skeleton: 14 chapter stubs and 4 appendices

appendices/appA_solution_summary.tex

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+\appendix
+
+\section{Solution Method Summary}
+\label{app:solution_summary}
+
+This appendix provides quick-reference tables for solution methods across all chapter topics.
+
+\begin{table}[htbp]
+\centering
+\caption{Solution Methods by Equation Type}
+\label{tab:solution_methods}
+\begin{tabular}{l l l}
+\toprule
+\textbf{Equation Type} & \textbf{Method} & \textbf{Key Formula} \\
+\midrule
+Separable ODE & Separation of variables & TBD \\
+Linear first-order & Integrating factor & TBD \\
+Exact equations & Potential function & TBD \\
+Bernoulli & Substitution & TBD \\
+Second-order homogeneous & Characteristic equation & TBD \\
+Second-order nonhomogeneous & Undetermined coefficients & TBD \\
+Second-order nonhomogeneous & Variation of parameters & TBD \\
+IVP with Laplace & Laplace transform & TBD \\
+Systems of ODEs & Eigenvalue method & TBD \\
+Series solutions & Power series & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

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}

appendices/appC_integral_tables.tex

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+\section{Integral Tables}
+\label{app:integral_tables}
+
+This appendix provides commonly used integral formulas encountered throughout the handbook.
+
+\subsection{Basic Integrals}
+\label{sec:appC_basic}
+
+\begin{table}[htbp]
+\centering
+\caption{Basic Integral Formulas}
+\label{tab:integrals_basic}
+\begin{tabular}{l l}
+\toprule
+\textbf{Integrand} & \textbf{Result} \\
+\midrule
+$\displaystyle \int x^n \, dx$ & TBD \\
+$\displaystyle \int \frac{1}{x} \, dx$ & TBD \\
+$\displaystyle \int e^{ax} \, dx$ & TBD \\
+$\displaystyle \int a^x \, dx$ & TBD \\
+$\displaystyle \int \sin(ax) \, dx$ & TBD \\
+$\displaystyle \int \cos(ax) \, dx$ & TBD \\
+$\displaystyle \int \tan(ax) \, dx$ & TBD \\
+$\displaystyle \int \sec^2(ax) \, dx$ & TBD \\
+$\displaystyle \int \csc^2(ax) \, dx$ & TBD \\
+$\displaystyle \int \sec(ax)\tan(ax) \, dx$ & TBD \\
+$\displaystyle \int \csc(ax)\cot(ax) \, dx$ & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}
+
+\subsection{Integrals Involving Exponential and Trigonometric Functions}
+\label{sec:appC_exptig}
+
+\begin{table}[htbp]
+\centering
+\caption{Exponential--Trigonometric Integrals}
+\label{tab:integrals_exptig}
+\begin{tabular}{l l}
+\toprule
+\textbf{Integrand} & \textbf{Result} \\
+\midrule
+$\displaystyle \int e^{ax}\sin(bx)\,dx$ & TBD \\
+$\displaystyle \int e^{ax}\cos(bx)\,dx$ & TBD \\
+$\displaystyle \int x e^{ax}\,dx$ & TBD \\
+$\displaystyle \int x \sin(ax)\,dx$ & TBD \\
+$\displaystyle \int x \cos(ax)\,dx$ & TBD \\
+$\displaystyle \int \ln(x)\,dx$ & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}
+
+\subsection{Integrals Involving Inverse Trigonometric Functions}
+\label{sec:appC_inverse_trig}
+
+\begin{table}[htbp]
+\centering
+\caption{Inverse Trigonometric Integrals}
+\label{tab:integrals_inverse_trig}
+\begin{tabular}{l l}
+\toprule
+\textbf{Integrand} & \textbf{Result} \\
+\midrule
+$\displaystyle \int \frac{1}{\sqrt{a^2 - x^2}}\,dx$ & TBD \\
+$\displaystyle \int \frac{1}{a^2 + x^2}\,dx$ & TBD \\
+$\displaystyle \int \frac{1}{x\sqrt{x^2 - a^2}}\,dx$ & TBD \\
+$\displaystyle \int \sqrt{a^2 - x^2}\,dx$ & TBD \\
+$\displaystyle \int \frac{1}{\sqrt{x^2 + a^2}}\,dx$ & TBD \\
+\bottomrule
+\end{tabular}
+\end{table}

appendices/appD_notation.tex

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+\section{Notation Glossary}
+\label{app:notation}
+
+This appendix provides a glossary of notation used throughout the handbook.
+
+\nomenclature{$y$}{Dependent variable; unknown function}
+\nomenclature{$y(t)$}{Dependent variable as a function of time $t$}
+\nomenclature{$y(x)$}{Dependent variable as a function of spatial variable $x$}
+\nomenclature{$x$}{Independent variable (spatial)}
+\nomenclature{$t$}{Independent variable (time)}
+\nomenclature{$\lambda$}{Eigenvalue; parameter in characteristic equation}
+\nomenclature{$\omega$}{Angular frequency}
+\nomenclature{$\omega_0$}{Natural angular frequency}
+\nomenclature{$\alpha, \beta, \gamma$}{General constants; damping ratio}
+\nomenclature{$\delta$}{Dirac delta function}
+\nomenclature{$\mu$}{Separation constant; parameter}
+\nomenclature{$\theta$}{Angle; phase shift}
+\nomenclature{$\phi$}{Eigenfunction; angle}
+\nomenclature{$A, B, C$}{General constants of integration}
+\nomenclature{$a, b, c$}{Coefficients in differential equations}
+\nomenclature{$n, m, k$}{Integer indices}
+\nomenclature{$f(t)$}{Input/forcing function}
+\nomenclature{$F(s)$}{Laplace transform of $f(t)$}
+\nomenclature{$\mathcal{L}$}{Laplace transform operator}
+\nomenclature{$\mathcal{L}^{-1}$}{Inverse Laplace transform}
+\nomenclature{$\mathcal{F}$}{Fourier transform operator}
+\nomenclature{$u(t)$}{Unit step (Heaviside) function}
+\nomenclature{$y_h$}{Homogeneous solution}
+\nomenclature{$y_p$}{Particular solution}
+\nomenclature{$W(y_1, y_2)$}{Wronskian of $y_1$ and $y_2$}
+\nomenclature{$\mathbf{A}$}{Coefficient matrix in systems}
+\nomenclature{$\mathbf{x}(t)$}{State vector}
+\nomenclature{$I_n$}{Identity matrix of size $n$}
+\nomenclature{$e^{\mathbf{A}t}$}{Matrix exponential}
+\nomenclature{$\mathbf{u}, \mathbf{v}$}{Vectors in phase plane}
+\nomenclature{$u(t-a)$}{Shifted unit step function}
+\nomenclature{$*$}{Convolution operator}

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

@@ -0,0 +1,39 @@
+\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

@@ -0,0 +1,54 @@
+\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

@@ -0,0 +1,44 @@
+\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

@@ -0,0 +1,59 @@
+\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

@@ -0,0 +1,44 @@
+\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

@@ -0,0 +1,49 @@
+\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

@@ -0,0 +1,49 @@
+\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

@@ -0,0 +1,49 @@
+\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}

main.tex

@@ -0,0 +1,40 @@
+\input{preamble.tex}
+
+\title{\textbf{Differential Equations Handbook}\\[0.5em]
+\normalsize A Complete Reference for ODE and Introductory PDE}
+\author{}
+\date{}
+
+\begin{document}
+
+\maketitle
+\thispagestyle{empty}
+
+\tableofcontents
+\newpage
+
+% ========== CHAPTERS ==========
+\input{chapters/ch01_introduction}
+\input{chapters/ch02_first_order}
+\input{chapters/ch03_qualitative}
+\input{chapters/ch04_second_order_homogeneous}
+\input{chapters/ch05_second_order_nonhomogeneous}
+\input{chapters/ch06_mechanical_applications}
+\input{chapters/ch07_laplace_transforms}
+\input{chapters/ch08_systems}
+\input{chapters/ch09_series_solutions}
+\input{chapters/ch10_fourier_series}
+\input{chapters/ch11_boundary_value_problems}
+\input{chapters/ch12_heat_equation}
+\input{chapters/ch13_wave_and_laplace}
+\input{chapters/ch14_nonlinear_systems}
+
+% ========== APPENDICES ==========
+\input{appendices/appA_solution_summary}
+\input{appendices/appB_transform_tables}
+\input{appendices/appC_integral_tables}
+\input{appendices/appD_notation}
+
+\printnomenclature
+
+\end{document}