Math 1a Spring 2021: Integration by parts (Manga style)
This pre-lecture is presented Manga style. We derive the method from the product rule, then look at a few examples, also a Merry-go-round example where two integration by parts steps brings us back. Finally, we look at the tabular integration method Tic-Tac-Toe.
This is also a bit of a technology test for me. Exploring developments of teaching with technology has always be an interest of mine. For me as a kid, over-head projectors had been the cutting edge technology, today a typical teacher can end up juggling dozens of different tools and technologies.
[ Technology note: One of the notable side effects was that the filter prevented a high resolution recording (I usually record in 4K). It is still amazing how computer vision technology (here a basic filter from snap cam) can process things in real time. An other interesting thing is that the Go Pro cameras and the snap cam camera have a slightly different timing. Even so aligned perfectly at the beginning, they start to run out of sync. Mixing different go pro cameras does not have this problem. I should have taken the sound footage of the snap cam even so it is of much lower quality than the usually excellent Go Pro sound. An other technology note: my main work imac workstation is end of life and starts to have problems (reboots, failures. 7 year workstations used every day also wear out). Saturday night, when the problems became more frequent, loosing hours of work, requiring to work through the night, I ordered one of the new mac mini's (new apple silicon). It arrived on Sunday at noon with a special courier! I did this project on that mac mini. Of course, this cheapest version of mac mini has only 500 Gig SSD and a typical Final cut project has close to 300-500 gig so that I even had to work on this 10 minute movie on an external 2TB SSD just forthe project itself. When I moved to Boston in 2000, I still had 1GBytes external hard drives connected with awful SCSII cables to a next workstation. Now, I'm a consumer doing occasional movies and have about 100 TBytes (including backups) at home alone. HD space requirements have exploded. ]