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71 
\newpage 
\newpage 
72 


73 

\chapter{Introduction} 
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\label{CHAP INTRO} 
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\input{intro} 
\input{intro} 
76 





77 
\chapter{Getting Started with Heat Diffusion} 
\chapter{Getting Started with Heat Diffusion} 
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\label{CHAP HEAT DIFF} 
\label{CHAP HEAT DIFF} 
79 
We start by examining a simple one dimensional heat diffusion equation. This problem provides a good starting example to build our knowledge of \esc and demonstrate how to solve simple partial differential equations (PDEs)\footnote{Wikipedia provides an excellent and comprehensive introduction to \textit{Partial Differential Equations} \url{http://en.wikipedia.org/wiki/Partial_differential_equation}, however their relevance to \esc and implementation should become much clearer as we develop our understanding further into the cookbook.} 
We start by examining a simple one dimensional heat diffusion equation. This problem provides a good starting example to build our knowledge of \esc and demonstrate how to solve simple partial differential equations (PDEs)\footnote{Wikipedia provides an excellent and comprehensive introduction to \textit{Partial Differential Equations} \url{http://en.wikipedia.org/wiki/Partial_differential_equation}, however their relevance to \esc and implementation should become much clearer as we develop our understanding further into the cookbook.} 
84 
\label{CHAP HEAT 2a} 
\label{CHAP HEAT 2a} 
85 
\input{example03} 
\input{example03} 
86 





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\chapter{Complex Geometries} 
\chapter{Complex Geometries} 
88 
\label{CHAP HEAT 2} 
\label{CHAP HEAT 2} 
89 
\input{steadystateheatdiff} 
\input{steadystateheatdiff} 