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diff --git a/Master/texmf-dist/doc/latex/presentations-en/pd-demo.tex b/Master/texmf-dist/doc/latex/presentations-en/pd-demo.tex new file mode 100644 index 00000000000..b1ac8578f98 --- /dev/null +++ b/Master/texmf-dist/doc/latex/presentations-en/pd-demo.tex @@ -0,0 +1,87 @@ +\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
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