skeleton: 14 chapter stubs and 4 appendices

chapters/ch01_introduction.tex

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+\section{Introduction}
+\label{ch:introduction}
+
+\subsection{Classification of ODEs}
+\label{sec:ch01_classification}
+
+% Content goes here
+
+\subsection{Direction Fields}
+\label{sec:ch01_direction_fields}
+
+% Content goes here
+
+\subsection{Existence and Uniqueness}
+\label{sec:ch01_existence_uniqueness}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch01_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch01_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch02_first_order.tex

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+\section{First-Order Methods}
+\label{ch:first_order}
+
+\subsection{Separable Equations}
+\label{sec:ch02_separable}
+
+% Content goes here
+
+\subsection{Linear First-Order (Integrating Factor)}
+\label{sec:ch02_linear_first_order}
+
+% Content goes here
+
+\subsection{Exact Equations}
+\label{sec:ch02_exact}
+
+% Content goes here
+
+\subsection{Bernoulli Equations}
+\label{sec:ch02_bernoulli}
+
+% Content goes here
+
+\subsection{Homogeneous Substitutions}
+\label{sec:ch02_homogeneous_substitutions}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch02_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch02_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch03_qualitative.tex

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+\section{Qualitative Analysis and Numerical Methods}
+\label{ch:qualitative}
+
+\subsection{Autonomous Equations and Phase Lines}
+\label{sec:ch03_autonomous_phase_lines}
+
+% Content goes here
+
+\subsection{Stability Analysis}
+\label{sec:ch03_stability}
+
+% Content goes here
+
+\subsection{Logistic Equation}
+\label{sec:ch03_logistic}
+
+% Content goes here
+
+\subsection{Euler's Method}
+\label{sec:ch03_eulers_method}
+
+% Content goes here
+
+\subsection{Applications (Cooling, Mixing, Falling Bodies)}
+\label{sec:ch03_applications}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch03_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch03_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch04_second_order_homogeneous.tex

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+\section{Second-Order Homogeneous}
+\label{ch:second_order_homogeneous}
+
+\subsection{Characteristic Equation}
+\label{sec:ch04_characteristic_equation}
+
+% Content goes here
+
+\subsection{Three Root Cases}
+\label{sec:ch04_three_root_cases}
+
+% Content goes here
+
+\subsection{Superposition Principle}
+\label{sec:ch04_superposition}
+
+% Content goes here
+
+\subsection{Wronskian and Linear Independence}
+\label{sec:ch04_wronskian}
+
+% Content goes here
+
+\subsection{Abel's Identity}
+\label{sec:ch04_abels_identity}
+
+% Content goes here
+
+\subsection{Reduction of Order}
+\label{sec:ch04_reduction_of_order}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch04_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch04_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch05_second_order_nonhomogeneous.tex

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+\section{Second-Order Nonhomogeneous}
+\label{ch:second_order_nonhomogeneous}
+
+\subsection{General Solution Structure}
+\label{sec:ch05_general_solution}
+
+% Content goes here
+
+\subsection{Undetermined Coefficients}
+\label{sec:ch05_undetermined_coefficients}
+
+% Content goes here
+
+\subsection{Variation of Parameters}
+\label{sec:ch05_variation_of_parameters}
+
+% Content goes here
+
+\subsection{Method Comparison}
+\label{sec:ch05_method_comparison}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch05_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch05_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch06_mechanical_applications.tex

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+\section{Mechanical Applications}
+\label{ch:mechanical_applications}
+
+\subsection{Spring-Mass Systems}
+\label{sec:ch06_spring_mass}
+
+% Content goes here
+
+\subsection{Damped Vibrations}
+\label{sec:ch06_damped_vibrations}
+
+% Content goes here
+
+\subsection{Forced Vibrations and Resonance}
+\label{sec:ch06_forced_vibrations}
+
+% Content goes here
+
+\subsection{RLC Circuits}
+\label{sec:ch06_rlc_circuits}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch06_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch06_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch07_laplace_transforms.tex

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+\section{Laplace Transforms}
+\label{ch:laplace_transforms}
+
+\subsection{Definition and Properties}
+\label{sec:ch07_definition_properties}
+
+% Content goes here
+
+\subsection{Transform Table}
+\label{sec:ch07_transform_table}
+
+% Content goes here
+
+\subsection{Inverse Transforms}
+\label{sec:ch07_inverse_transforms}
+
+% Content goes here
+
+\subsection{Solving IVPs}
+\label{sec:ch07_solving_ivps}
+
+% Content goes here
+
+\subsection{Step and Delta Functions}
+\label{sec:ch07_step_delta}
+
+% Content goes here
+
+\subsection{Convolution}
+\label{sec:ch07_convolution}
+
+% Content goes here
+
+\subsection{Transfer Functions}
+\label{sec:ch07_transfer_functions}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch07_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch07_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch08_systems.tex

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+\section{Systems of Linear ODEs}
+\label{ch:systems}
+
+\subsection{Matrix Form}
+\label{sec:ch08_matrix_form}
+
+% Content goes here
+
+\subsection{Eigenvalue Method}
+\label{sec:ch08_eigenvalue_method}
+
+% Content goes here
+
+\subsection{Phase Plane Analysis}
+\label{sec:ch08_phase_plane}
+
+% Content goes here
+
+\subsection{Stability}
+\label{sec:ch08_stability}
+
+% Content goes here
+
+\subsection{Matrix Exponential}
+\label{sec:ch08_matrix_exponential}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch08_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch08_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch09_series_solutions.tex

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+\section{Series Solutions}
+\label{ch:series_solutions}
+
+\subsection{Power Series Method}
+\label{sec:ch09_power_series}
+
+% Content goes here
+
+\subsection{Euler--Cauchy Equations}
+\label{sec:ch09_euler_cauchy}
+
+% Content goes here
+
+\subsection{Frobenius Method}
+\label{sec:ch09_frobenius}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch09_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch09_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch10_fourier_series.tex

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+\section{Fourier Series}
+\label{ch:fourier_series}
+
+\subsection{Fourier Coefficients}
+\label{sec:ch10_fourier_coefficients}
+
+% Content goes here
+
+\subsection{Orthogonality}
+\label{sec:ch10_orthogonality}
+
+% Content goes here
+
+\subsection{Even/Odd Functions}
+\label{sec:ch10_even_odd}
+
+% Content goes here
+
+\subsection{Half-Range Expansions}
+\label{sec:ch10_half_range}
+
+% Content goes here
+
+\subsection{Complex Fourier Series}
+\label{sec:ch10_complex_fourier}
+
+% Content goes here
+
+\subsection{Convergence and Gibbs Phenomenon}
+\label{sec:ch10_convergence_gibbs}
+
+% Content goes here
+
+\subsection{Parseval's Identity}
+\label{sec:ch10_parseval}
+
+% Content goes here
+
+\subsection{Applications to ODEs}
+\label{sec:ch10_applications_odes}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch10_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch10_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch11_boundary_value_problems.tex

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+\section{Boundary Value Problems}
+\label{ch:boundary_value_problems}
+
+\subsection{BVP vs IVP}
+\label{sec:ch11_bvp_vs_ivp}
+
+% Content goes here
+
+\subsection{Eigenvalue Problems}
+\label{sec:ch11_eigenvalue_problems}
+
+% Content goes here
+
+\subsection{Sturm--Liouville Form}
+\label{sec:ch11_sturm_liouville}
+
+% Content goes here
+
+\subsection{Orthogonality Theorem}
+\label{sec:ch11_orthogonality_theorem}
+
+% Content goes here
+
+\subsection{Eigenfunction Expansions}
+\label{sec:ch11_eigenfunction_expansions}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch11_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch11_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch12_heat_equation.tex

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+\section{Heat Equation}
+\label{ch:heat_equation}
+
+\subsection{Physical Derivation}
+\label{sec:ch12_physical_derivation}
+
+% Content goes here
+
+\subsection{Separation of Variables}
+\label{sec:ch12_separation_of_variables}
+
+% Content goes here
+
+\subsection{Dirichlet Boundary Conditions}
+\label{sec:ch12_dirichlet}
+
+% Content goes here
+
+\subsection{Neumann Boundary Conditions}
+\label{sec:ch12_neumann}
+
+% Content goes here
+
+\subsection{Steady-State Solution}
+\label{sec:ch12_steady_state}
+
+% Content goes here
+
+\subsection{Source Terms}
+\label{sec:ch12_source_terms}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch12_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch12_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch13_wave_and_laplace.tex

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+\section{Wave and Laplace Equations}
+\label{ch:wave_and_laplace}
+
+\subsection{Wave Equation Derivation}
+\label{sec:ch13_wave_derivation}
+
+% Content goes here
+
+\subsection{d'Alembert's Solution}
+\label{sec:ch13_dalembert}
+
+% Content goes here
+
+\subsection{Finite String and Standing Waves}
+\label{sec:ch13_finite_string}
+
+% Content goes here
+
+\subsection{Two-Dimensional Wave Equation}
+\label{sec:ch13_2d_wave}
+
+% Content goes here
+
+\subsection{Laplace's Equation in Rectangles}
+\label{sec:ch13_laplace_rectangles}
+
+% Content goes here
+
+\subsection{Laplace's Equation in Polar Coordinates}
+\label{sec:ch13_laplace_polar}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch13_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch13_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

chapters/ch14_nonlinear_systems.tex

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+\section{Nonlinear Systems}
+\label{ch:nonlinear_systems}
+
+\subsection{Equilibrium Points}
+\label{sec:ch14_equilibrium}
+
+% Content goes here
+
+\subsection{Jacobian Linearization}
+\label{sec:ch14_jacobian}
+
+% Content goes here
+
+\subsection{Trace-Determinant Classification}
+\label{sec:ch14_trace_determinant}
+
+% Content goes here
+
+\subsection{Hartman--Grobman Theorem}
+\label{sec:ch14_hartman_grobman}
+
+% Content goes here
+
+\subsection{Limit Cycles}
+\label{sec:ch14_limit_cycles}
+
+% Content goes here
+
+\subsection{Lotka--Volterra Predator-Prey}
+\label{sec:ch14_lotka_volterra}
+
+% Content goes here
+
+\subsection{Summary}
+\label{sec:ch14_summary}
+
+% Summary table at end of chapter
+\begin{table}[htbp]
+\centering
+\caption{Chapter Summary}
+\label{tab:ch14_summary}
+\begin{tabular}{l l}
+\toprule
+\textbf{Concept} & \textbf{Key Formula/Method} \\
+\midrule
+TBD & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}