) would use differential equations. This will require some thinking out of the
box. If you need help finding a topic, don’t hesitate to get in touch with me. If you do decide to simply
use a problem similar to a textbook word exercise, don’t worry, this item is only worth one point.
How to Write an Abstract
Formal research papers always include an abstract, which summarizes what will be presented in the
paper. It is customary to use the royal “we” in an abstract. Here is a resource
(https://writing.wisc.edu/handbook/assignments/writing-an-abstract-for-your-research-paper/) on how to
write an abstract.
When you’re using math to solve a problem in a work setting, you would need to explain why you are
using a particular formula (preceding statement) and you would need to interpret your results
(concluding statement). For example, suppose you are modeling the size of a population with a
function . You need to report the population starting size, so you compute . If
as the solution, you would be correct, however, this information is only accessible to people who are
comfortable with functions and use precalculus regularly. If instead you write
“The starting point occurs when x=0. I will compute in order to determine the size of the
population at time x=0.
The size of the population is 100 at the starting point.”
the information is accessible to a larger audience. For full credit, make sure to include a statement
before a computation to explain why you’re doing that computation, and then a statement after the
computation to interpret the results.
Your conclusion must include an unanswered question for your reader to ponder after learning about
your project. This question must be specific enough for full credit. Think about something that you
might be interested in exploring further but have not have time to yet. The question should build on
your work, and the reader should at least have a starting point in regards to answering this question
after reading your work.
You may request to use a calculator or computer software if your project requires lengthy
computations. However, make sure to get my approval for calculator use for this project. Start by
sending me a message or dropping in to office hours and we can discuss it.