Exploring Multivariable Calculus!

Welcome to Exploring Multivariable Calculus!  This website is dedicated to helping you explore multivariable calculus, differential equations, and some three-dimensional topics within linear algebra and single variable calculus.

Watch this 3-minute video about this project on the 2020 STEM for all Video Showcase.  And read this article about how Professor Shelby Stanhope has used CalcPlot3D and 3D-printed models to transform the way multivariable calculus is taught at the United States Air Force Academy.  Professor Stanhope is a CalcPlot3D project team member.

As you explore the visualization tools found on this site, I think you will enrich your understanding of the geometric aspects of the concepts of multivariable calculus, differential equations, and single-variable calculus.  My goal is to enhance the geometric intuition of calculus students so that they are able to visualize the concepts and actually “see” the rich visual relationships and interactions described by the calculus concepts.

As an instructor, I often found it difficult to draw the three-dimensional concepts clearly on the chalkboard and found myself waving my hands to try to get students to see what I was seeing.  Using these visualization tools, I can show students a much clearer picture of what I have been describing verbally.

CalcPlot3D is a free online visualization app designed for exploring the concepts of multivariable calculus!  It can also be used to explore concepts from many other math, physics and other STEM courses.  Use the link above to access it!

As a JavaScript app, CalcPlot3D should run well in any modern browser not only on computers (in Chrome) but also on tablets and phones. Currently, most of the features of the Java version of CalcPlot3D have been recreated in the JavaScript app version.  I recommend using the Chrome browser on computers since it supports the most current JavaScript features.

There are even some new features introduced in the new app, including:

• The user can create 3D regions with top and bottom surfaces as well as being restricted to a 2D domain in the xy-plane specified by two functions of x or of y.
• The user can vary the rectangular uv-domain of a parametric surface in the 2D trace plane.

This web project is being developed with support from the National Science Foundation under the grants, NSF-IUSE 2121152 (2021-Present), DUE-IUSE 1524968 (2015-2019) and DUE-CCLI 0736968 (2008-2012).  Some support was also received from two Xerox STEM grants.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.