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.