%% %% An UIT Edition example %% %% Example 04-03-1 on page 75. %% %% Copyright (C) 2012 Vo\ss %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% %% See http://www.latex-project.org/lppl.txt for details. %% % Show page(s) 1,2,3 %% ==== \PassOptionsToClass{}{beamer} \documentclass{exabeamer} \usepackage[utf8]{inputenc} %\StartShownPreambleCommands \mode
{% only article mode \usepackage{fullpage} \usepackage[linktocpage]{hyperref} } \mode{% only slides \setbeamertemplate{background canvas}[vertical shading][bottom=red!10,top=blue!10] \usetheme{Warsaw} \usefonttheme[onlysmall]{structurebold} } %\StopShownPreambleCommands \begin{document} \title{Introduction to analytic geometry} \author{Gerhard Kowalewski} \date{1910} \frame{\titlepage} \section*{Overview} \begin{frame}{Overview} \tableofcontents[part=1,pausesections] \end{frame} \AtBeginSubsection[]{\begin{frame} \frametitle{Overview} \tableofcontents[current,currentsubsection] \end{frame} } \part{Main part} \section{Research and studies} \begin{frame}{The integral and its geometric applications.} We assume that the theory of irrational numbers is known. \end{frame} \subsection{Interval} \begin{frame}{Definition} The \emph{interval} $\langle a,b\rangle$ consists of all numbers $x$ that satisfy the condition $a\le x\le b$. \end{frame} \subsection{Sequence of numbers} \begin{frame}{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{frame} \subsection{Limits} \begin{frame}{Definition of a limit} $\lim x_n=g$ means that almost all members of the sequence are within each neighbourhood of $g$. \end{frame} \subsection{Convergence criterion} \begin{frame}{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{frame} \end{document}