We define $$\begin{equation} y'(t_i)=f(t_i,y_i) \tag{16} \end{equation}$$ and if we truncate $\Delta$ at the first derivative, we have $$\begin{equation} y_{i+1}=y(t_i) + hf(t_i,y_i) + O(h^2), \tag{17} \end{equation}$$ which when complemented with $t_{i+1}=t_i+h$ forms the algorithm for the well-known Euler method. Note that at every step we make an approximation error of the order of $O(h^2)$, however the total error is the sum over all steps $N=(b-a)/h$, yielding thus a global error which goes like $NO(h^2)\approx O(h)$.