Computer Lab for Differential Equations & Dynamical Systems Courses

该项目的目标是建立一个计算机实验室，用于动力系统和微分方程式课程的教学。在过去的几年里，Dynamic小组的成员一直在参与这些领域的本科课程的全面更新。最近的技术进步已经深刻地改变了这些课程可以而且应该被教授的方式。不再有必要花大量时间在微分方程式课堂上教授食谱解题方法。相反，使用技术，学生可以象征性地计算这些解决方案。然后，他们可以从几何角度查看解决方案，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，现在在动力学课程中，甚至可以向一年级的学生介绍当代数学主题，如混沌行为、Julia集、事实数据压缩等。这个项目的目标是提供计算设备，使学生能够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.