A Laboratory Approach to Introductory Differential Geometry

点击翻译按钮获取中文摘要

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.