\section{Transform Tables}
\label{app:transform_tables}

This appendix provides Laplace and Fourier transform tables for quick reference.

\subsection{Laplace Transform Table}
\label{sec:appB_laplace_table}

\begin{table}[htbp]
\centering
\caption{Common Laplace Transforms}
\label{tab:laplace_transforms}
\begin{tabular}{l l}
\toprule
\textbf{$f(t)$} & \textbf{$\mathcal{L}\{f(t)\} = F(s)$} \\
\midrule
$1$ & TBD \\
$t^n$ & TBD \\
$e^{at}$ & TBD \\
$\sin(\omega t)$ & TBD \\
$\cos(\omega t)$ & TBD \\
$e^{at}\sin(\omega t)$ & TBD \\
$e^{at}\cos(\omega t)$ & TBD \\
$\sinh(at)$ & TBD \\
$\cosh(at)$ & TBD \\
$t^n e^{at}$ & TBD \\
$t \sin(\omega t)$ & TBD \\
$t \cos(\omega t)$ & TBD \\
$u(t-a)$ (unit step) & TBD \\
$\delta(t-a)$ (Dirac delta) & TBD \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Fourier Transform Table}
\label{sec:appB_fourier_table}

\begin{table}[htbp]
\centering
\caption{Common Fourier Transforms}
\label{tab:fourier_transforms}
\begin{tabular}{l l}
\toprule
\textbf{$f(x)$} & \textbf{$\hat{f}(k)$} \\
\midrule
$e^{iax}$ & TBD \\
$e^{-a|x|}$ & TBD \\
$\mathrm{rect}(x)$ & TBD \\
$\delta(x)$ & TBD \\
Gaussian $e^{-ax^2}$ & TBD \\
\bottomrule
\end{tabular}
\end{table}
