Universidad Autónoma de Yucatán mathematics bachelor's thesis (community)

\chapter*{Ap\'endice A}
\addcontentsline{toc}{chapter}{Apéndice A}
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\chapter*{Conclusiones}
\addcontentsline{toc}{chapter}{Conclusiones}
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\pagenumbering{arabic}
\setcounter{page}{1}
\chapter{Introducci\'on}
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\section{Objetivo}
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\chapter{Marco te\'orico} %\label{mteorico}
Puedes citar de la siguiente manera: \cite{Boyce1965,Currie2012, Groetsch1993,Stewart2008}. Lo que cites aparecerá en la bibliografía.

\section{Definiciones, teoremas y demostraciones}
\begin{definicion}
Una funci\'on $f$ es lipschitziana si...
\end{definicion}

\begin{teorema}
Sea $f$ continua en $[a,b]$. Entonces...
\end{teorema}

\begin{proof}
Aqu\'i va la demostraci\'on.\\
Como $f$ es continua...
\end{proof}

\begin{ejemplo}
La funci\'on $f(x)=|x|$ es lipschitziana.
\end{ejemplo}

\section{Agregar ecuaciones}

Para agregar ecuaciones
\begin{equation}\label{cons_moment}
    \frac{\partial u}{\partial t}+u\cdot\nabla u=\frac{\mu}{\rho}\nabla^{2} u-\frac{1}{\rho}\nabla p+f,
\end{equation}
Para hacer referencia a la Ecuaci\'on \eqref{cons_moment} poniendole una etiqueta (label). Si no quieres enumerarla usa un asterisco en el entorno
\begin{equation*}
    \frac{\partial u}{\partial t}+u\cdot\nabla u=\frac{\mu}{\rho}\nabla^{2} u-\frac{1}{\rho}\nabla p+f,
\end{equation*}

Si la ecuaci\'on es muy larga la puedes dividir
\begin{multline}\label{osc_comp2}
    \sin^{2}{\theta}+ 2\sin{\theta}\cos{\theta} +\frac{\sin{\theta}\sin{\phi}} +\left(\frac{2\pi}{2}\right)^{2}(\sin{\phi}\cos{\phi}\sin^{2}{\theta})\\ +\frac{2}{\pi}(\sin{\phi}+\cos{\phi}) + 2\sin{\theta}\cos{\theta} =0.
\end{multline}

\section{Agregar tablas y combinar celdas}

\begin{table}[h!] % h indica 'here' es la ubicacion de la tabla
    \centering
    \caption{Titulo de la tabla}
    \begin{tabularx}{0.4\textwidth}{cccc} % c es la columna
        \hline
         & Ramas & $a_4$ & $a_3$\\ \hline
        \multirow{2}{*}{$x$} & A & $0$ & $0$ \\
        &B & $1\times10^{-4}$ & $-1\times10^{-4}$ \\ \hline
    \end{tabularx}
    \label{tab:tabla1}
\end{table}
Para hacer referencia a la Tabla \ref{tab:tabla1}

\section{Agregar im\'agenes y grupos de imágenes}
\begin{figure}[ht]
   \centering
   \includegraphics[scale=0.2]{figuras/ejemplo1.PNG}
   \caption{Figura1}
   \label{fig:figura1}
\end{figure}

\begin{figure}[h!]
    \centering
    \subfloat[Subfigura1]{
    \includegraphics[scale=0.2]{figuras/identidad.PNG}
    \label{fig:ineal}}
    \subfloat[Subfigura2]{
    \includegraphics[scale=0.2]{figuras/parabola.PNG}
    \label{fig:parab}} 
    \caption{Figura2}
   \label{fig:figura2}
\end{figure}
Puedes hacer referencia a la Figura \ref{fig:figura1} o a la Figura \ref{fig:ineal}.

\chapter{Metodolog\'ia}
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\chapter{Resultados}
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\pagenumbering{roman}
\chapter*{\color{white}Dedicatoria}
%\addcontentsline{toc}{chapter}{Dedicatoria} %esto es para que aparezca en el índice
\phantomsection
\begin{flushright}
    \textit{Dedicatoria o ep\'igrafe}
\end{flushright}

\newpage
\chapter*{Agradecimientos}
\addcontentsline{toc}{chapter}{Agradecimientos}
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\newpage
\chapter*{Resumen}
\addcontentsline{toc}{chapter}{Resumen}
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%----------------------------------------------------------
% Autor: Karla A. Figueroa
% email: [email protected]

% Comparto la plantilla del documento que hice para escribir
% mi tesis de licenciatura.
% Cumple con los requisitos de la Facultad de Matemáticas
% de la UADY: páginas a una sola cara, numeración romana
% hasta antes de la introduccion, datos de portada, etc.
% Agregué paquetes y algunos comentarios de su función,
% asi como ejemplos de su uso.
%---------------------------------------------------------
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\parindent = 0mm % Sin sangría
\usepackage[T1]{fontenc}
% --- Paquetes de mates ---
\usepackage{mathptmx}
\usepackage{mathrsfs}
\usepackage{mathtools}
\usepackage{latexsym,amssymb,amsfonts,amsthm}
\usepackage{amsmath}
% --- Imágenes ---
\usepackage{graphicx} % insertar imégenes
\usepackage{subfig} % insertar varias imagenes
% --- Formato ---
\usepackage{color}
\usepackage{array}
\usepackage{multirow} % combina celdas
\usepackage{xcolor, colortbl}
\usepackage[spanish, es-lcroman, es-tabla]{babel}\decimalpoint % Idioma español
\usepackage{caption} % Paquete para personalizar captions
\captionsetup{font=footnotesize} % Configura el tamaño de la fuente para captions
\usepackage{tabularx}
\usepackage{xfrac}
% --- Estilo ---
\usepackage{fancyhdr}
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\fancyfoot[R]{\thepage}} %enumera las páginas a la derecha
\pagestyle{fancy}
\fancyhf{}
\fancyfoot[R]{\thepage}
\renewcommand{\headrulewidth}{0pt} %quita la linea del encabezado de pagina
% --- Estilo para resultados ---
\theoremstyle{plain}
\newtheorem{teorema}{Teorema}[section]
\newtheorem{lema}[teorema]{Lema}
\newtheorem{proposicion}[teorema]{Proposición}
\newtheorem{corolario}[teorema]{Corolario}
% --- Estilo para definiciones, etc ---
\theoremstyle{definicion}
\newtheorem{definicion}[teorema]{Definición}
\newtheorem{ejemplo}[teorema]{Ejemplo}
\newtheorem{observacion}[teorema]{Observación}
\renewcommand{\proofname}{Demostración} %cambia el nombre a demostracion

\usepackage{natbib}
\usepackage{hyperref} %permite poner hiperreferencias o links
\usepackage[nottoc]{tocbibind} %agrega la bibliografia al indice


% --- DOCUMENTO ---
% se modifica el contenido en cada archivo .tex que se
% encuentra dentro de la carpeta 'capitulos'
% si no necesitas aguna sección solo debes comentarla
\begin{document}

% --- Portada ---
% debes agregar tus datos en el archivo portada.tex
\include{portada}

% --- Resumen, dedicatoria, agradecimientos ---
\include{capitulos/resumen-y-mas}

% --- Tabla de contenidos ---
\hypersetup{pdfborder=0 0 0} %quita los recuadros del vinculo
\renewcommand*\contentsname{\'Indice general} %renombra el índice
\tableofcontents %crea el índice
\listoffigures
\listoftables

% --- Cuerpo de la tesis ---
\include{capitulos/introduccion}
\include{capitulos/objetivo}
\include{capitulos/marco-teorico}
\include{capitulos/metodologia}
\include{capitulos/resultados}
\include{capitulos/concluisones}
\include{capitulos/apendice}

% --- Bibliografía ---
\bibliographystyle{plainnat} %las referencias con nombre
%\bibliographystyle{unsrt} %las referencias con número
\bibliography{referencias} %aqui pones tu archivo .bib

\end{document}

\begin{titlepage}
\thispagestyle{empty}
\begin{center}

% --- ESCUDO UADY ---
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        \parbox[c][6cm][c]{4cm}{
            \centering
            LOGO \\
            AQUÍ
        }}\\[0.5cm]
\end{center}
% por derechos de autor no incluyo la imagen del escudo pero
% puedes incluirla como 'escudo-uady' y quitar el recuadro
% --- UNIVERSIDAD Y FACULTAD ---
{\Large \MakeUppercase{Universidad Aut\'onoma de Yucatán}}\\
{\large \MakeUppercase{Facultad de Matem\'aticas}}\\
{\large \MakeUppercase{Licenciatura en Matem\'aticas}}\\[1cm]
% --- TÍTULO DE LA TESIS ---
\MakeUppercase{\large {Commodo ipsum ad nisi eiusmod exercitation eiusmod exercitation sit consectetur}}\\[1.2cm]
% --- T E S I S ---
{\huge T \hspace{1cm} E \hspace{1cm} S \hspace{1cm} I \hspace{1cm} S}\\[1.2cm]
% --- GRADO Y AUTOR ---
\MakeUppercase{Que para obtener el t\'itulo de:}\\
\MakeUppercase{\large{Licenciado(a) en Matem\'aticas}}\\[0.5cm]
\MakeUppercase{Presenta:}\\
\MakeUppercase{\large{Alumno de la universidad}}\\[0.5cm]
% --- ASESOR ---
\MakeUppercase{Director de tesis:}\\
\MakeUppercase{\large{Dr. Asesor de tesis}}\\[1.2cm]
% --- LUGAR Y AÑO ---
\MakeUppercase{M\'erida, Yucat\'an, 2025}\\

\end{center}
\end{titlepage}

@book{Stewart2008,
   abstract = {- La obra tiene una presentacion clara y selectiva. Stewart conduce al estudiante a lo largo de un material crucial mediante una forma sencilla, correcta y analitica.},
   author = {James Stewart},
   doi = {10.1093/nq/CLX.apr04.243},
   issn = {00293970},
   journal = {Notes and Queries},
   title = {Calculo de una variable. Trascendentes tempranas},
   volume = {160},
   year = {2008}
}
@book{Groetsch1993,
   abstract = {Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book are: causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.},
   author = {Charles W. Groetsch},
   doi = {10.1007/978-3-322-99202-4},
   journal = {Inverse Problems in the Mathematical Sciences},
   title = {Inverse Problems in the Mathematical Sciences},
   year = {1993}
}
@book{Boyce1965,
   abstract = {Qué son las ecuaciones diferenciales. Ecuaciones diferenciales ordinarias de primer orden. Aplicaciones de las ecuaciones diferenciales de primer orden. Ecuaciones diferenciales de orden superior. Aplicación de las ecuaciones diferenciales de segundo orden. Resolución de ecuaciones diferenciales mediante series. Transformadas de Laplace. Series de Fourier. Métodos numéricos para resolver ecuaciones diferenciales},
   author = {William Boyce and Richard DiPrima},
   issn = {2357-4100},
   issue = {4},
   journal = {Revista Colombiana de Matemáticas},
   title = {Ecuaciones Diferenciales y Problemas con Valores en la Frontera},
   volume = {7},
   year = {1965}
}
@book{Currie2012,
   abstract = {Fundamental Mechanics of Fluids, Fourth Edition addresses the need for an introductory text that focuses on the basics of fluid mechanics-before concentrating on specialized areas such as ideal-fluid flow and boundary-layer theory. Filling that void for both students and professionals working in different branches of engineering, this versatile instructional resource comprises five flexible, self-contained sections: Governing Equations deals with the derivation of the basic conservation laws, flow kinematics, and some basic theorems of fluid mechanics. Ideal-Fluid Flow covers two- and three-dimensional potential flows and surface waves. Viscous Flows of Incompressible Fluids discusses exact solutions, low-Reynolds-number approximations, boundary-layer theory, and buoyancy-driven flows. Compressible Flow of Inviscid Fluids addresses shockwaves as well as one- and multidimensional flows. Methods of Mathematical Analysis summarizes some commonly used analysis techniques. Additional appendices offer a synopsis of vectors, tensors, Fourier series, thermodynamics, and the governing equations in the common coordinate systems. The book identifies the phenomena associated with the various properties of compressible, viscous fluids in unsteady, three-dimensional flow situations. It provides techniques for solving specific types of fluid-flow problems, and it covers the derivation of the basic equations governing the laminar flow of Newtonian fluids, first assessing general situations and then shifting focus to more specific scenarios. The author illustrates the process of finding solutions to the governing equations. In the process, he reveals both the mathematical methodology and physical phenomena involved in each category of flow situation, which include ideal, viscous, and compressible fluids. This categorization enables a clear explanation of the different solution methods and the basis for the various physical consequences of fluid properties and flow characteristics. Armed with this new understanding, readers can then apply the appropriate equation results to deal with the particular circumstances of their own work.},
   author = {I G Currie},
   edition = {4th},
   isbn = {978-1439874608},
   journal = {Fundamental Mechanics of Fluids: Fourth Edition},
   publisher = {CRC Press},
   title = {Fundamental mechanics of fluids},
   year = {2012}
}