Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

Abstract

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 this approach, including parameter estimation.

Keywords:

• Differential equation
• first order
• second order
• learning in context
• modeling
• technology
• data
• parameter estimation

Additional information

Notes on contributors

Brian Winkel

Since moving to Emeritus status in May 2011 at the United States Military Academy at West Point, Brian Winkel has enjoyed the attendant freedom to pursue his own interests at his own pace. This has led to revisits to and publishing of previous discovered teaching approaches. While he misses his former role as mentor to younger faculty through personal contact he realizes the potential to reach colleagues through writing. His background is in abstract algebraic inquiry—quotient rings of Noetherian rings to be specific, but over the years (many) he has enjoyed discovering and teaching applications of mathematics. He is the founder and Editor Emeritus of the journal, PRIMUS – Problems, Resources, and Issues in Mathematics Undergraduate Studies, and also founder and Editor Emeritus of the journal Cryptologia. He is currently Director of SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations at www.simode.org.