The Euler method works by discretizing time into small steps and using the derivative (rate of change) to predict the future state of the system. Mathematically, if we have a differential equation of the form dy/dt = f(t, y), the Euler method approximates the solution by:
yn+1 = yn + h * f(tn, yn)
Where h is the time step, yn is the current state, and yn+1 is the next state.
