EXPO 2026: "Modeling Calculus: Eighteen Years of Rethinking “First Calculus” Through DE"

Описание: Sat | 1:30 PM–2:00 PM ET
Mariah Birgen; Department of Mathematics, Computer Science, and Physics, Wartburg College, Waverly, IA USA

Abstract: Since 2008, Wartburg College's Modeling Calculus sequence has replaced the traditional limits-derivatives-integrals-series pipeline with a year-long, modeling-first curriculum grounded in differential equations. Rather than treating modeling as an occasional application, the first course takes real questions — How often should I take my cold medicine? and What angle should I hit my driver to maximize distance? — and develops the calculus needed to answer them. Students meet derivatives as instantaneous rates of change via difference quotients and secant/tangent lines, then move almost immediately into first-order differential equations, slope fields, and Euler's method, so they never again ask, "When will I ever use this?"
Topics include exponential and logistic population models, Newton’s law of heating and cooling, mechanical models (air resistance, springs, bungee jumping), numerical integration, systems of differential equations (predator-prey, SIR, malaria), and multi-dose drug models, supported by tools such as Vensim PLE and InsightMaker.com. Communication is built into the course through structured modeling reports and projects drawn from circuits, rockets, hot air balloons, and disease dynamics.
This talk will outline the course design and rationale, highlight representative modeling arcs, and share reflections from long-term implementation, including student reactions and preparation for later differential equations and upper-level applied courses.

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