Constructing ideas and evaluation techniques to understand the effect of climate and temperature on pattern dynamics. Questions such as these introduce the use of mathematics in an applied setting of current interest, introduce basic concepts of resource management and ecology, and challenge students at any level, from just out of calculus to beginning graduate school. My field of research is nonlinear analysis, in particular bifurcation analysis of nonlinear PDEs. After developing an interest in dynamical system's methods, I initiated an undergraduate course in dynamics, intended to put some emphasis on applicational aspects and numerical exploration. For the latter I wrote an easy to use package for the investigation of dynamical systems, which can show state space, attractors, basins of attraction, bifurcations and invariant manifolds, thus giving students an immediate illustration of concepts learned in class.
Dynamics lends itself to interesting and creative undergraduate research projects.
The following is a list of some of the projects students have done for this course. Any one of them could be extended into an appropriate R.E.U. summer project. Analysis of Computer Generated Data from Atmospheric Models Attractor Reconstruction Capsizing of a Ship Distinguishing Chaos from Noise Iterated Function Systems 7. Some years ago Gunderson developed an algorithm for partitioning a distribution of points in space into subclusters for the purpose of doing visual image analysis. Extraordinarily unlikely exclusions may be used to develop confidence that the underlying dynamics is not stochastic.