Applets for multivariable calculus

When I was in Portland a few weeks ago for MathFest 2009 I attended the minicourse Creating Demonstrations and Guided Explorations for Multivariable Calculus using CalcPlot3D by Paul Seeburger.

Paul has created some applets to be used in calculus classes (mostly, but not exclusively, multivariable calculus). They can be found on his Exploring Multivariable Calculus web page. The main applet is called the CalcPlot3D Exploration Applet. About it he writes the following.

CalcPlot3D is a web-based visual exploration environment for multivariable calculus. It is intended to help students to visualize the geometric nature of many of the concepts of multivariable calculus. Graphs of up to four functions of two-variables can be graphed simultaneously along with any number of additional points, vectors, and space-curves. Contour plots can be graphed and viewed in 2D or explored in the context of the three-dimensional surface plots to which they correspond.

A screenshot of the applet is shown below.

Picture 1

[Note: at the time of the minicourse the applet wouldn’t run on Safari on a Mac (it worked fine on Firefox), but it seems to work for me now, so I assume he fixed the problem.]

Paul has other applets on his web page too. In fact, he has some applets that go with specific figures in a variety of popular textbooks (Larson Calculus, 9th ed., Anton ET Calculus, 8e, Salas Calculus, 10th ed.).

I have to mention one of the least essential, but coolest features of CalcPlot3D—it is possible to view the figures in 3D. Bring in a handful of blue/red 3D glasses and amaze your students. (The 3D effects work on a computer display and when projected onto a screen in the front of the room.)


  1. samjshah says:

    That’s a great resource. Thanks!

    I’ve collected some visualizations for MV Calc (, but I think this one might take the cake. I have to play with it a bit to be sure…

    1. Sam, Thanks for the link to your collection of applets. That’s a great resource! Dave

  2. Thanks for the post, Dave!

    You did a great job of summarizing what is available and including links. There are quite a few Single Variable Calculus applets among those on my website, but the best material (in my opinion) is certainly the multivariable calculus applet.

    I appreciate your help in sharing this project with others!


    1. Paul, thank you for the cool applets!

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