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Thomas J. Pfaff – PRIMUS, 2024
The logistic differential equation is ubiquitous in calculus and differential equations textbooks. If the model is developed from first principles in these courses, it is usually done in an abstract mathematical way, rather than in one based in ecology. In this short note, we look at examples of how the model is derived in mathematical texts and…
Descriptors: Calculus, Mathematics Instruction, Textbooks, Ecology
Lucas, Krista L.; Lucas, Timothy A. – PRIMUS, 2022
It is increasingly important for mathematics students to engage in active learning along with discussion of material with their peers. "Slopes" is a mobile application designed to visualize solutions to differential equations and support active learning in the classroom. We implemented group activities using "Slopes" into an…
Descriptors: Mathematics Instruction, Equations (Mathematics), Active Learning, Computer Oriented Programs
T. Clark – PRIMUS, 2024
A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the…
Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Equations (Mathematics)
Ding, Wandi; Florida, Ryan; Summers, Jeffery; Nepal, Puran; Burton, Ben – PRIMUS, 2019
We share our experience and lessons learned from using Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations (SIMIODE) modeling scenarios in our Differential Equations I class at Middle Tennessee State University. Specific projects with Python codes are presented. Discussions are brought forth on how to…
Descriptors: Calculus, College Mathematics, Mathematics Instruction, Mathematical Models
Kadas, Z. – PRIMUS, 2018
We make a case for including difference equations, in particular the discrete logistic equation, in basic differential equations courses. Contrasting the behavior of discrete and continuous models enriches students' understanding of both modeling and differential equations. To facilitate sharing discrete population models with students, some…
Descriptors: Equations (Mathematics), Mathematics Instruction, College Mathematics, Undergraduate Study
Linhart, Jean Marie – PRIMUS, 2019
This article describes a method for using the United States Census data to open a differential equations course. The question of finding a model for the United States population data gives students a first experience with creating a model using differential equations, and also understanding derivatives, what they mean, and how to calculate them in…
Descriptors: Census Figures, Equations (Mathematics), Calculus, Mathematical Models
Spindler, Richard – PRIMUS, 2019
Project-based learning supports unique and authentic problems in differential equations courses. An intuitive, interesting and deep differential equations project is described. The description illustrates a case study of guiding students through a complex project and the technical and personal rewards gained from it. Valuable advice is provided to…
Descriptors: Student Projects, Calculus, Equations (Mathematics), Mathematics Instruction
Livingston, Colleen – PRIMUS, 2019
This paper describes an activity using a dog treat ball to introduce systems of first-order differential equations. Beads are placed in the first of two hemispherical chambers of a food-dispensing dog toy. As the ball is turned, students track the number of beads in the first chamber, the second chamber, and the exterior of the ball. Students…
Descriptors: Calculus, Equations (Mathematics), Spreadsheets, Toys
Winkel, Brian – PRIMUS, 2015
We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…
Descriptors: College Mathematics, Undergraduate Study, Mathematics Instruction, Equations (Mathematics)
Shelton, Therese; Laurent, Theresa; Agyemang-Barimah, Beulah – PRIMUS, 2019
We present adaptable activities for models of drug movement in the human body -- pharmacokinetics -- that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models,…
Descriptors: Equations (Mathematics), Active Learning, Calculus, Pharmacology
Diedrichs, Danilo R. – PRIMUS, 2019
Harvesting models based on ordinary differential equations are commonly used in the fishery industry and wildlife management to model the evolution of a population depleted by harvest mortality. We present a project consisting of a series of scenarios based on fishery harvesting models to teach the application of theoretical concepts learned in a…
Descriptors: Mathematical Models, Equations (Mathematics), Calculus, Industry
Ekici, Celil; Plyley, Chris – PRIMUS, 2019
Following a modeling-first approach to differential equations, inquiry-based learning activities on modeling and controlling the growth of locally relevant species, such as lionfish or sea turtles, are developed by the authors. Emerging exemplary practices are presented, building towards a balanced teaching of differential equations involving…
Descriptors: Calculus, Mathematics Instruction, Inquiry, Mathematical Models
McCarthy, Chris; Lan, Jie; Li, Jieying – PRIMUS, 2019
We present noncompetitive adsorption as "particles in a box with one sticky wall." We start with a general model that can be modeled as a simple ordinary differential equation (ODE). To verify the ODE students run a computer simulation. The ODE's solution imperfectly fits the simulation's data. This leads to the diffusion partial…
Descriptors: Equations (Mathematics), Mathematical Models, Problem Solving, Computer Simulation
Czocher, Jennifer A.; Tague, Jenna; Baker, Greg – PRIMUS, 2019
In this paper, we tell a story of iterative design and continual improvement of an asynchronous technological resource, pencasts, to support development of students' modeling skills while studying at home. Our students were typically engineering majors, enrolled in differential equations as a prerequisite for their subsequent engineering courses.…
Descriptors: Homework, Mathematical Models, Technology Uses in Education, Asynchronous Communication
Starling, James K.; Povich, Timothy J.; Findlay, Michael – PRIMUS, 2016
We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…
Descriptors: Undergraduate Study, College Mathematics, Mathematics Instruction, Equations (Mathematics)