StellarEuler’s Method is a procedure for approximating a solution to a differential equation or approximating a point on a solution curve when an exact formula is not available. Starting from an initial condition, the method uses the slope given by the differential equation to move forward in small steps. At each step, the slope determines the change in y, and then that new point becomes the starting point for the next step. In AP Calculus, this topic is BC only.
The basic update rule is , where is the slope from the differential equation at the current point and is the step size. Smaller step sizes usually produce better approximations because the method follows the local slope information more closely. Euler’s Method connects slope fields and numerical approximation, showing how differential equations can be used even when no explicit solution is known.