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.
