Modeling Approach in Students’ Learning and Appreciation of Differential Equations
0Day 2 | 2:00 PM–2:30 PM
"Modeling Approach in Students’ Learning and Appreciation of Differential Equations"
Presented by:
Biyong Luo, University of Massachusetts, Dartmouth MA USA
https://qubeshub.org/community/groups/simiode/expo/2025
Abstract: During the last ten years, I have taught ODEs for science and engineering majors. The objectives of the course are expansive: to understand the fundamental methods of ODEs and the mastering qualitative analysis and numerical methods in solving nonlinear differential equations, and gaining substantive understanding of mathematical modeling with ODEs or other advanced methods. In this talk, I will share my thoughtful design of course materials and modeling approach based on Zill’s book. Models and Projects: Modified logistical model, Modeling forced damped harmonic oscillators, Simple modeling spread of a contagious disease, and project 1 of Modeling complicated pollution and public policy, project 2 of a logistical population model with harvest for chapter 1-5. Two Species Models with predator-prey, competing and cooperating. Project 1of an arms race and project 2 of a modified predator-prey interaction model for chapter 7-10. The outcomes and student feedback to this dynamic curriculum have been impressive. Many students expressed their deep appreciation of how this class provided a solid foundation for other challenging courses such as biochemistry and mechanical engineering. It is the emphasis on how differential equations can applied to real-world situations, enhancing students’ learning and appreciation of ODEs that I believe we will be able to show the learner that mastery of differential equations can be impactful across a variety of careers.