Teaching a Modern ODE Course

Attending MAA MathFest 2014 in Portland, Oregon? Stop by this informational session on teaching a modern ODE course.

Hilton and Executive Tower

22nd Floor

Mount St. Helens Suite

Friday, August 8

3:30pm

The differential equations course has changed radically over the last quarter century.  Easy access to powerful computation has enabled visualization to play a much larger role. The increasing mathematization of the life sciences has greatly expanded the kinds of models available for investigation. The advent of dynamical systems has made new kinds of questions imaginable and accessible. A modern ODE course has to take all this progress into account, though it is perhaps not clear exactly how to do so.  Anne Noonburg―University of Hartford and author of OrdinaryDifferential Equations from Calculus to Dynamical Systems―and Steve Kennedy―Carleton College and MAA Books Sr. Acquisitions Editor―will lead a discussion focused on how best to react to these changes in your ODE course. We will ask such questions as:

• What is the appropriate role of modeling in the ODE course?
• How do we balance the needs of physics, biology and engineering majors in the course?
• What are good sources of deep and interesting models?
• How much emphasis on numerical methods is appropriate?
• Similarly how much dynamical systems theory and visualization?
• What is the appropriate role of technology and what are good choices?
• Is a Linear Algebra prerequisite necessary, or can the needed material fit in the ODE course?

MAA Books Beat: Extraordinary Book on Ordinary Differential Equations

Written by Steve Kennedy, MAA Books Beat is a column written for MAA FOCUS. Extraordinary Book on Ordinary Differential Equations appears in the April/May 2014 issue.

Mathematics changes slowly; the mathematics curriculum changes even more slowly. A few years ago, to celebrate the tercentenary of L'Hôpital's Calculus, some colleagues and I read it seminar-style. The most striking thing about the experience was that his table of contents looked shockingly similar to our departmental calculus syllabus. That being said, in the 30 years I've been teaching collegiate mathematics, there is one course in the undergraduate math curriculum that has changed dramatically–the course in ordinary differential equations (ODE).

These changes are rooted in the calculus reform movement of the late 1980s and early 1990s, the easy access to powerful computing and visualization, and the rise of dynamical systems theory and its accompanying qualitative point of view.

The calc reform movement taught us to explain everything from graphical, numerical, and symbolic perspectives. Computing, of course, made it possible to do this in effective ways, especially the numerical and graphical bits. Dynamical systems provided entirely new ways of thinking about the evolution and bifurcation of systems.

The New on View

All these changes are fully on view in Virginia (“Anne”) Noonburg's Ordinary Differential Equations from Calculus to Dynamical Systems, newly released by the MAA. Noonburg has a distinguished record of research in dynamical systems, especially concentrating on equations that model biological systems. You clearly see these intellectual interests in this book.