Comparing Sage and Mathematica for an Introductory Course
I'm working with a committee that's revising the undergraduate math curriculum for UCLA biology majors. We're getting rid of a lot of paper and pencil calculation that's hardly ever used in mathematical biology and introducing a lot of modeling, dynamical systems and computer work. Earlier, we decided to use Mathematica for the course, but I recently learned about Sage and like the idea of using a free program with similar features to Mathematica.
While the students will be learning some programming during the course, that's not our emphasis and they need to be able to use a fairly high level of interactivity from the beginning. (For example, they should be able to interactively manipulate function parameters in the first or at worst second lab session.) Since I'm very much a newcomer to Sage, I want to ask more experienced users how hard it would be to reproduce the functionality of this Mathematica notebook in Sage. I've seen the slider examples, but they use quite a bit of code. An equivalent to Equation Trekker, which allows you to specify initial condition for a two-ODE system by clicking on the phase plane, would also be very useful. Has anyone coded such a thing for Sage?