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\input{../user/copyrights} 
\input{../user/copyrights} 
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\begin{abstract} 
\begin{abstract} 
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\esc is a \pyt based environment that has been developed to solve complex mathematical models, particularly coupled, nonlinear and timedependent partial differential equations. The intention of this cookbook, is to give new \esc users a comprehensive introduction, and to create a fundamental knowledge base and example set, that can be used as templates or references for new problems. Although most of the examples in this cookbook are focused on the disciplines of geophysics and geology they all provide solid introduction to \esc and its capabilities. 
\esc is a \pyt based environment that has been developed to solve complex mathematical models, particularly coupled, nonlinear and timedependent partial differential equations. The intention of this cookbook is to introduce new users to \esc and provide a set of examples which demonstrate the major concepts and can be adapted to new problems. Although most of the examples in this cookbook are focused on the disciplines of geophysics and geology, they provide solid introduction to \esc and its capabilities. 
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\end{abstract} 
\end{abstract} 
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\tableofcontents 
\tableofcontents 
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\chapter{Getting Started with Heat Diffusion} 
\chapter{Getting Started with Heat Diffusion} 
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\label{CHAP HEAT DIFF} 
\label{CHAP HEAT DIFF} 
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We start by examining a simple one dimensional heat diffusion equation. This problem provides good starting example to build our knowledge on \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.} 
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\input{example01} 
\input{example01} 
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\input{example02} 
\input{example02} 
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