skeleton: 14 chapter stubs and 4 appendices

appendices/appB_transform_tables.tex

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+\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}