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Welcome to Exploring Multivariable Calculus! This website is dedicated to exploring calculus visually using the computer. In particular, it's focused on helping you explore multivariable calculus and some three-dimensional topics within 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 instuctor home page.)
This web project is being developed with support from the National Science Foundation under the grant, DUE-CCLI 0736968.
In the left panel, you will also find a link to the main Multivariable Exploration applet and links to various focused applets in this collection.
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.
NEW FEATURES:
9-10-2009 Added the ability to view the TNB-Frame for space curves. Also the Osculating Circle and curvature value can be displayed. See the View menu on the Add a Space Curve dialog.
8-1-2009 Added a scripting feature that allows you to create a dynamic slideshow by saving slides of objects you have created in the applet. This slideshow can then be saved locally as an editable script file. You can then load the script in at a later time (perhaps during class) as part of a demonstration or by students as a guided exploration. If you are interested in more information on this feature, please ask me for the documentation (as it has not yet been posted). This scripting feature was the focus of a minicourse I presented at MathFest 2009 in Portland, OR. I hope to present this minicourse again soon, perhaps at MathFest 2010 and/or the 2011 JMM.
3-17-2009 Added a new Guided Tour/Tutorial for CalcPlot3D. You can access it here or in the CalcPlot3D applet from the Help menu.
3-5-2009 Parametric Surfaces can now be graphed. Find them on the Graph menu! See the list of examples on the Examples menu in the Parametric Surface dialog. Have fun exploring!
2-10-2009 You can now use 3D glasses to get a more convincing 3D view of the 3D plots in CalcPlot3D. You can use Red-Cyan/Red-Blue 3D glasses for almost all of the options, but there is one option for the Amber-Blue 3D glasses that were recently distributed for the Super Bowl halftime feature, and there is an option for Red-Green 3D glasses too. There are also two options for viewing the images in 3D without 3D glasses: Stereo Pair and Cross-eyed. Try these new viewing options out by selecting them from the View Settings menu in the applet. Let me know what you think! Click here for the 3D View Help to see more details.
The following PDF documents give more information about the goals and current state of the project.
If the applet does not work, you need to simply Click here to install the newest version of the Java Plugin on your browser.
Posted by Paul Seeburger on 2/4/08; 11:18:44 AM
from the dept.
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Exploring Multivariable Calculus
