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\@writefile{toc}{\contentsline {section}{\numberline {2}Build a 2D steady heat code}{2}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {1}Function to return variable indices.}{2}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {2}Identifying and setting Dirichlet conditions.}{2}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {3}Approximating the Laplacian.}{2}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {4}Solve the linear system.}{3}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {5}Get the RMS error.}{3}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {6}Creating a contour plot of the solution.}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Exercise \#1: Solver for the 2D steady heat equation}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Moving to a 2D time-dependent problem}{4}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {7}Create U\tmspace  +\thinmuskip {.1667em} X\tmspace  +\thinmuskip {.1667em} Y arrays.}{4}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {8}An outline of the time loop.}{4}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {9}Think about the boundary condition as a linear equation.}{5}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {10}Identifying and setting Dirichlet conditions.}{5}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {11}Get the RMS error.}{5}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {12}Creating a contour plot of the solution.}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Exercise \#2: Create the general heat equation code}{6}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {13}Use boundary conditions everywhere.}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Designing the forward Euler engine}{6}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {14}The forward Euler "engine".}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Exercise \#3: A forward Euler solver for the 2D heat equation}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {8}Designing the backward Euler engine}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {9}Exercise \#4: A backward Euler solver for the 2D heat equation}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {10}Designing the Crank Nicolson engine}{7}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {15}Setting a Crank Nicolson matrix entry.}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {11}Exercise \#5: A Crank Nicolson solver}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {12}Homework: A theta method solver}{7}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {16}Adding theta as in input parameter.}{8}}