How to motivate the teaching of differential equations?

[matqkks]

I will have to teach a first course in differential equations. A good motivator might be to promulgate modelling with differential equations but I have seen some teachers have made polemic against modelling. Are there any really good resources on modelling with differential equations? I want something which will have an impact and motivate the learner. I am not really looking for artificial engineering examples but some bona fide real applications.

Also, would like to bring in some history of differential equations to motivate the learner.

 

[R.M.]

A few examples from the sciences come to mind: motion of a pendulum, position of a spring, predator/prey models, population growth/decay, Newton's law of cooling.

One I've done before is to heat up a container of water and take its temperature with a digital thermometer every 2 minutes for about 20-30 minutes (I have a student keep track of time). Record the data in an excel spreadsheet and plot the temp/time curve. It's a good discussion opener.