$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
What to learn in the start-up example; generalizations
- Generalize the example to \( u'(t)=-a(t)u(t) + b(t) \)
- Present additional methods for the general nonlinear ODE \( u'=f(u,t) \),
which is either a scalar ODE or a system of ODEs
- How to access professional packages for solving ODEs
- How our model equations like \( u'=-au \) arises in a wide range
of phenomena in physics, biology, and finance
