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+\newcommand*\Q[2]{\frac{\partial #1}{\partial #2}}
+
+\section[slide=false]{Overview}
+\begin{slide}[toc=,bm=]{Overview}
+\tableofcontents[type=1]
+\end{slide}
+
+\section[slide=false]{Research and studies}
+\begin{slide}[toc=The Integral]{The integral and its geometric applications.}
+The first Green equation:
+\begin{align}\label{green}
+\underset{\mathcal{G}\quad}\iiint\!
+ \left[u\nabla^{2}v+\left(\nabla u,\nabla v\right)\right]d^{3}V
+ =\underset{\mathcal{S}\quad}\oiint u\Q{v}{n}d^{2}A
+\end{align}
+
+The Green equation (\ref{green}) will be checked later.
+
+\begin{itemize}
+ \item<1-> A line with \texttt{itemize}.
+ \begin{itemize}
+ \item<2> A line with \texttt{itemize}.
+ \begin{enumerate}
+ \item<1> A line with \texttt{enumerate}.
+ \item<-3> Another one \ldots
+ \end{enumerate}
+ \item<3-> A line with \texttt{itemize}.
+ \end{itemize}
+ \item<4-> A line with \texttt{itemize}.
+\end{itemize}
+\end{slide}
+\subsection{Interval}
+\begin{slide}{Definition}
+The \emph{interval} $\langle a,b\rangle$ consists of all numbers $x$ that
+satisfy the condition $a\le x\le b$.
+\end{slide}
+\subsection{Sequence of numbers}
+\begin{slide}{Definition of a sequence}
+A \emph{sequence of numbers} or \emph{sequence} is created by replacing each member
+of the infinite sequence of numbers $1,2,3,\ldots$ by some rational or irrational
+number, i.\,e.\ each $n$ by a number $x_n$.
+\end{slide}
+\subsection{Limits}
+\begin{slide}{Definition of a limit}
+$\lim x_n=g$ means that almost all members of the sequence are within each
+neighbourhood of $g$.
+\end{slide}
+\subsection{Convergence criterion}
+\begin{slide}{Definition of convergence}
+\textbf{Convergence criterion}: The sequence $x_1,x_2,x_3,\ldots$ converges if and
+only if \textbf{each} sub-sequence $x^\prime_1,x^\prime_2, x^\prime_3,\ldots$
+satisfies the relation $\lim(x_n-x^\prime_n)=0$.
+\end{slide}
+
+\endinput
+
+
+%%% new text above
+
+
+
+\begin{slide}{Definition}
+The \emph{interval} $\langle a,b\rangle$ contains all numbers $x$ that satisfy
+the condition $\le x \le b$.
+\end{slide}
+\subsection{Series of numbers}
+\begin{slide}{Definition of the series}
+A \emph{series of numbers} or \emph{series} is created by replacing each
+member of the infinite series of numbers $1,2,3,\ldots$ by some rational or
+irrational number, i.e.\ each $n$ by a number $x_n$.
+\end{slide}
+\subsection{Limits}
+\begin{slide}{Definition of limits}
+%CJ both the above lines said "limes" rather than "limits" - bit odd!
+$\lim x_n=g$ means that almost all members of the series are within each
+environment of $g$.
+%CJ that sounds odd/wrong - perhaps: $\lim x_n=g$ means that as n increases, the members of the series get closer to the value $g$
+\end{slide}
+\subsection{Convergence criteria}
+\begin{slide}{Definition of convergence}
+\textbf{Convergence criteria}. The series $x_1,x_2,x_3,\ldots$ converges
+if and only if \textbf{each} sub series $x^\prime_1,x^\prime_2,
+x^\prime_3,\ldots$ satisfies the relation $\lim(x_n-x^\prime_n)=0$.
+\end{slide}
+
+
+\endinput \ No newline at end of file