Exploring Multivariable Calculus!

Hyperboloid of one sheetKlein BottleFigure 8 Klein Surface

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 a 3-minute video about this project on the 2020 STEM for all Video Showcase.

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.

The new JavaScript version of CalcPlot3D is ready for use!  Use the link above to access it!  To access the Java applet version of CalcPlot3D (or another of my Java applets) see my Calculus Java Applets page.

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.

National Science Foundation logoThis 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.