Marshall University Math Colloquium
Friday, November 5,
3:00 P.M.
Smith Hall 509
Kelli Hall and Elizabeth Duke
“Time
Scale Calculus and Dynamical Systems”
Abstract: In his
1988 Ph. D. dissertation, Stefan Hilger united
continuous and discrete calculus under one calculus system—time-scale calculus.
Employing the delta or Hilger derivative, time-scale
calculus derives its beauty from the ability to perform on a “mixed” domain,
which combines discrete and continuous data sets. Hilger’s
calculus relies on the idea that we can use the same differentiation and
integration systems and change only the time scale from discrete (or
“isolated”) to continuous (or “dense”) and vice versa, rather than changing the
calculus system. This talk examines the connection between Hilger’s
work and the field of dynamical systems by exploring the possibilities for
using time scales to shed light on the gap between solutions of the logistic
equation in difference and differential calculus. We draw this parallel through
an example, which models population with the logistic equation.
Snacks will be served.
Next Colloquium: November 19.