Fellow Math Profs, I need your help!

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lohai0:
I have been tasked to come up with projects that are interesting to the students and make some of the more abstract concepts in Calculus III accessible. This week, the class is building a hyperbolic plane to investigate saddle points. I have a min/max project on stock portfolios ready to go for the next chapter, and a decent thing ready for polar and spherical coordinate integration.

However, I can't come up with anything that exciting about this next chapter, which is about gradients and directional derivatives. Does anyone know of an activity to have students work with this that is more than finding the hot spot in a microwave or working with topographical maps?

niceday:
Quote from: lohai0 on February 17, 2013,  6:09:48 pm

I have been tasked to come up with projects that are interesting to the students and make some of the more abstract concepts in Calculus III accessible. This week, the class is building a hyperbolic plane to investigate saddle points. I have a min/max project on stock portfolios ready to go for the next chapter, and a decent thing ready for polar and spherical coordinate integration.

However, I can't come up with anything that exciting about this next chapter, which is about gradients and directional derivatives. Does anyone know of an activity to have students work with this that is more than finding the hot spot in a microwave or working with topographical maps?

Not exactly what you are looking for but fun and beautiful:

lohai0:
We're using the soccer ball construction in class. It seemed too hard to teach everyone to crochet.

daniel_von_flanagan:
By the time a student is this far along, why isn't the math itself interesting?  For example, the subtle distinction between the gradient and the total derivative.  (Can you tell from the gradient whether the function is differentiable?  Given an n-tuple of functions of n variables, can you tell whether this is the gradient of a function?)  Most of the concrete applications involve  a fair amount of linear algebra and possibly things like integrals along  path; you might not have done this yet.

You could talk about steepest ascent, then mess with them and give them a hemstitching example. - DvF

lohai0:
Quote from: daniel_von_flanagan on February 17, 2013,  8:39:30 pm

By the time a student is this far along, why isn't the math itself interesting?  For example, the subtle distinction between the gradient and the total derivative.  (Can you tell from the gradient whether the function is differentiable?  Given an n-tuple of functions of n variables, can you tell whether this is the gradient of a function?)  Most of the concrete applications involve  a fair amount of linear algebra and possibly things like integrals along  path; you might not have done this yet.

You could talk about steepest ascent, then mess with them and give them a hemstitching example. - DvF

I'm with you, but Calc III is primarily a service course for science majors here, so they are not always as into the math as you'd think for the level. Our student population is not particularly academically strong, so it's less about interesting activities and more about concrete ones. Maybe topographic maps is the way to go.