notation.tex

\chapter*{Notation and Commands}

\textbf{Vectors}
\begin{dingautolist}{202}
\item {\bf Vectors} $\vector{x}, \vector{y},\vector{z} ... \vector{u},\vector{w} $  \verb|\vector|
\item {\bf Points } $\point{x}$  \verb|\point|
\item $\colpoint{x_1 \\ x_n}$   \verb|\colpoint{x_1  \\ x_n}|
\item  $\rowpoint{x_1 , x_n}$   \verb|\rowpoint{x_1  , x_n}|
% \item Basis $E=\{\vector{e}_1,\dots \vector{e}_n\}$
\item Ordered Basis $E=(\vector{e}_1,\dots \vector{e}_n)$
\item Canonical Bases of $\bbR^3$ $\vector{i}, \vector{j}, \vector{k}$
\item Vector in coordinates $[\vector{v}]_E$  or $[\vector{v}]$ 
\item Dot Product $\bp$ \verb|\bp|
\item Cross Product $\cross$ \verb|\cross|
\item Norm $\norm{\vector{x}}$  \verb|\norm{\vector{x}}|
\end{dingautolist}

\textbf{Functions}
\begin{dingautolist}{202}
\item real function of a real variable  $f(x)$. 
\item scalar field   $f(\vector{x})$  $\varphi(\vector{x})$
\item vector field  $\funvect{f}(\vector{x})$   \verb|\funvect{f}(\vector{x})|.
\end{dingautolist}

\textbf{Differential Operators}

\begin{dingautolist}{202}
\item Derivative $ \deriv{a}{f}$  \verb| \deriv{a}{f}|
\item dx $\dx$ \verb|\dx|
\item Gradient $\grad$. 
\item Partial derivative $\partial_1$
\end{dingautolist}

\textbf{Integrals}

\begin{dingautolist}{202}
\item normal $\hat{\vector{n}}$
\item integral $\int$
\end{dingautolist}

\textbf{Tensors}
\begin{dingautolist}{202}
\item vector  $v^ie_i$
\item covector $v_ie^i$
\item Linear Transformation $a_i^jv^j$
\item Covariant  $k$-tensor is $T\colon V^k \to \mathbb{R}$
\item  Contravariant $k$-tensor is  $T\colon (V^*)^k\to \mathbb{R}$.
\item Cristoffel $\christoffel{i}{j}{k}$ \verb|\christoffel{i}{j}{k}|
\end{dingautolist}