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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
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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
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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
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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
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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)
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Bibi, Aisha; Ahmad, Mushtaq; Shahid, Wajeeha; Zamri, Sharifa NorulAkmar Syed; Abedalaziz, Nabeel Abdallah Mohammad – International Electronic Journal of Mathematics Education, 2019
Teaching and learning of differential equations (DEs) have a prominent role in all the fields of education. In spite of its prominence and frequent applications, teaching and learning of DEs is still considered as one of the most difficult, particularly at pre-university level. This is because, the topic of differential equation along with…
Descriptors: Calculus, Equations (Mathematics), Undergraduate Students, College Mathematics
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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
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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
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Winkel, Brian J. – International Journal of Mathematical Education in Science and Technology, 2012
This article offers modelling opportunities in which the phenomena of the spread of disease, perception of changing mass, growth of technology, and dissemination of information can be described by one differential equation--the logistic differential equation. It presents two simulation activities for students to generate real data, as well as…
Descriptors: Mathematical Models, Calculus, Diseases, Class Activities
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Camporesi, Roberto – International Journal of Mathematical Education in Science and Technology, 2016
We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…
Descriptors: Algebra, Calculus, Equations (Mathematics), Mathematics Instruction
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Sochacki, James S.; Thelwell, Roger; Tongen, Anthony – PRIMUS, 2019
How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…
Descriptors: Calculus, Mathematics Instruction, Mathematical Models, Problem Solving
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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)
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Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2019
Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive…
Descriptors: Mathematics Instruction, Problem Solving, Equations (Mathematics), Teaching Methods
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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
Khotimah, Rita Pramujiyanti; Masduki – Online Submission, 2016
Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…
Descriptors: Calculus, Mathematics Instruction, Problem Solving, Teacher Improvement
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