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).
- 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.
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.
NOTES on using the Java version of CalcPlot3D and other Java applets:
The newest version of Firefox (starting with version 52) that released mid-March no longer supports Java applets like the Java version of CalcPlot3D and the CalcGrapher applet (and Chrome has not supported Java applets for over a year). Happily we do still have some options to continue to run Java applets. Java applets will still run in Internet Explorer 11, in all older versions of Firefox (version 51 and before) and in the new Extended Support Release versions of Firefox, versions 52+ (see below).
If you are having trouble now getting my Java applets to run, here are some useful links about this issue in Firefox and how to install an updated version of Firefox (Extended Support Release) that will still support Java applets until 2018 (in the 32-bit version).
Below are the direct links to download the correct version of Firefox (Extended Support Release) that most of you will need to continue running my Java applets. If you need other versions of Firefox for other languages or operating systems see the paragraph and link below these.
U.S. English: Windows 32-bit download: https://download.mozilla.org/?product=firefox-52.0.1esr-SSL&os=win&lang=en-US
Mac 32-bit download: https://download.mozilla.org/?product=firefox-52.0.1esr-SSL&os=osx&lang=en-US
The following link is for the download page for the Extended Support Release of the current version of Firefox. Be sure to select the option for your system that is NOT 64-bit. That is, it will be the 32-bit version. Only the 32-bit version will run Java applets. You may still need to install the Java plugin again, although if it was already installed and updated on your computer, it may well already be there.
Note that you will need to click to Activate Java on the applet page once you install this version of Firefox and open the first Java applet page. You can trust it for good and not be asked each time you run it.
Please let me know if you have any further trouble, but this ESR version of Firefox should take care of any issues for the remainder of 2017. It installs just like a normal Firefox and is the most up-to-date version in every respect.
If the Java applets on this site still do not work for you on a computer using the Extended Support Release of Firefox or Internet Explorer 11, you most likely need to Click here to install the newest version of the Java Plugin on your browser.
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.
Instructors: 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.
The following PDF documents give more information about the goals and current state of the project.