\documentclass[../script.tex]{subfiles}
%! TEX root = ../../script.tex

\begin{document}
    \chapter{Multivariable Calculus}
    \vspace*{\fill}\par
    \pagebreak  

    \subfile{sections/partial_total_diff.tex}
    \subfile{sections/higher_derivs.tex}
    \subfile{sections/functionseq_and_diff.tex}
    \subfile{sections/banach_implicit.tex}
\end{document}