## Day 3 of using modeling

Today I taught how to solve 1st order diff eqs using the integration factor.  This is one I derive because I think it's too magical to say "use mu = e^(integral P(x) dx)".  My favorite and most successful way of teaching this is to show the steps, say, "Hey, wouldn't it be great if "mu(x)*[y'+P(x)y]" simply equaled "d/dx mu(x)*y".  Once they agree (with an example) that makes things easy to solve -- I then set those two expressions equal to each other to find mu(x).  It's what I call a "pencils down moment" -- you can hear the pencils as they drop them  on the desks -- something I want them to see and understand, but not something I will test them on.

I usually do a bunch of examples -- this time I did one simple one and one slightly more complex, and then I gave them 1-13-T-Mma-SleuthingWithDifferentialEquations-TeacherVersion.pdf, selecting just the Death of an Actor task.  I emphasize that we could solve it by separation of variables, but the task was to use the skills we just learned.

This time, we didn't have enough time to finish it in class -- which worked out well.  I instructed them to make it neat and easy to read, along with, in words, an explanation of what was calculated and what it meant to the situation.  By the end of the semester, I hope to get them to create more and more formal work, so this was a good step towards that goal.

The whole class (minus one person) is now signed up for a group I set up here at Simiode.  I hope for them to post their thoughts about how they think the modeling-based approach is working, along with comments about the open source textbook.  If they can channel their in-class enthusiasm to the blog, I am excited to see the results!