Euler approximation

Euler approximations use tangent lines beginning at an initial point and continuing at a given step size to approximate the numerical value of a differential equation at a given point. These approximations are found using Euler's recursive formula.

Euler's Recurssive Forumula: y=y_o+h•F(x_o,y_o)

1. The inital point is (x_o,y_o)
2. The slope is F(x_o,y_o)
3. The step size is h
4. The approximated value is y

If the function is concave down, the approximation will be an overestimate, and if the function is concave up, the approximation will be an underestimate. (Concavity is found using the second derivative test.) These approximations are more accurate with smaller step sizes.