DE Model Project
Guidelines & Rubric · MATH 341 Differential Equations · Fall 2026
1 Overview
Differential equations are one of the most powerful tools humans have developed for understanding the natural and social world. Almost every field—from biology and chemistry to economics, engineering, and sociology—relies on differential equation models to describe how things change. The DE Modeling Project asks you to find and explain one such model that connects to something you care about.
This is a low-stakes, high-curiosity assignment (5% of your overall course grade). The goal is not to push you through difficult calculations, but to help you see differential equations in the wild and practice explaining mathematical ideas clearly. Think of it as a scientific communication exercise: you are translating a real-world phenomenon into the language of differential equations for an audience of your peers.
2 Learning Goals
By completing this project you will:
- Identify a real-world phenomenon that is naturally described by a differential equation.
- Correctly state the differential equation (or system) associated with that phenomenon.
- Define all variables and parameters in the model.
- Interpret what the differential equation says qualitatively about the behavior of the phenomenon.
- Communicate mathematical and scientific ideas clearly to a general audience.
3 What to Do
3.1 Choose a Topic
Pick any real-world phenomenon that is modeled by a differential equation or a system of differential equations. The topic should be one that genuinely interests you—it might connect to your major, a hobby, a current event, or just something you are curious about. There are no restrictions on field or subject matter, provided a differential equation is meaningfully involved.
- Biology & medicine: population growth, disease spread (SIR model), pharmacokinetics, neuron firing, tumor growth.
- Physics & engineering: Newton’s law of cooling, spring-mass oscillators, RC/RL circuits, fluid flow, orbital mechanics.
- Chemistry: reaction kinetics, radioactive decay chains.
- Economics & finance: supply-and-demand dynamics, capital growth (Solow model), option pricing.
- Ecology: predator-prey dynamics (Lotka–Volterra), logistic growth with harvesting.
- Social science & other: rumor/information spread, traffic flow, arms race models.
3.2 Create a Poster or Slide Deck
Your final product will be either:
- A poster — a single-page document (PDF) formatted to be read as a self-contained display, or
- A slide deck — a set of slides (PDF,
.pptx, or.key) containing approximately 5–8 slides.
Choose whichever format you prefer. Both are equally acceptable. Regardless of format, your work must address all five elements described below.
3.3 Required Elements
Your poster or slide deck must clearly address the following five elements. These correspond directly to the rubric criteria in Section 6.
3.3.1 Element 1 — Context & Motivation
Describe the real-world phenomenon. What is happening? Why is it interesting or important? Make it clear to the reader why a differential equation is a natural mathematical tool for studying this phenomenon.
3.3.2 Element 2 — The Differential Equation
State the differential equation (or system) explicitly. Define every variable and every parameter. Identify the type of differential equation (for example: first-order linear, autonomous system, second-order constant-coefficient). You do not need to derive the equation from first principles, but you should be able to describe informally where it comes from.
3.3.3 Element 3 — Interpretation & Insight
What does the differential equation tell us about the phenomenon? Discuss the qualitative behavior: Does the solution grow or decay? Are there equilibria? Does the system oscillate? Connect the mathematical behavior back to the real-world meaning. You do not need to solve the equation analytically, but you should describe what solutions look like and what they represent.
3.3.4 Element 4 — Sources
Cite at least two credible sources. Appropriate sources include textbooks, peer-reviewed articles, and reputable reference sites (e.g., university lecture notes, scientific databases). Wikipedia is acceptable as a starting point but should not be your only source. Include full references in a format of your choice (APA, MLA, or any standard citation style).
3.3.5 Element 5 — Clarity & Presentation
Your work should be well-organized and easy to follow. Use correct mathematical notation. Label figures and diagrams if you include them. Write in a way that a classmate with a calculus background—but who has not yet seen your specific model—could read and understand.
3.4 Optional Computational Component
You are encouraged but not required to include a computational element such as a numerical solution plot, a phase portrait, or a simulation generated with Python, SageMath, or another tool. If you include computational work, briefly describe what you computed and what the output shows. Refer to the Python Reference page on the course website for examples.
4 Timeline & Milestones
| When | Milestone | What to do |
|---|---|---|
| Week 7 approx. Oct. 21 |
Topic Proposal due | Submit a 1-paragraph proposal (see Section 5). Approval or feedback returned within one week. |
| Weeks 8–12 | Work period | Develop your poster or slide deck. Office hours are available for feedback on drafts. |
| Week 12/13 approx. Nov. 14 |
Final submission due | Submit your completed poster (PDF) or slide deck (PDF, .pptx, or .key) via the course LMS. |
5 Topic Proposal Guidelines
Submit a short proposal (one paragraph, roughly 100–200 words) via the course LMS by the Week 7 deadline. Your proposal should answer the following questions:
- What phenomenon are you going to model?
- What differential equation (or type of differential equation) is involved?
- Why did you choose this topic?
- What sources do you plan to consult?
Your proposal will be reviewed and returned with one of three responses:
- Approved — proceed as planned.
- Approved with suggestions — your topic is fine; feedback is offered to help you focus or strengthen the project.
- Needs revision — your topic needs adjustment (e.g., a differential equation is not clearly involved). You will receive specific guidance and must resubmit within one week.
Topics are first-come, first-served within the class. Once a topic is approved for one student, no other student may choose the identical model (for example, only one student may do the basic SIR epidemic model). Distinct variants or applications of a model are fine—the goal is simply to ensure variety across the class.
6 Rubric
Each of the five elements is scored on a 4-point scale. The total score is out of 20 points, which is then converted to the 5% weight in the overall course grade.
| Criterion | Excellent (4) | Proficient (3) | Developing (2) | Incomplete (1) |
|---|---|---|---|---|
| 1. Context & Motivation | The real-world phenomenon is clearly identified and explained. The reader understands why a DE naturally arises here. The motivation is compelling and well-situated. | The phenomenon is identified and the connection to DEs is explained, but motivation could be more thorough or precise. | The phenomenon is mentioned but the connection to DEs is vague or superficial. | The real-world context is missing, unclear, or unrelated to differential equations. |
| 2. The Differential Equation | The DE (or DE model) is stated clearly and correctly. Variables and parameters are defined. The type of DE is identified (e.g., first-order, linear, autonomous). | The DE is stated and variables are mostly defined, but some details (parameter meaning, type) are missing. | A DE is presented but contains errors, or variables/parameters are undefined. | No DE is stated, or what is presented is not a recognizable differential equation. |
| 3. Interpretation & Insight | The student clearly explains what the DE says about the phenomenon. Qualitative behavior (e.g., growth, decay, oscillation, equilibria) is discussed and connected to reality. | Some interpretation is given but it is incomplete, or the connection back to the real-world phenomenon is thin. | Interpretation is present but largely superficial or contains misconceptions. | Little or no interpretation of the DE in context is provided. |
| 4. Sources & Accuracy | At least two credible sources are cited. All mathematical and factual claims are accurate. Sources are appropriate (textbooks, peer-reviewed articles, or reputable reference sites). | Sources are cited but one is weak, or minor inaccuracies are present that do not undermine the main claims. | Sources are present but insufficient, poorly cited, or factual errors are significant. | No sources are cited, or the work contains major factual or mathematical errors. |
| 5. Clarity & Presentation | The poster or slide deck is well-organized and visually clear. Mathematical notation is used correctly. The audience can follow the narrative without confusion. | Generally clear and organized, with minor lapses in notation, layout, or flow. | Some sections are unclear or disorganized, or mathematical notation is used inconsistently. | The work is difficult to follow, poorly organized, or mathematical notation is largely absent or incorrect. |
| Total Score | / 20 | |||
7 Score-to-Grade Conversion
| Score | Grade | Description |
|---|---|---|
| 18–20 | A | Excellent work — the model is clearly situated, the DE is correctly stated, variables are defined, and real-world implications are thoughtfully interpreted. |
| 15–17 | B | Solid work — the model is well-chosen and mostly explained, with only minor gaps in depth or clarity. |
| 12–14 | C | Adequate work — the basic elements are present but the treatment is superficial or contains notable gaps. |
| < 12 | D/F | Work does not meet the minimum standards for one or more criteria. |
8 Academic Honesty & Use of AI
8.1 Academic Honesty
This is an individual assignment. All written content and explanations must be your own. You may consult sources freely (and must cite them), but you may not copy text from sources into your submission. Copying without attribution constitutes plagiarism and is subject to the University’s Academic Code of Honesty.
8.2 Use of AI
The course AI policy (see syllabus) applies to this project. You may use AI tools for tasks such as locating references, checking notation, or getting feedback on the clarity of your writing. You may not use AI to generate the substantive content of your project—the identification of your model, the explanation of what the differential equation says, and the interpretation of its behavior must reflect your own understanding.
You should be able to explain every claim and equation in your submission independently and in detail. If you use AI assistance, note briefly how you used it (a one-sentence acknowledgment at the end of your submission is sufficient).
9 Submission Instructions
- Submit your work via the course learning management system by the posted deadline.
- Posters must be submitted as a PDF.
- Slide decks may be submitted as PDF,
.pptx, or.key. - File name: use the format
LastName_DEProject(e.g.,Smith_DEProject.pdf). - Late submissions will be accepted up to 48 hours after the deadline with a 10% per-day deduction. Extensions must be requested by email at least 24 hours before the deadline.
10 Getting Help
You are encouraged to visit office hours at any stage of the project — to discuss topic ideas, get feedback on a draft, or ask questions about the mathematics. The Writing Center (see syllabus) is also a valuable resource for feedback on clarity and organization.
Wednesdays and Fridays 10:00–11:30 am, LSC 319A. Additional appointments available by email: jason.graham@scranton.edu.