\documentclass[../script.tex]{subfiles}

% !TEX root = ../../script.tex

\begin{document}
    \chapter{Real Analysis: Part I} 
    \vspace*{\fill}\par
    \pagebreak  

    \subfile{sections/elem_ineqs.tex}
    \subfile{sections/seq_and_lims.tex}
    \subfile{sections/conv_of_series.tex}
\end{document}