The Motivated Analysis course is up to 7 handouts and 27 videos as of September 14. Pretty soon (I hope) the course will get to a few exciting waypoints:
- Proving Duhamel’s Principle in a general setting, using distributions and convolutions
- Pinning down the precise definition of a distribution (partly motivated by what Duhamel will tell us)
- Going back to the original mass-spring system, but this time forcing with sine waves, not hammers, to start the story of Fourier analysis–a story that will get intimately intertwined with distributions.
I’d love any feedback you have if you are following along (even in a non-serious way). In particular, it would be good to know if there is a desire for more practice-type problem sets (in addition to the problems in the handouts, which develop the ideas). Now, I’m not saying I’ll produce reams of extra problems, but I realize that as it is there might not be quite enough practice for a student to really master the ideas as we go.