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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
Peer reviewed
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
Peer reviewed
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
Peer reviewed
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
Peer reviewed
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)
Peer reviewed
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
Peer reviewed
Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2019
Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.Motivated by the work of…
Descriptors: Teaching Methods, Mathematics Instruction, Calculus, Motion
Peer reviewed
Aisha, Bibi; Zamri, Sharifa NorulAkmar Syed; Abdallah, Nabeel; Abedalaziz, Mohammad; Ahmad, Mushtaq; Satti, Umbreen – Malaysian Online Journal of Educational Sciences, 2017
In this study, different factors affecting students' differential equations (DEs) solving abilities were explored at pre university level. To explore main factors affecting students' differential equations problem solving ability, articles for a 19-year period, from 1996 to 2015, were critically reviewed and analyzed. It was revealed that…
Descriptors: Equations (Mathematics), Problem Solving, Secondary School Students, Literature Reviews
Peer reviewed
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
Peer reviewed
Azevedo, Douglas; Valentino, Michele C. – International Journal of Mathematical Education in Science and Technology, 2017
In this note, we propose a generalization of the famous Bernoulli differential equation by introducing a class of nonlinear first-order ordinary differential equations (ODEs). We provide a family of solutions for this introduced class of ODEs and also we present some examples in order to illustrate the applications of our result.
Descriptors: Generalization, Calculus, Validity, Mathematical Logic
Peer reviewed
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
Peer reviewed
Hyland, Diarmaid; van Kampen, Paul; Nolan, Brien C. – International Journal of Mathematical Education in Science and Technology, 2018
This paper reports on the first part of a multiphase research project that seeks to identify and address the difficulties encountered by physics students when studying differential equations. Differential equations are used extensively by undergraduate physics students, particularly in the advanced modules of their degree. It is, therefore,…
Descriptors: Foreign Countries, Outcomes of Education, Teaching Methods, Equations (Mathematics)
Peer reviewed
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
Peer reviewed