Teaching Differential Equations with Modeling-First Scenarios

Dialogs, Methods, and SIMIODE Resources

Brian J. Winkel

• Publisher: American Mathematical Society
• Year: 2026
• Topic: Mathematics
• eBook ISBN:
  9781470485047
• Subtopic: Mathematics General
• Index: Mathematics

Written by the founder of SIMIODE (Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations), this book provides a collection of resources that facilitate a modeling-first approach to teaching differential equations. Each of the forty-three chapters presents a unique, realistic, and classroom-tested modeling scenario, covering diverse topics such as chemical kinetics, stochastic processes, circuit tuning, and stadium design. The modules are standalone, meaning they can easily be introduced into an instructor's differential equations course. Through these activities, students discover how differential equations arise naturally and appreciate their importance. The material is presented in an informal style, taking the form of conversations between two colleagues discussing the underlying modeling scenarios. These colleagues share their methods, pedagogical approaches, and experiences, answering questions which arise about how to teach modeling. These dialogs also provide scaffolding, advice and reflections for faculty considering introducing active-learning opportunities into their classes. Teaching Differential Equations with Modeling-First Scenarios offers a friendly introduction to modeling activities in the undergraduate classroom, with only prior exposure to derivatives being required. For the instructor, a desire to engender an attitude of experimentation, investigation, and excitement in their students is the most important prerequisite. Materials supporting the scenarios will be available on the AMS Bookstore at www.ams.org/bookpages/clrm-78 and on the SIMIODE webpage.

Table of contents

• Cover
• Title page
• Copyright
• Contents
• Preface
• Chapter 1. Death and Immigration
• Chapter 2. Falling Column of Water
• Chapter 3. Sublimation of Dry Ice
• Chapter 4. Slick Oil Slick Modeling
• Chapter 5. Hang Time
• Chapter 6. Deep Well Timing
• Chapter 7. Chord Path Time
• Chapter 8. Falling Coffee Filters
• Chapter 9. Intraocular Surgery Recovery
• Chapter 10. Evaporation
• Chapter 11. Cooling It
• Chapter 12. Building an Ant Tunnel
• Chapter 13. Chemical Kinetics
• Chapter 14. Ramp Bounce
• Chapter 15. Frequency Response
• Chapter 16. LSD
• Chapter 17. Struggle for Existence
• Chapter 18. Mystery Circuit
• Chapter 19. Chemical Optimization
• Chapter 20. Stochastic Processes
• Chapter 21. Tuned Mass Dampers
• Chapter 22. Machine Replacement
• Chapter 23. Guitar Tuning
• Chapter 24. College Savings
• Chapter 25. Dog Drugs
• Chapter 26. Ice Melt
• Chapter 27. Disease Spread
• Chapter 28. Time of Death
• Chapter 29. Water Clock
• Chapter 30. Drug Administration
• Chapter 31. Cloth Dry
• Chapter 32. Rocket Flight
• Chapter 33. Stadium Design
• Chapter 34. Catapult Launch
• Chapter 35. Falling in Water
• Chapter 36. Circuit Tuner
• Chapter 37. River Crossing
• Chapter 38. Dialysis
• Chapter 39. Insect Colony Survival
• Chapter 40. Pursuit Models
• Chapter 41. Acorns, Rodents, and Snakes
• Chapter 42. Lipoprotein Modeling
• Chapter 43. Trig Function Approximation
• Postlude –Make That Prelude
• Bibliography
• Index