by Cindy Kaus which described all of the pathological examples of things that can go wrong -- everything from discontinuous functions to differentiable functions whose mixed partials are not equal. Students were asked to prove these facts about the functions and were given some guidance about how to do it in Mathematica. In Spring 2002 Dan Drake completely rewrote the entire thing as a Mathematica notebook, which had two advantages for us: (1) consistency, because now all of the labs were in notebook form, and (2) he could include graphing commands and other pictures to help make his point. Dan wrote pages and pages of terrific explanations which helped a lot; the only overlap with Cindy's original lab were the four exercises, although he restated and split those into steps to help students along.It was still a very hard assignment. People weren't learning the subtle details in the labs, and we weren't using the really pathological examples later on in the course anyway. In January 2004 I revamped the lab to be more interactive and example-driven. The exercises have been scaled back and are based on the examples. Hopefully this version will go over well.
Everything up to example 1 was written by Dan, as well as the excellent explanation of the "technical definition" of differentiability. Example 3 is an expansion of an example he added to the lab, and exercise 3 is a slight reworking of his version of one of Cindy's exercises. There's not much else left of Cindy's original lab, I guess. Example 3 is based on her "Example (i)."
This version is copyright 2004 by Jonathan Rogness (rogness@math.umn.edu), with the exception of those parts described above, which are copying 2002 by Dan Drake and 2000 by Cindy Kaus. All of us have agreed to use the same license, so this lab 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/
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!