A Laboratory Approach to Introductory Differential Geometry

微分几何入门的实验室方法

• 批准号: 9254322
• 负责人: Thomas Banchoff
• 金额: $ 9.98万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-02-15 至 1996-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9254322&HistoricalAwards=false
• 关键词: Laboratory; Approach; Introductory; Differential; Geometry

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.

曲线和曲面的微分几何具有重要的 在巩固基础微积分课程标准中的作用 和线性代数。 本主题提供了以下工具 几何现象的可视化和应用， 物理学、工程学、计算机科学和其他领域 数学 该主题特别适合于 交互式计算机图形学 在这个项目中， 移动式交互式计算机图形实验室 模块正在开发中。 这些材料可用于 补充微积分和线性代数的标准课程，或者 作为初等微分标准教科书的补充 几何 这些材料也可以提供基础 来建立一个实验室密集的微分几何 当然了 创新包括使用新的“超文本”工具 用于交互和响应以及计算机图形的使用 以增强可视化体验。 每个模块都提供 一个单一的主题或相关的主题，说明了例子， 学生可以根据问题进行修改， 建议. 这些模块是在演示中编写的- 调查模式，非常适合合作和 合作活动。 目标学生受众包括 学生考虑集中在数学，物理， 工程学和计算机科学。