Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or ...microscopic variables, even though no equations are explicitly given on the macroscopic level. This will facilitate a study of how the model behavior depends on parameter values including an understanding of transitions between different types of qualitative behavior. These methods are introduced and explained for traffic jam formation and emergence of oscillatory pedestrian counter flow in a corridor with a narrow door.
This paper discusses experience with alternative assessment strategies for an introductory course in dynamical systems, where the use of computer algebra and calculus is fully integrated into the ...learning process, so that the standard written examination would not be appropriate. Instead, students' competence was assessed by grading three large scale projects submitted during the course of the semester, supplemented by an oral examination. The oral required students' to discuss their electronic toolbox of symbolic, numerical and graphical code fragments collected from the electronic textbook and their project reports, and to demonstrate its robustness by trying to solve an unseen problem using it. (Contains 1 figure.)
