Added notation pages for major sections.

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Bokuan Li
2026-04-23 02:56:47 -04:00
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\chapter{Notations}
\label{chap:dg-notations}
Differential geometry is the study of things invariant under change of notation.
\begin{tabular}{lll}
\textbf{Notation} & \textbf{Description} & \textbf{Source} \\
\hline
$\mathcal{H}(E;F)$, $\mathcal{R}(E;F)$ & Space of derivatives; space of remainders in an $\mathcal{HR}$-system. & \autoref{definition:derivative-system} \\
$D_{\mathcal{HR}} f(x_0)$ & $\mathcal{HR}$-derivative of $f$ at $x_0$. & \autoref{definition:space-differentiability} \\
$\mathcal{R}_\sigma^n(E; F)$, $\mathcal{R}_\sigma(E;F)$ & $\sigma$-small functions of order $n$; order 1. & \autoref{definition:differentiation-small} \\
$D_\sigma f(x_0)$ & $\sigma$-derivative of $f$ at $x_0$. & \autoref{definition:derivative-sets} \\
$D_\sigma^n f$ & $n$-fold $\sigma$-derivative. & \autoref{definition:n-differentiable-sets} \\
$x^{(k)}$ & Tuple of $x$ repeated $k$ times. & \autoref{proposition:multilinear-derivative} \\
$D^+f(x)$ & Right derivative of $f$ at $x$. & \autoref{definition:right-differentiable-mvt} \\
\end{tabular}