Integrating Instructional Computing Into Differential Equations Courses

这个项目的基础是，微分方程提供了一个很好的机会来学习真实的世界是如何工作的，一个很好的方法是通过探索特定的现实世界的问题，这种探索可以是有趣的。该项目利用了哈佛联合会的“三法则”（几何、数字和代数地呈现事物）的增强版。增强功能始终提供真实世界的解释和应用。 传统上，微分方程入门课程集中在手工寻找几个标准类型方程的封闭形式解。这个项目的重点是帮助学生更好地理解这些方程的含义。它强调理解关键概念，例如线性、平衡点、稳定性以及对初始条件或参数的依赖性。 为了使探索和好奇心的后续行动成为整个课程的现实目标，该项目为学生提供了一个强大的工具，计算机代数系统Maple。Maple绘制解决方案和方向字段，这是几何表示事物的关键。还有其他命令可以在数值级别和代数级别执行相同的操作。此外，该项目还促进学生更多地参与学习过程。合作学习是该课程的一个重要方面。为培训班编写的材料将在新闻部网站上提供。

The basis of this project is that differential equations present an excellent opportunity to learn how the real world works, that a good way to do this is by exploring specific real-world problems, and that this exploration can be fun. The project makes use of an enhanced version of the Harvard Consortium's `Rule of Three` (present things geometrically, numerically, and algebraically). The enhancement consistently provides real-world interpretations and applications. Traditionally, introductory differential equations courses concentrate on finding, by hand, closed form solutions to a few standard types of equation. This project focuses on helping students achieve a better understanding of the meanings of these equations. It emphasizes understanding key concepts such as linearity, equilibrium points, stability, and dependence on initial conditions or parameters. To make exploring and following up on curiosity a realistic goal throughout the course, the project supplies students with a powerful tool, the computer algebra system Maple. Maple plots the solutions and direction fields which are the keys to presenting things geometrically. There are other commands to do the same at the numeric level, and at the algebraic level. In addition, the project promotes a much greater involvement in the learning process on the part of the students. Cooperative learning is a significant aspect of the course. Material developed for the course will be available on the Department's web site.