Commit 03c16cef authored by Olivier's avatar Olivier

Appendix:Notation: Laplacian is now defined, + added total derivative

parent aa656e0e
......@@ -27,10 +27,10 @@
Subscribt “av.” indicates “average”.
\item[lowercase symbols]%
Specific values: property per unit mass. For example, $ b \equiv B/m $.
\item[operators] Differential $\diff$, partial differential $\partial$, finite differential $\delta$, exponential $\exp x \equiv e^x $, natural logarithm $\ln x \equiv \log_e x$.
\item[operators] Differential $\diff$, partial differential $\partial$, finite differential $\delta$, total (alt.: subtantial) derivative $\text{D}/\text{D}t$ (def. eq.~\ref{eq_totaltimederivative} p.\pageref{eq_totaltimederivative}), exponential $\exp x \equiv e^x $, natural logarithm $\ln x \equiv \log_e x$.
\item[vectors] Vectors are always written with an arrow. Velocity is $\vec V \equiv (u, v, w)$, alternatively written $u_i \equiv (u, v, w)$. The norm of a vector $\vec A$ (positive or negative) is $|\vec A|$, its length (always positive) is $||\vec A||$.
\item[vector calculus]%
Dot product $\vec A \cdot \vec B$; cross product $\vec A \wedge \vec B$; gradient $\gradient{A}$ (def. eq.~\ref{eq_def_gradient} p.~\pageref{eq_def_gradient}); divergent $\divergent{\vec A}$ (def. eq.~\ref{eq_def_divergent} p.\pageref{eq_def_divergent}); Laplacian $\laplacian{\vec A}$; curl $\curl{\vec A}$.
Dot product $\vec A \cdot \vec B$; cross product $\vec A \wedge \vec B$; gradient $\gradient{A}$ (def. eq.~\ref{eq_def_gradient} p.~\pageref{eq_def_gradient}); divergent $\divergent{\vec A}$ (def. eq.~\ref{eq_def_divergent} p.\pageref{eq_def_divergent}); Laplacian $\laplacian{\vec A}$ (def. eq.~\ref{eq_def_laplacian} p.\pageref{eq_def_laplacian}); curl $\curl{\vec A}$.
\item[units] Units are typed in roman (normal) font and colored gray (\SI{1}{\kilogram}). In sentences units are fully-spelled and conjugated (one hundred \si{watts}). The \si{liter} is noted \si{\liter} to increase readablility ($\SI{1}{\liter} \equiv \SI{e-3}{\metre\cubed}$). Units in equations are those from \textit{système international} (\textsc{si}) unless otherwise indicated.
\item[numbers] The decimal separator is a comma, the decimal exponent is preceded by a dot, integers are written in groups of three ($\SI{1,234e3} ~=~ \num{1234}$). Numbers are rounded up as late as possible and never in series. Leading and trailing zeroes are never indicated.
\end{description}
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