polish: cross-reference verification and final formatting

- Fix overfull hbox in ch05 method comparison table (118pt -> resolved)
- Fix overfull hbox in ch09 verification equation (147pt -> split with align)
- Fix overfull hbox in ch08 phase plane table (16pt -> p-column width)
- Fix overfull hbox in appA VOP formula (70pt -> inline textstyle)
- Fix overfull hbox in appB Fourier series table (70pt -> resizebox)
- Fix overfull hbox in appB common integrals table (tabular width)
- Fix overfull hbox in appB Laplace properties table (tabular width)
- Fix float too large in ch06 TikZ resonance figure (scale + clip)
- Fix text overfull in ch03 terminal velocity paragraph
- Fix ch09 summary table width with @{} column specifiers
This commit is contained in:
Worker Agent
2026-06-04 19:30:31 -05:00
parent 18811c2d09
commit c46724301a
7 changed files with 30 additions and 25 deletions

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@@ -723,17 +723,17 @@ Both undetermined coefficients (UC) and variation of parameters (VoP) find parti
\centering
\caption{Undetermined coefficients vs.\ variation of parameters}
\label{tab:ch05_method_comparison}
\begin{tabular}{l l l}
\begin{tabular}{p{2.8cm} p{4.8cm} p{6.2cm}}
\toprule
\textbf{Aspect} & \textbf{Undetermined Coefficients} & \textbf{Variation of Parameters} \\
\midrule
Applicable $g(x)$ & Polynomials, $e^{\alpha x}$, $\sin(\beta x)$, $\cos(\beta x)$, and their sums/products & \emph{Any} continuous $g(x)$ (in principle) \\
Requires $y_h$? & Only for overlap check (modification rule) & Yes --- need a full fundamental set \\
Applicable $g(x)$ & Polynomials, $e^{\alpha x}$, $\sin/\cos(\beta x)$, sums/products & \emph{Any} continuous $g(x)$ (in principle) \\
Requires $y_h$? & Only for overlap check & Yes --- need a full fundamental set \\
Requires $W(x)$? & No & Yes \\
Normalized form? & Not required & \textbf{Required} (coefficient of $y''$ must be~1) \\
Computation & Algebra (solve linear system) & Integration (may be difficult or non-elementary) \\
Speed (simple $g(x)$) & Fast --- algebraic, no integrals & Slower --- integrals needed \\
Speed (complex $g(x)$) & \textbf{Not applicable} --- method fails & Always applicable (if integrals exist) \\
Speed (complex $g(x)$) & \textbf{N/A} --- method fails & Always applicable (if integrals exist) \\
\bottomrule
\end{tabular}
\end{table}