Lyapunov Function Level-Set Explorer (example of what educational tools you can build with Claude AI's Frontend Builder Skill)

Speaking of phase portraits, I've recently put together a Lyapunov function level-set explorer, which is embedded below (and linked here). I built this with Claude AI's relatively new frontend skill builder, which basically lets you draw out what you want an interface to look like and have it animate it for you (and then iterate on the results). You can ask it a question ("Show me how compound interest works!") or be more specific ("Build an interactive demo that uses these CSS design elements and is shaped like..."). 

This tool has been great for building interactive demonstrations for my IEE/CSE 598 (Bio-Inspired AI and Optimization course) (and then Claude Code manages the GitHub Pages deployment for me). The Lyapunov function level-set explorer (which does let you integrate trajectories on a phase portrait) didn't really fit in that class, but I built it as a favor for another faculty member. I decided to park these random demonstrations at a different GitHub Pages deployment just in case I want to add more random demonstrations later.

Advanced Zoom: Using Slides as Virtual Background

There is a beta feature in Zoom (version 5.2.0 and higher) that is easy to miss but can make for a slightly more exciting way to share slides. When sharing your screen, try clicking on the "Advanced" tab (top center) to reveal several useful options:

There is a beta feature, "Slides as Virtual Background," that lets you choose a slide presentation. Sadly, it only supports PowerPoint presentations at the moment. This is strange because it first converts the PPTX to a PDF and then displays the PDF instead (which means your animations and slide transitions will be removed). So it seems like they should be able to support a PDF directly. I am hoping that will be added in the future.

Once you select a presentation, it will display behind you. It shows you a slide advancer (to move through your presentation). It also allows you to move yourself around the slide and re-scale your size. You can do this live, which lets you place yourself next to important features of the slide (or move yourself off of important features). By default, it scales you down and puts you in the bottom right corner.

Again, this will be much nicer when it supports PDF's in general (as opposed to just PPTX). 

CAVEAT ABOUT RECORDINGS: For now, the merged video (showing speaker on top of slides) will only record if you select to record locally. Cloud recordings will capture the unmerged view. I suspect that eventually they will implement this feature in their cloud backend and the merged view will be able to be seen there too. However, at least for now, if you do this and want it recorded, make sure that you record locally.