A Laboratory Approach to Introductory Differential Geometry

曲线曲面的微分几何在巩固微积分和线性代数基础课程中起着重要作用。该主题提供了几何现象的可视化工具，以及应用于物理、工程、计算机科学和其他数学领域的工具。这门学科特别适合于交互式计算机图形学。在这个项目中，正在开发一套完整的可移植的、交互式的计算机图形学实验室模块。这些材料可用于补充微积分和线性代数的标准课程，或补充初等微分几何的标准教科书。这些材料还可以提供基础，在此基础上建立一门强化的实验室微分几何课程。创新包括使用新的“超文本”工具进行交互和响应，以及使用计算机图形学来增强可视化体验。每个模块提供一个主题或相关主题，并举例说明，学生可以根据问题和建议进行修改。这些模块是以演示-调查模式编写的，非常适合合作和协作活动。目标学生受众包括考虑集中学习数学、物理、工程和计算机科学的学生。

Differential geometry of curves and surfaces has an important role in solidifying the standard courses in beginning calculus and linear algebra. The topic provides the tools for visualization of geometric phenomena and for applications to physics, engineering, computer science, and other areas of mathematics. The subject is particularly well-suited to interactive computer graphics. In this project, a complete set of transportable, interactive computer graphics laboratory modules is being developed. The materials can be used to supplement standard courses in calculus and linear algebra, or to supplement a standard textbook in elementary differential geometry. The materials can also provide the foundation on which to build a laboratory intensive differential geometry course. Innovations include the use of new "hypertext" tools for interaction and response, and the use of computer graphics to enhance the visualization experience. Each module presents a single topic or related topics, illustrated by examples that can be modified by students in response to questions and suggestions. The modules are written in a demonstration- investigative mode, well suited for cooperative and collaborative activities. The target student audience includes students considering concentrations in mathematics, physics, engineering, and computer science.