Solving differential equations with Euler's method

Mathematica, WolframAlpha, and Grapher provide tools for solving differential equations. But you don't get to see what's happening under the hood. Differential equations often don't have a tidy closed form solution, and a numerical method is needed. Euler's method requires only a differential equation (not necessarily separable), and an initial value.

That said, there are a few steps in using Euler's method, and after spending a couple of days on it in class, I decided it might be helpful to have a graphical organizer. I came up with this (also available as pdf):

This screencast shows how it can be used.

Here's an example Excel spreadsheet that can be adapted to solve first degree differential equation, or you can use this Google spreadsheet.

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