## A Progress Report: At the End of Week 4

Week 4:

I had to limit my lab to 50 minutes of a 75 minute period.  I covered autonomous differential equations, equilibrium points and phase lines in the first 15 minutes.  The students transitioned quickly from lecture to lab.  I was happy about that.

Mindful that our first test is next week, I created a lab that included 5 questions all of which could be done by hand.  I stressed to the students that I wanted them to realize that the difficult part of a real differential equations problem would be the creating of the differential equation, identifying the initial condition(s) and answering the questions posed.  The purpose of the lab was to have them solve several initial problems using the power of a computer algebra system.  As always the stress was on the mathematics involved.

This lab was not very ambitious but it was very successful.  There is a precision necessary when using a computer algebra system that often is missing when students try to state both initial conditions and other information given.  Now rather than saying statements like "The temperature after an hour is 89 degrees,"  students say T(1) = 89.  We have solved initial value problems by hand in lecture.  We have solved modeling problems in the lab.  Students have solved modeling problems by hand for homework.  (They need to do that to be ready for the common final.)  It has worked out surprisingly well.  The lab exercises have required that they decide what differential equation models the situation and what initial condition is given.  It also requires that they state very precisely what extra information is given.  Solving by hand is rather straightforward, albeit potentially unnecessary, when the stress has been put on what I believe is the important part of a modeling problem.

There will be no lab in week 5 because I need to devote that time for review for the test.  The lab day will be a question and answer period instead.

I will keep you informed.  Please contact me at rosemary.farley@manhattan.edu if you are a student or teacher and I will give you access to a Project area in SIMIODE where you can find materials appropriate to you from my Blog references.