# The MV Calculus Final Projects

Last week my multivariable calculus class turned in their final projects, and made presentations. Of all my classes this year, by any metric, this course was my most successful. I loved seeing their final projects, and the amount of work and dedication they devoted to them. The best part: they were super proud of their projects too.

I made a post about coming up a list of fourth quarter final projects a while back. My big fear with these projects was senioritis. The projects are designed to be largely self-directed, and if a student got lazy, well, …, that would spell disaster. Luckily, none of the students in the class fell prey to that dreaded disease. My kids are great kids, so that helped. But also I let them pretty much have free reign on their projects and kept emphasizing they should pick something they WANTED to have FUN with. Lastly I met with them weekly to help them out and keep tabs on their progress — prodding them a bit here and there.

Without further ado, the four projects:

1. One student actually created a harmonograph (a device which draws damped Lissajous curves).

Yes, that is his video of his harmonograph.

2. One student researched Maxwell’s Equations and read A Student’s Guide to Maxwell’s Equations (Fleisch). He produced a written paper explaining the integral and differential forms of Maxwell’s equations.

3. One student created a giant wooden and wire sculpture (titled “The Visualizer”) which illustrated a lot of what we’ve learned about curves in 3-space. Namely, he illustrated arc length, vector equations for curves, curvature, and the tangent, normal, and binormal vector with his sculpture. He also wrote an associated paper which is to be used with the sculpture to examine these ideas in more detail.

4. One student took foam board and cut a whole bunch of figures (from the simple square to weird and complex shapes). He then calculated the center of gravity of these figures theoretically, and tested to see if the figures would balance at that point. Then he extended this by making figures with non-homogeneous density, calculated the center of gravity of these figures theoretically, and tested to see if the figures would balance at that point.

I mean, seriously, look at that. Amazing. These kids got into it, because it was their own thing. Because they weren’t really worried about their final grades. (I let them grade themselves.) I am going to miss these miscreants a lot next year.

1. David P says:

Do you have a picture of the wire sculpture that you could post? It sounds interesting.

2. Very cool. I love the video.

I second the request for a picture of the sculpture!

3. samjshah says:

@David @Jackie: The only picture I have has the student in it too. So I don’t feel comfortable posting it. Sorry! Next year I’ll keep this in mind!

4. Wow, Sam. That video is great, what a cool way to end the year. I imagine they were genuinely proud of what they’d built. That’s a rare achievement.

5. Very cool! Where did he (you?) find the instructions for building the harmonograph?

6. samjshah says:

@Nick: I know they were, and I really was too. I invited the math teachers and the physics teachers to our project share on the last day of class. I actually felt they were proud of the Kepler paper they wrote (https://samjshah.com/2008/12/07/keplers-laws-reprise/) too. They wanted to send it to their AP Calc teacher!

@Dave: He didn’t use instructions. I pointed him to a bunch of websites and videos, and he used the “freestyle school of carpentry.” There was a great amount of true engineering there: anticipating problems and preventing them before they arose, and then troubleshooting problems once they arose. The hardest part for my student was reducing the amount of friction so the harmonograph would draw for a long period of time.