\relax \providecommand\tcolorbox@label[2]{} \@writefile{toc}{\contentsline {section}{\numberline {1}In real life, systems follow hidden laws}{1}} \@writefile{toc}{\contentsline {section}{\numberline {2}The SIR ODE model of an epidemic}{2}} \@writefile{toc}{\contentsline {section}{\numberline {3} {\it {sir\_ode.m}}: Population conservation}{4}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {1}Outline of sir\_deriv.}{4}} \@writefile{toc}{\contentsline {section}{\numberline {4} {\it {sphere\_ode}}: Distance conservation}{5}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {2}Outline for sphere\_deriv.m}{5}} \@writefile{toc}{\contentsline {section}{\numberline {5} {\it {pendulum\_ode()}}: Energy conservation}{7}} \@writefile{toc}{\contentsline {section}{\numberline {6}Solve pendulum with euler(), rk2(), and midpoint() }{9}} \@writefile{toc}{\contentsline {section}{\numberline {7} {\it {predator\_ode}}: A hidden conservation law}{9}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {3}Outline for computing conserved quantity.}{10}} \@writefile{toc}{\contentsline {section}{\numberline {8}Homework \#8}{10}} \@writefile{toc}{\contentsline {section}{\numberline {9}Extra credit}{11}}