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appendix.lyx
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appendix.lyx
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#LyX 2.0 created this file. For more info see http://www.lyx.org/
\lyxformat 413
\begin_document
\begin_header
\textclass scrbook
\use_default_options false
\maintain_unincluded_children false
\language english
\language_package default
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\index Index
\shortcut idx
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\end_index
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\paragraph_indentation default
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\end_header
\begin_body
\begin_layout Section
Notation and Symbols
\end_layout
\begin_layout Standard
\begin_inset CommandInset label
LatexCommand label
name "sec:Notation-and-Symbols"
\end_inset
\end_layout
\begin_layout Itemize
The capital Greek letter sigma ''
\begin_inset Formula $\sum$
\end_inset
'' (
\bar under
s
\bar default
igma like
\bar under
s
\bar default
um) denotes a sum over several elements.
Usually the components of the sum are indexed with lower case roman letters
starting from ''
\begin_inset Formula $i$
\end_inset
''.
The starting index is indicated below the ''
\begin_inset Formula $\sum$
\end_inset
'' and final index is indicated on top.
For example, the sum over
\begin_inset Formula $n$
\end_inset
real numbers
\begin_inset Formula $x_{1},...,x_{n}\in\mathbb{R}$
\end_inset
is denoted by
\begin_inset Formula
\begin{eqnarray*}
x_{1}+...+x_{n} & = & \sum_{i=1}^{n}x_{i}.
\end{eqnarray*}
\end_inset
Sometimes, when summing over all elements of a set, the set is indicated
below the sigma.
For example, summing all elements of the set
\begin_inset Formula $A=\{1,2,3,4,...,15\}$
\end_inset
, could be written as
\begin_inset Formula $\sum_{x\in A}x$
\end_inset
as well as
\begin_inset Formula $\sum_{n=1}^{15}n$
\end_inset
.
\end_layout
\begin_layout Itemize
The capital Greek letter pi ''
\begin_inset Formula $\Pi$
\end_inset
'' is used in an analogous manner for products, i.e.
\begin_inset Formula
\begin{eqnarray*}
x_{1}\cdot...\cdot x_{n} & = & \prod_{k=1}^{n}x_{k}.
\end{eqnarray*}
\end_inset
\end_layout
\end_body
\end_document