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The world's simplest (?) ODE: $$ \begin{equation*} u'(t) = -au(t),\quad u(0)=I,\ t\in (0,T] \end{equation*} $$
We can learn a lot about numerical methods, computer implementation, program testing, and real applications of these tools by using this very simple ODE as example. The teaching principle is to keep the math as simple as possible while learning computer tools.
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