NSF Logo Exploring Multivariable Calculus
Dynamic Visualization Tools for Multivariable Calculus (Developed with support from the NSF: DUE-IUSE #1524968 and DUE-CCLI #0736968)


CalcPlot3D JavaScript App

CalcPlot3D Java Applet

Professor Seeburger's Faculty Webpage

Dynamic Calculus - Additional Calculus Visualizations

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Welcome to Exploring Multivariable Calculus!  This website is dedicated to exploring calculus, differential equations and other mathematics visually using the computer.  In particular, it's focused on helping you explore multivariable calculus, differential equations, and some three-dimensional topics within linear algebra and single variable calculus.  In the left panel, you will find a link to another area of my website that is focused on single variable calculus as well as a link to my instructor home page.

This web project is being developed with support from the National Science Foundation under the grants, DUE-IUSE 1524968 (2015-Present) and DUE-CCLI 0736968 (2008-2012).

CalcPlot3D was developed as a Java applet under a first NSF grant between 2008 and 2012. This applet can still be used effectively in teaching and learning multivariable calculus, but it is getting more difficult to access it. Firefox and Internet Explorer 11 still allow signed Java applets like this one and the many others on my website to run. However, because it is becoming increasingly difficult to run Java applets, I have begun to convert the CalcPlot3D visualization tool to JavaScript. As a JavaScript app, it should run well not only on computers (in Chrome), but also on tablets and even phones. Currently most of the features of the Java version of CalcPlot3D have been recreated in the JavaScript app version. There are even some new features introduced in the new app! These new features include:

  • The user can create 3D regions with top and bottom surfaces as well as being resticted 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.

Links to both versions of the CalcPlot3D visualization tool can be found in both the left and right sidebars. The first one is the newly developed JavaScript version of CalcPlot3D, and the second is the previously developed Java version of CalcPlot3D.

Why use visualizations like those found here to explore multivariable calculus?  As you begin to explore the Java applets found on this site, I think you will find a richer understanding of the geometric aspects of the concepts of multivariable 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.  Now that I have these computer visualization tools, I feel I can show students a much clearer picture of what I have been describing verbally.

The JavaScript version of CalcPlot3D should work on any modern browser on any mobile device (phone or tablet) and on any computer. I recommend using the Chrome browswer on computers, since it supports the most current JavaScript features.

If the Java applets on this site do not work for you on a computer using Firefox or Internet Explorer 11, you most likely need to  Click here to install the newest version of the  Java Plugin on your browser.




  • CalcPlot3D is included as a resource in the Multivariable Calculus Course Community at the MAA's MathDL website. (Also see the main Course Community page.)  Please visit the CalcPlot3D resource page there and RATE it!  Also please consider adding a comment (anonymous) and/or start/add to a discussion thread about this applet and how you have used it.

    There are also a number of other useful resources for teaching/learning multivariable calculus in this collection that you may find useful.

  If you are an instructor using this project in any way, please send me an email
to let me know of your interest.  I would love to see more people using the materials from this project, and it is important that I be able to report how the project is doing to the NSF.

I also encourage anyone who is interested in this project to take the time to write something on the discussion board.  You will need to become a member to do this, but I am the only one who will see this member information.  It is a private website, and membership makes it easier to keep spam from being placed on the discussion board.  Please consider sharing ways you have used the project materials with your class, any special projects you have used with your multivariable calculus class, any real-life applications or examples you have found especially useful in this class, links to other useful materials for multivariable calculus on the web, etc.  My goal for this discussion is to make it a place for us to exchange ideas and further enrich the resources of this website for teaching and learning multivariable calculus.

The following PDF documents give more information about the goals and current state of the project.

Discuss (1 response)



Archive and Beta Test Version Link

App and Applet Links

NEW! JavaScript App, CalcPlot3D This one runs on phones, tablets, and in the Chrome browser on computers.

Multivariable Calculus Exploration Java Applet, CalcPlot3D

This version of the Java applet opens it in its own window: CalcPlot3D

To open the Java applet using Java Web Start (allowing it to run on your computer later without an internet connection) click the button below:

Note that this will create a shortcut to CalcPlot3D on your desktop as well as on your Start menu.

Video Tutorials

Topical Visualization Examples

Vector Projection Visualization (JavaScript)

Curvature & Osculating Circle Example (Java)

TNB-Frame Example (Java)

A Line Integral of a Vector Field with 0 Work (Java)

Computing Volumes:

Washer Method (Java applet)

Shell Method (Java applet)

Volumes of a Common Cross-Section (Java applet)

Exploration Activities

Dot Product Exploration/Assessment  (10 - 15 minutes)

Cross Product Exploration/Assessment  (10 - 15 minutes)

Velocity-Acceleration Exploration/Assessment  (about 1 hour)

Lagrange Multiplier Exploration/Assessment  (about 1 hour)

(Note:  If possible, please complete the entire activity once you begin.)

Before you attempt an exploration, please try the CalcPlot3D applet using the link above.  This way, you will find out if you need to update your Java Plugin in your browser or possibly use a different browser to complete the exploration without technical difficulties.

This page was last updated: Dec. 21, 2016

Copyright 2017 Exploring Multivariable Calculus

Creative Commons License
Exploring Multivariable Calculus by Paul Seeburger is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.
Clarified rights and restrictions of the license for this project can be found at http://web.monroecc.edu/calcNSF/LicenseTerms.

"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 (NSF)."



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