This blog entry provides a helpful follow-up for a couple of calculus-related topics that we covered during the Mathematics Tutorial.
- See page 12 of the above-referenced lecture note. There, the equation for a parabola () appears, and the claim that dy/dx = 2x is corroborated by solving the following expression: .In the 11-minute Khan Academy video at https://youtu.be/HEH_oKNLgUU, Sal Kahn takes on the solution of this problem in a very succinct and easy-to-comprehend fashion.
- On pp. 18-23 of the Mathematics Tutorial, I showed how y = ex can be approximated with a Taylor polynomial centered at x=0 for values ranging from -2 to +2. In his video lesson entitled “Visualizing Taylor polynomial approximations”, Sal Kahn essentially replicates the work I did; the main difference between my example and Sal’s example is that Sal approximates y = ex with a Taylor polynomial centered at x=3 instead of x=0. The important insight provided in both cases is that the accuracy of Taylor polynomial approximations increases as the order of the polynomial increases.