\relax 
\providecommand\tcolorbox@label[2]{}
\@writefile{toc}{\contentsline {section}{\numberline {1}Every approximation is wrong. Can we estimate how wrong?}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Compare big and small step approximations}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {3}{\it  {expsin\_rk1\_double.m}} uses the step doubling technique}{2}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {1}Error estimate by step doubling.}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Using the error estimate}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Extrapolation squeezes information out of a pair of solutions}{4}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {2}Extrapolation for the expsin ODE.}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {6}{\it  {expsin\_rk1\_higer.m}} compares rk1() and rk2() solutions}{6}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {3}Estimate error by comparing two Runge-Kutta solutions.}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {7}The NORMAL ODE example}{8}}
\@writefile{toc}{\contentsline {section}{\numberline {8} Homework \#5}{8}}