At UGA, graduate students in Mathematics are put into teaching roles as soon as our second year, so the department provides certain training courses for first-year students. As a part of this training course, we chose various topics from Multivariable Calculus to present, so we could be critiqued and receive feedback on our lecturing styles.
This write-up is just 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 slightly unmotivated, and really think it is a travesty that it is so divorced from the generalization of moments in probability theory (which recover familiar concepts such as the expected value and variance), so I tried to approach it in a slightly different way than the usual textbook treatment.
Hope you all enjoy the read! Feel free to let me know if you have ideas for improvements or any feedback.