This sketch explores Euler's method for approximating a solution to a differential equation. It includes a brief explanation of the concept and a simple example of the calculations, as well as a depiction of the method with a variable interval and a variable number of iterations. The slope field cannot be adjusted very easily (to reflect alternate differential equations) but the axes can be differently scaled to explore a variety of scenarios. The software does not allow a function of two variables, so the construction is not easily generalized. The featured slope field goes with the differential equation dy/dx=x^2+y.
Keywords: euler, euler's method, euler's approximation, slope field, differential equation, local linearity, solution curve