Week 1 went well!
The students completed the first two scenarios in the remote class on the hotel population -- without new guests being added and then with new guests being added. They had to complete the 'with new guests being added' with 5 different initial values to show a nice family of curves (two initial values were below the steady state value - and one of those was zero, one was at the steady state solution, and two above.) There were interesting comments on the 'did this surprise you' question, including that students thought the initial value would change the shape more than it did and that starting at zero -- and still ending up at the same steady state solution -- was surprising.
The following class (the project had to be turned in before class) was really productive, talking about what the model was -- and the fact that in 'real life' we see the solutions and are trying to match models to what we saw. It's a great opportunity to go over boring vocabulary in a way that ties it to something less boring. Initial values, transient solutions, steady state, family of curves, etc.
I ended class with phase portraits and how it could be used to match the curves we saw in the hotel example.
I need to think about what I'm doing for next week - the topics include separation and linear methods. I might go with the dog drug question, asking them to watch the video on how to solve separable equations first.