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.
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.
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.