At UGA, graduate students in Mathematics are put into teaching roles by our second year, so the department provides training courses for us in our first year. As a part of this training course, we chose various topics from Multivariable Calculus to present, so we could receive feedback on our lecturing styles.
This write-up is a quick refinement of the talk I gave, which was on computing moments and centers of mass of solid bodies. I found the treatment in most Calculus texts to be unmotivated – it’s a travesty that it’s often divorced from the notion of moments from probability theory, which recover familiar concepts such as the expected value and variance.
With that in mind, I tried to approach it in a slightly different way.