Cool. Sounds like you're in grad school right now, yeah? I know differential geometry is not exactly the same as differential topology, but I remember taking differential topology in grad school. I was always amused that we never actually evaluated any integrals that didn't come out to a very simple number (generally 0).
If I were writing this as a web page, though, I would definitely include a few graphs to explain the calculus concepts. The amount of calculus you need here is pretty intuitive once you draw a couple of pictures.
Ultimately you're limited in not having graphs, which always limits the intuitiveness of any calculus-explainers.