Computer Lab for Differential Equations & Dynamical Systems Courses

本计画的目标是建立一个电脑实验室，以供动力系统与微分方程课程教学之用。 在过去几年中，动态小组的成员参与了这些领域本科生课程设置的全面更新。 最近的技术进步已经深刻地改变了这些课程可以和应该教授的方式。 不再需要在微分方程课上花费大部分时间教授食谱求解方法。 相反，使用技术，学生可以象征性地计算这些解决方案。 然后他们可以几何地观察解，他们可以看到相平面如何随着参数的变化而变化，他们可以探索分叉现象。 此外，现在可以在动力学课程中向一年级学生介绍诸如混沌行为、Julia集、事实数据压缩等当代数学主题。 这个项目的目标是提供计算设备，使学生可以从这些类型的丰富活动中受益。

The goal of this project is to set up a computer laboratory for use in the teaching of Dynamical Systems and Differential Equations courses. For the past several years, members of the dynamics group have been involved in a complete updating of course offerings at the undergraduate level in these areas. Recent advances in technology have profoundly changed the way these courses can and should be taught. No longer is it necessary to spend the bulk of time in differential equations classes teaching cookbook methods of solution. Rather, using technology, students can compute these solutions symbolically. Then they can view solutions geometrically, they can see how phase planes change as parameters vary, and they can explore bifurcation phenomena. Also, it is now possible in dynamics courses to introduce even first-year students to such contemporary topics in mathematics as chaotic behavior, Julia sets, factual data compression, and more. The goal of this project is to provide the computational equipment so that students can benefit from these types of enriching activities.