Credits

The ArcLength section of this lab is a substantial rewrite of the old ArcLength lab written by Cindy Kaus, which was actually written in .  Exercises 1 and 3 are the same, but the text surrounding them has been completely changed.  The introduction and the section about line integrals of scalar functions are both brand new.  In other words, this lab was basically written from scratch, except for two of the exercises.  The section on line integrals was added in March 2004; the rest of it was written in February 2002.

The old exercise 2 went something like this: start with two completely different arcs, and estimates of their lengths.  If you evaluate the derivatives at the point t=π/2 for each parametrization, you find that the second arc's tangent vector is longer than the other.  From this the students were asked to extrapolate that the arc length estimate of the second curve is less accurate.  At best this wasn't the whole story; at worst it's an incorrect claim.  (Maybe I was misinterpreting the problem?)  In any case, I hope the current exercise 2 does a better job.

"Segments" and "Estimate" are part of a package used in the old lab.  Evidently this package was from Lafayette, although I haven't found any references to it at Lafayette's web site.  To avoid licensing issues I may go back and write new versions of these commands, but the documentation with the commands says they can be freely used.  You can find this in the math2374.nb file.

Note that this lab used to include the animation commands which were moved to Lab 2A (Parametrizing Curves).  To fill the space I added the section about line integrals.

Other than the exercises from Cindy Kaus, this lab is copyright 2002, 2004 by Jonathan Rogness (rogness@math.umn.edu).  We've both 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!

Created by Mathematica  (November 6, 2004)