Computer Lab for Differential Equations & Dynamical Systems Courses

微分方程计算机实验室

• 批准号: 9750457
• 负责人: Robert Devaney
• 金额: $ 3.5万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9750457&HistoricalAwards=false
• 关键词: Computer; Lab; Differential; Equations; &amp

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.

本计画的目标是建立一个用于动力系统和微分方程课程教学的计算机实验室。在过去的几年里，动力学小组的成员已经参与了这些领域本科阶段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大量的时间来教授解法。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上看解，他们可以看到相平面如何随着参数的变化而变化，他们可以探索分岔现象。此外，现在在动力学课程中，甚至可以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。该项目的目标是提供计算机设备，以便学生可以从这些类型的丰富活动中受益。