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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)
Ethan Berkove; Ben Galluzzo – PRIMUS, 2024
This curated collection covers a selection of PRIMUS articles published over a roughly 12-year period that focus on modeling and applications. The collection includes sections on individual projects, courses with a significant modeling component, and modeling and applications in extracurricular settings and throughout the curriculum.
Descriptors: Mathematics Education, Undergraduate Study, Mathematical Models, Mathematical Applications
Gordon, Sheldon P.; Gordon, Florence S. – PRIMUS, 2023
This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…
Descriptors: College Mathematics, Introductory Courses, Statistics Education, Algebra
Jungck, John R. – PRIMUS, 2022
Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…
Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Models, Learning Modules
Pulley, Melissa; Rodriguez, Leoncio; Lewis, Matthew; Kohler, Brynja; Gordillo, Luis – PRIMUS, 2022
Inspired by the approach first employed by C.S. Holling in his classic "disc experiment," this article provides a sequence of learning activities that increase students' understanding of the mechanisms behind saturating effects in predator-prey scenarios. The proposed lesson is recommended for inclusion in courses that address…
Descriptors: Biology, Science Instruction, Interdisciplinary Approach, Learning Activities
Ayalew, Mentewab; Hylton, Derrick; Sistrunk, Jeticia; Melton, James; Johnson, Kiandra; Voit, Eberhard – PRIMUS, 2022
The integration of biology with mathematics and computer science mandates the training of students capable of comfortably navigating among these fields. We address this formidable pedagogical challenge with the creation of transdisciplinary modules that guide students toward solving realistic problems with methods from different disciplines.…
Descriptors: Biology, Science Instruction, Mathematics Instruction, Interdisciplinary Approach
Stoner, Melissa A.; Joyner, Robert L. – PRIMUS, 2022
Relating mathematics learned in the classroom to real situations increases student motivation and enhances learning. In this paper, we provide an example of a classroom application of calculus to physiology in two courses: "Differential Equations" and "Calculus I for Biology and Medicine." We designed and implemented a project…
Descriptors: Mathematics Instruction, Calculus, Mathematical Models, Physiology
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
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
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
Clark, Thomas J. – PRIMUS, 2019
The first day of many mathematics classes is filled with the formalities of the syllabus and a lecture introduction to the course content. Here, an alternative is presented where modeling is placed as the centerpiece to orient students to the work of differential equations; namely, to capture as beautifully and compactly as possible through the…
Descriptors: Equations (Mathematics), Calculus, Mathematical Models, College Mathematics
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
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
Rasmussen, Chris; Dunmyre, Justin; Fortune, Nicholas; Keene, Karen – PRIMUS, 2019
This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…
Descriptors: Mathematical Models, Teaching Methods, Mathematics Instruction, Inquiry
Anderson, Jeffrey A.; McCusker, Michael V. – PRIMUS, 2019
We present a new learning activity that enables students to apply eigenvalue theory to investigate a practical modeling problem. We demonstrate how to build a spring-coupled pair of pendula and describe how students can measure the movements of these pendula using open-source image processing software. We then illustrate how to analyze this…
Descriptors: Mathematics Instruction, College Mathematics, Experiential Learning, Learning Activities