54 lines
1.2 KiB
TeX
54 lines
1.2 KiB
TeX
\section{Transform Tables}
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\label{app:transform_tables}
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This appendix provides Laplace and Fourier transform tables for quick reference.
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\subsection{Laplace Transform Table}
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\label{sec:appB_laplace_table}
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\begin{table}[htbp]
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\centering
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\caption{Common Laplace Transforms}
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\label{tab:laplace_transforms}
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\begin{tabular}{l l}
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\toprule
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\textbf{$f(t)$} & \textbf{$\mathcal{L}\{f(t)\} = F(s)$} \\
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\midrule
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$1$ & TBD \\
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$t^n$ & TBD \\
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$e^{at}$ & TBD \\
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$\sin(\omega t)$ & TBD \\
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$\cos(\omega t)$ & TBD \\
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$e^{at}\sin(\omega t)$ & TBD \\
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$e^{at}\cos(\omega t)$ & TBD \\
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$\sinh(at)$ & TBD \\
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$\cosh(at)$ & TBD \\
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$t^n e^{at}$ & TBD \\
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$t \sin(\omega t)$ & TBD \\
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$t \cos(\omega t)$ & TBD \\
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$u(t-a)$ (unit step) & TBD \\
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$\delta(t-a)$ (Dirac delta) & TBD \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Fourier Transform Table}
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\label{sec:appB_fourier_table}
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\begin{table}[htbp]
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\centering
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\caption{Common Fourier Transforms}
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\label{tab:fourier_transforms}
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\begin{tabular}{l l}
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\toprule
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\textbf{$f(x)$} & \textbf{$\hat{f}(k)$} \\
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\midrule
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$e^{iax}$ & TBD \\
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$e^{-a|x|}$ & TBD \\
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$\mathrm{rect}(x)$ & TBD \\
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$\delta(x)$ & TBD \\
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Gaussian $e^{-ax^2}$ & TBD \\
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\bottomrule
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\end{tabular}
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\end{table}
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