A Laboratory Approach to Introductory Differential Geometry

曲线与曲面的微分几何在微积分和线性代数基础课中具有重要的巩固作用。本主题为几何现象的可视化提供了工具，并将其应用于物理、工程、计算机科学和其他数学领域。这个主题特别适合交互式计算机图形学。在这个项目中，一套完整的可移动的、交互式的计算机图形实验室模块正在开发中。这些材料可以用来补充微积分和线性代数的标准课程，也可以用来补充初等微分几何的标准教科书。这些材料也可以为建立一个实验室强化的微分几何课程提供基础。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来增强可视化体验。每个模块呈现一个单独的主题或相关的主题，通过例子来说明，学生可以根据问题和建议修改这些例子。这些模块以示范-调查模式编写，非常适合合作和协作活动。目标学生群体包括考虑主修数学、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.