An exploration of Euler’s method

My older son is studying calculus and my younger son is studying algebra this year.  I’d run across some problems on Euler’s method looking at old BC calculus exams, but we are still a long way from talking about Euler’s method in the calculus course.  However, as my younger son begins to study lines, I thought it might be fun to do some visuals on slope fields and just touch on Euler’s method as a way of talking about slope.

Here’s how I introduced the topic:

Next I gave them a neat visual example -> wind speed and direction on the earth

Now I moved to Mathematica to talk about slope fields in general. The two specific slope fields we looked at here were (in calculus language) dy/dx = y and dy/dx = x.

Finally I had the boys choose their own fields and try to describe them ahead of time:

Definitely a fun project. The mathematical idea behind Euler’s method isn’t that hard and kids can understand the concept pretty easily. I really had a lot of fun exploring the ideas of slope fields with the boys this morning.