Dynamic Visualization Tools for Multivariable Calculus

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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.