Credits

This lab is a descendent of an earlier lab on Tangent Planes written by Cindy Kaus.  Dan Drake did a major rewrite in 2002, and then I overhauled it again in February 2004.  We changed the focus a little bit, and added a few things here and there; having taught this lab for a few years now, we've learned what the sticking points are for students, so I've tried to add extra explanations in these parts.  I also changed the exercises, except for #1, which Dan wrote, and the pseudo-exercise in the "Conspiracy Theory" section, which is also Dan's.  I changed the rest of them so we'd have a little variety; the previous exercises have been used for the last 4 years or so.

It's a little difficult to completely describe who did what, but here's an attempt:

-- I don't believe any of the writing is Cindy's; the only thing remaining is her choice of the surface and the point where we find the tangent planes.

-- The "Plotting Planes" and "Tangent Plane Conspiracy Theory" sections are all Dan's; at most I changed a few words here or there, or added a Live command.

-- The other sections are fairly major rewrites of Dan's original sections.  A lot of his original text remains.  Some of it remains but has been modified a bit, because of reorganization, etc.  Some of it is new text added by me.  To make things more complicated, it's all intertwined; many paragraphs combine Dan's writing with mine.

[ Update (Fall 2004): switching textbooks really messed this lab up.  We used to parametrize "general" cross sections, i.e. the points in the surface over any line in the xy-plane which went through the appropriate surface.  In the new textbook, students know about parametric equations of lines, but not parametric curves, and not the tangent vector of a parametric curve.  I had to gut that section and replace it with a version where we only use tangent vectors derived from the partial derivatives.  Ah well. ]

This would be a major mess, but fortunately we've all agreed to use the same license, and it works out.  The current version of the lab is copyright 2004 by Jonathan Rogness (rogness@math.umn.edu) and is protected by the Creative Commons Attribution-NonCommercial-ShareAlike License.  You can find more information on this license at http://creativecommons.org/licenses/by-nc-sa/1.0/.   (As mentioned, parts of this are copyright 2000 by Cindy Kaus and 2002 by Dan Drake and are protected under the same license.)

Although it's not specifically required by the license, I'd appreciate it if you let me know if you use parts of our labs, just so I can keep track of it.  Please send me any questions or comments!

Created by Mathematica  (October 4, 2004)