Dynamic Visualization Tools for Multivariable Calculus

数学科学（21）这个项目是重铸现有的多变量微积分可视化工具集到一个基于Web的Java应用程序，可在一个开放访问服务器上用于STEM课程。该应用程序的目的是支持学生对多元微积分中涵盖的概念的几何直觉的发展，帮助他们更深入地理解概念，并在概念之间建立视觉联系。PI正在使用此应用程序编写指导探索实验室活动，以便教师可以鼓励学生在正式课堂之外使用这些工具。此外，一系列额外的独立Java小程序的创建正在进行中，这些小程序演示和探索微积分的主要三维概念，包括旋转体积和常见横截面体积，以及多变量微积分中的其他主题。这些独立模块使教师能够快速演示某些概念，并显示一般可视化探索工具中不容易表示的特定信息。这些小应用程序的定制是可能的，允许将喜爱的功能和设置以及相关参数保存在由父小应用程序生成的定制网页中，然后可以将其张贴在用户自己的网站上。该项目的智力价值在于PI的经验，PI已经创建了90多个Java小程序，支持四种主要的微积分教科书（Anton，托马斯，瓦尔贝格和Salas）。此外，正在开发的动态可视化工具增强了多元微积分的教学和学习。该项目正在对数学科学界产生更广泛的影响，为教育工作者提供可靠的可视化工具，以提高他们的微积分教学。此外，这些工具可用于工程和物理课程。所有的小程序和支持材料都通过MathDL网站和国家会议演示文稿发布和广泛传播。

Mathematical Sciences (21) This project is recasting an existing Multi-variable Calculus Visualization tool set into a web-based Java application available on an open access server for use in STEM courses. The purpose of the application is to support the development of students' geometric intuition about the concepts covered in multi-variable calculus, helping them to understand concepts more deeply and make connections between concepts visually. The PI is writing guided exploration laboratory activities using this application so that faculty can encourage students to use these tools outside of the formal classroom. In addition, the creation of a series of additional stand-alone Java applets is underway that demonstrate and explore the major three-dimensional concepts of calculus, including volumes of revolution and volumes of common cross-sections, as well as other topics in multi-variable calculus. These stand-alone modules enable instructors to quickly demonstrate certain concepts as well as display specific information not easily represented in the general visualization-exploration tool. Customization of these applets is possible allowing favorite functions and settings and relevant parameters to be saved in a custom web page, generated by the parent applet, which can then be posted on the user's own website. The intellectual merit of the project lies in the experience of the PI who has created more than ninety Java applets supporting four major calculus textbooks (Anton, Thomas, Varberg, and Salas). Furthermore, the dynamic visualization tools under development enhance the teaching and learning of multi-variable calculus. The project is exerting a broader impact on the mathematical sciences community by providing reliable visualization tools for educators to use to enhance their teaching in calculus. Moreover, the tools are usable in engineering and physics classes. All applets and support materials are being published and widely disseminated through the MathDL site and national conference presentations.