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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.
The following PDF documents give more information about the goals and current state of the project.
ANNOUNCEMENTS:
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.
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.
March 12-13, 2010 I will be presenting on this project at ICTCM (the International Conference on Technology in Collegiate Mathematics) in Chicago.
Links: http://www.ictcm.org/program/disSession.asp?sessionName=Research%20and%20Dissemination
http://www.ictcm.org/program/disSession.asp?sessionName=Calculus
August 5-7, 2010 I will be presenting a 4-hour minicourse on this project at MathFest 2010 in Pittsburgh, PA. Please consider attending, if you are a calculus professor interested in this project.
#6 — Creating Demonstrations and Guided Explorations for Multivariable Calculus using CalcPlot3D
Paul Seeburger, Monroe Community College
Part 1: Friday, August 6, 3:30 p.m. – 5:30 p.m.
Part 2: Saturday, August 7, 3:30 p.m. – 5:30 p.m.
It is often difficult for students to develop an accurate and intuitive understanding of the geometric relationships of calculus from static diagrams alone. This course explores a collection of freely available Java applets designed to help students make these connections. Our primary focus will be visualizing multivariable calculus using CalcPlot3D, a versatile new applet developed by the presenter through NSF-DUE-0736968. Participants will also learn how to customize this applet to create demonstrations and guided exploration activities for student use. Images created in this applet can be pasted into participants’ documents. See http://web.monroecc.edu/calcNSF/. Some basic HTML experience is helpful. All participants are expected to bring a laptop computer to the minicourse.
This minicourse includes 2-hours on how to use the main project applet, CalcPlot3D, and 2 hours on how to create and edit scripts using CalcPlot3D. Scripts allow you to create demonstrations, student explorations, or customized versions of the applet that start with the functions and curves you desire. For more information on the conference see: http://www.maa.org/mathfest/mathfest.cfm
For the official announcement of this minicourse, see Minicourse #6 at:
http://www.maa.org/mathfest/minicourses.cfm
I also plan to present two other contributed paper sessions related to this project at MathFest 2010.
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.
If the applet does not work, you need to simply Click here to install the newest version of the Java Plugin on your browser.
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Exploring Multivariable Calculus
