\documentclass[11pt]{article}
\usepackage[margin=1in]{geometry}
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\title{CEA Equilibrium Derivatives\\Finite-Difference Convergence Studies}
\author{Chemical Equilibrium with Applications}
\date{\today}

\begin{document}

\maketitle

\tableofcontents
\clearpage

% ============================================================================
\section{HP Problem: Enthalpy-Pressure}
% ============================================================================

The HP problem solves for equilibrium given specified enthalpy and pressure.
The plots below show finite-difference convergence studies for derivatives
with respect to enthalpy (H), pressure (P), and mixture composition ($w_0$).

\subsection{Temperature Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{hp_temperature_derivative_convergence.pdf}
    \caption{Temperature derivative convergence for HP problem}
\end{figure}

\subsection{Entropy Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{hp_entropy_derivative_convergence.pdf}
    \caption{Entropy derivative convergence for HP problem}
\end{figure}

\subsection{Species Concentration Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{hp_species_derivative_convergence.pdf}
    \caption{Species concentration derivative convergence for HP problem}
\end{figure}

\clearpage

% ============================================================================
\section{SP Problem: Entropy-Pressure}
% ============================================================================

The SP problem solves for equilibrium given specified entropy and pressure.
The plots below show finite-difference convergence studies for derivatives
with respect to entropy (S), pressure (P), and mixture composition ($w_0$).

\subsection{Temperature Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{sp_temperature_derivative_convergence.pdf}
    \caption{Temperature derivative convergence for SP problem}
\end{figure}

\subsection{Enthalpy Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{sp_enthalpy_derivative_convergence.pdf}
    \caption{Enthalpy derivative convergence for SP problem}
\end{figure}

\subsection{Species Concentration Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{sp_species_derivative_convergence.pdf}
    \caption{Species concentration derivative convergence for SP problem}
\end{figure}

\clearpage

% ============================================================================
\section{SV Problem: Entropy-Volume}
% ============================================================================

The SV problem solves for equilibrium given specified entropy and volume.
The plots below show finite-difference convergence studies for derivatives
with respect to entropy (S), volume (V), and mixture composition ($w_0$).

\subsection{Enthalpy Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{sv_enthalpy_derivative_convergence.pdf}
    \caption{Enthalpy derivative convergence for SV problem}
\end{figure}

\subsection{Temperature Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{sv_temperature_derivative_convergence.pdf}
    \caption{Temperature derivative convergence for SV problem}
\end{figure}

\subsection{Species Concentration Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{sv_species_derivative_convergence.pdf}
    \caption{Species concentration derivative convergence for SV problem}
\end{figure}

\clearpage

% ============================================================================
\section{TP Problem: Temperature-Pressure}
% ============================================================================

The TP problem solves for equilibrium given specified temperature and pressure.
The plots below show finite-difference convergence studies for derivatives
with respect to temperature (T), pressure (P), and mixture composition ($w_0$).

\subsection{Enthalpy Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{tp_enthalpy_derivative_convergence.pdf}
    \caption{Enthalpy derivative convergence for TP problem}
\end{figure}

\subsection{Entropy Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{tp_entropy_derivative_convergence.pdf}
    \caption{Entropy derivative convergence for TP problem}
\end{figure}

\subsection{Species Concentration Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{tp_species_derivative_convergence.pdf}
    \caption{Species concentration derivative convergence for TP problem}
\end{figure}

\clearpage

% ============================================================================
\section{TV Problem: Temperature-Volume}
% ============================================================================

The TV problem solves for equilibrium given specified temperature and volume.
The plots below show finite-difference convergence studies for derivatives
with respect to temperature (T), volume (V), and mixture composition ($w_0$).

\subsection{Enthalpy Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{tv_enthalpy_derivative_convergence.pdf}
    \caption{Enthalpy derivative convergence for TV problem}
\end{figure}

\subsection{Entropy Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{tv_entropy_derivative_convergence.pdf}
    \caption{Entropy derivative convergence for TV problem}
\end{figure}

\subsection{Species Concentration Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{tv_species_derivative_convergence.pdf}
    \caption{Species concentration derivative convergence for TV problem}
\end{figure}

\clearpage

% ============================================================================
\section{UV Problem: Internal Energy-Volume}
% ============================================================================

The UV problem solves for equilibrium given specified internal energy and volume.
The plots below show finite-difference convergence studies for derivatives
with respect to internal energy (U), volume (V), and mixture composition ($w_0$).

\subsection{Enthalpy Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{uv_enthalpy_derivative_convergence.pdf}
    \caption{Enthalpy derivative convergence for UV problem}
\end{figure}

\subsection{Temperature Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{uv_temperature_derivative_convergence.pdf}
    \caption{Temperature derivative convergence for UV problem}
\end{figure}

\subsection{Species Concentration Derivatives}
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{uv_species_derivative_convergence.pdf}
    \caption{Species concentration derivative convergence for UV problem}
\end{figure}

\end{document}
