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1074 lines
30 KiB
1074 lines
30 KiB
\documentclass{latexkurs}
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\subtitle{Grafiken erstellen mit \LaTeX{}}
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\date{2015-12-14}
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\def\TikZ{Ti\emph{k}Z}
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%%%%%%
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\begin{document}
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\begin{frame}
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\frametitle{Grafiken erstellen in \LaTeX}
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\onslide<+->
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\LaTeX\ stellt von sich aus Möglichkeiten bereit, Graphiken zu erzeugen:
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\begin{itemize}
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\item<2-> die \texttt{picture}-Umgebung
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\item<2-> \texttt{pict2e}, um die \texttt{picture}-Umgebung zu erweitern
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\item<2-> \texttt{epic}, \textit{enhanced picture}
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\item<2-> \texttt{eepic}, \textit{enhanced epic}
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\item<2-> \texttt{pmgraph}, \textit{poor man graphics}
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\item<3-> \alert<3-5>{pstricks}
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\begin{itemize}
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\item<4-> schnell (nutzt Postscript)
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\item<5-> funktioniert nicht mit \texttt{pdftex} und \texttt{luatex}
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\end{itemize}
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\item<6-> \alert<6->{\TikZ}
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\begin{itemize}
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\item<7-> portabel
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\item<8-> langsamer als \texttt{pstricks}
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\item<9-> subjektiv einfacher als \texttt{pstricks}
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\end{itemize}
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\end{itemize}
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\end{frame}
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\begin{luacode}
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function weierstrass(x0, x1, n, a, b, epsilon)
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local dx = (x1 - x0) / n
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local x = x0
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local out = assert(io.open("tmp.data", "w"))
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local y, k, dy
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while (x <= x1) do
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y = 0
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k = 0
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repeat
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dy = math.pow(a, k) * math.cos(math.pow(b, k) * math.pi * x)
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y = y + dy
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k = k + 1
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until (math.abs(dy) < epsilon)
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out:write(x, " ", y, "\string\n")
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x = x + dx
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end
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out:close()
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end
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\end{luacode}
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\directlua{weierstrass(-2,2,500,0.3,5,1.e-12)}
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\begin{frame}
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\frametitle{Weierstraß-Funktion mit \TikZ\ und Lua}
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\begin{equation*}
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x \mapsto \sum_{n=0} ^\infty a^n \cos(b^n \pi x)
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\end{equation*}
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\begin{center}
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\begin{tikzpicture}
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\begin{axis}[axis lines=middle, ymin=-1.5, ymax=1.75]
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\addplot[thin, blue] table {tmp.data};
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\end{axis}
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\end{tikzpicture}
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\end{center}
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\end{frame}
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\section{Grundlagen von \TikZ}
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\begin{frame}[fragile]
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\frametitle{Wie? }
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\onslide<+->
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Um \TikZ\ in \LaTeX\ zu nutzen:
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\begin{itemize}
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\item<+-> \lstinline!\usepackage{tikz}!
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\item<+-> Aller Code zwischen \lstinline!\begin{tikzpicture}! und
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\lstinline!\end{tikzpicture}! wird von \LaTeX\ an \TikZ\
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abgegeben.
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\end{itemize}
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\onslide<+->
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\begin{block}{\textcolor{red}{\textbf{ACHTUNG!}}}
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\TikZ\ ist eine eigene \enquote{Sprache}!
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\end{block}
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\end{frame}
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\begin{frame}[fragile,t]
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\frametitle{Die \texttt{tikzpicture} Umgebung.}
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\begin{lstlisting}
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\begin{tikzpicture}
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CODE
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\end{tikzpicture}
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\end{lstlisting}
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\pause
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Kann zum Beispiel in \texttt{figure} Umgebung eingebettet werden.
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\begin{lstlisting}
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\begin{figure}[h]
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\centering
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\begin{tikzpicture}
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CODE
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\end{tikzpicture}
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\caption{some caption}
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\label{fig:someref}
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\end{figure}
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Let's draw some lines.}
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\centering
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\pause
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\begin{columns}
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\begin{column}{0.3\linewidth}
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\centering
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\tikzexternalenable
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\begin{tikzpicture}[step=0.3]
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\draw<2->[red] (0,0) -- (2,3);
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\draw<3->[thick,blue] (1,1) -- (1,3);
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\uncover<4->{\draw[step=0.3] (0,0) grid (3,3);}
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\end{tikzpicture}
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\tikzexternaldisable
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\end{column}
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\begin{column}{0.7\linewidth}
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\begin{lstlisting}[frame=none]
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\begin{tikzpicture}
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\draw[red] (0,0) -- (2,3); (*@\pause @*)
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\draw[thick,blue] (1,1) -- (1,3); (*@\pause @*)
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\draw[step=.3] (0,0) grid (3,3);
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\end{tikzpicture}
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\end{lstlisting}
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\end{column}
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\end{columns}
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\pause
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\medskip
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\begin{columns}
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\begin{column}{0.3\linewidth}
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\centering
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\tikzexternalenable
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\begin{tikzpicture}[step=0.3]
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\draw<5->[red,->] (0,0) -- (2,3);
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\draw<6->[blue,dashed] (1,1) -- (1,3);
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\uncover<7->{\draw[dotted] (0,0) grid (3,3);}
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\end{tikzpicture}
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\tikzexternaldisable
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\end{column}
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\begin{column}{0.7\linewidth}
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\begin{lstlisting}[frame=none]
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\begin{tikzpicture}[step=0.3]
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\draw[red,->] (0,0) -- (2,3); (*@\pause @*)
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\draw[blue,dashed] (1,1) -- (1,3); (*@\pause @*)
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\draw[dotted] (0,0) grid (3,3);
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\end{tikzpicture}
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\end{lstlisting}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}[fragile,t]
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\frametitle{Even more lines.}
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\pause
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\begin{columns}
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\begin{column}{0.3\linewidth}
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\centering
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\tikzexternalenable
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\begin{tikzpicture}[step=0.4,scale=0.8]
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\uncover<2->{\draw[red!50,thick,<<-] (0,0) -- (2,3);}
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\draw<3->[line width=4pt,blue] (1,1) -- (0,2);
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\uncover<4->{\draw[dotted] (0,0) grid (3,3);}
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\end{tikzpicture}
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\tikzexternaldisable
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\end{column}
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\begin{column}{0.7\linewidth}
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\begin{lstlisting}[frame=none]
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\begin{tikzpicture}[scale=0.8,step=0.4]
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\draw[red!50,thick,<<-] (0,0) -- (2,3); (*@\pause @*)
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\draw[line width=4pt,blue] (1,1) -- (0,2); (*@\pause @*)
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\draw[dotted] (0,0) grid (3,3);
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\end{tikzpicture}
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\end{lstlisting}
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\end{column}
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\end{columns}
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\pause
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\medskip
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\begin{columns}
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\begin{column}{0.3\linewidth}
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\centering
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\tikzexternalenable
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\begin{tikzpicture}[every node/.style={below}]
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\tikzset{step=0.3}
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\draw<5->[red] (0,0) -- (2,3) node[above] {a};
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\draw<6->[blue,dashed] (1,1) rectangle (2,2);
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\uncover<7->{\draw[dotted] (0,0) node {0} grid (3,3);}
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\draw<8->[fill,,opacity=0.3] (1,1) circle(.707);
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\end{tikzpicture}
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\tikzexternaldisable
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\end{column}
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\begin{column}{0.7\linewidth}
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\begin{lstlisting}[frame=none]
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\begin{tikzpicture}[step=0.3]
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\tikzset{every node/.style={below}}
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\draw[red] (0,0) -- (2,3) node[above] {a}; (*@\pause @*)
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\draw[blue,dashed] (1,1) rectangle (2,2); (*@\pause @*)
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\draw[dotted] (0,0) node {0} grid (3,3); (*@\pause @*)
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\draw[fill,opacity=0.3] (1,1) circle(1);
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\end{tikzpicture}
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\end{lstlisting}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Let's get curvy}
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\pause
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\begin{columns}
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\begin{column}{0.3\linewidth}
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\centering
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\tikzexternalenable
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\begin{tikzpicture}
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\coordinate (a) at (0,0);
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\coordinate (b) at (0,1);
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\coordinate (c) at (1,1);
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\coordinate (d) at (3,2);
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\draw[blue] (a) -- (d);
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\draw<2-> (a)..controls (b) and (c)..(d);
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\draw<3->[green,bend left=30] (a) to (d);
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\draw<4->[red,out=90, in=-90] (a) to (d);
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\draw<5-> ($(a)!0.5!(d)$) ellipse (1 and 0.5);
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\end{tikzpicture}
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\tikzexternaldisable
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\end{column}
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\begin{column}{0.7\linewidth}
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\begin{lstlisting}[mathescape=false,frame=none]
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\usetikzlibrary{calc}
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\begin{tikzpicture}
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\coordinate (a) at (0,0);
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\coordinate (b) at (0,1);
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\coordinate (c) at (1,1);
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\coordinate (d) at (3,2);
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\draw[blue] (a) -- (d);
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\draw (a)..controls (b) and (c)..(d); (*@\pause @*)
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\draw[green,bend left=30] (a) to (d); (*@\pause @*)
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\draw[red,out=90, in=-90] (a) to (d); (*@\pause @*)
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\draw ($(a)!0.5!(d)$) ellipse(1 and 0.5);
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\end{tikzpicture}
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\end{lstlisting}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Zickzack}
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\pause
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\begin{columns}
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\begin{column}{0.3\linewidth}
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\centering
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\begin{tikzpicture}
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\coordinate (a) at (0,0);
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\coordinate (b) at (1,1);
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\coordinate (c) at (3,2);
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\draw<2->[blue] (a) -- (c);
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\draw<3-> (a)--(b)--(c);
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\begin{scope}[yshift=1cm,dashed,thick]
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\coordinate (a) at (0,0);
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\coordinate (c) at (3,2);
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\uncover<6->{\draw[red] (a)--(b)--(c);}
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\node<7->[draw,circle through=(a)] at (b){};
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\end{scope}
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\end{tikzpicture}
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\end{column}
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\begin{column}{0.7\linewidth}
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\begin{lstlisting}[mathescape=false,frame=none]
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\usetikzlibrary{through}
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\begin{tikzpicture}
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\coordinate (a) at (0,0);
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\coordinate (b) at (1,1);
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\coordinate (c) at (3,2);
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\draw[blue] (a) -- (c);(*@\pause @*)
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\draw (a)--(b)--(c);(*@\pause @*)
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\begin{scope}[yshift=1cm,dashed,thick] (*@\pause @*)
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\coordinate (a) at (0,0);
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\coordinate (c) at (3,2);(*@\pause @*)
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\draw[red] (a)--(b)--(c);(*@\pause @*)
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\node[(*@draw@*),circle through=(a)] at (b){};
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\end{scope}
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\end{tikzpicture}
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\end{lstlisting}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Eine andere Sicht.}
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\pause
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\begin{columns}
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\begin{column}{0.2\linewidth}
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\centering
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\begin{tikzpicture}
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\tikzset{tomsbox/.style={rectangle, draw, very thick,
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minimum size=7mm, rounded corners=2mm}}
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\node[tomsbox] (1) at (0,0) {$T_1$};
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\node[tomsbox] (2) [below=of 1] {$T_2$};
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\node[tomsbox] (3) [below=of 2] {$T_3$};
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\node[tomsbox] (4) [below=of 3] {$T_4$};
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\draw (1)--(2)--(3)--(4);
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\end{tikzpicture}
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\end{column}
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\begin{column}{0.8\linewidth}
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\begin{lstlisting}[mathescape=false,frame=none]
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\usetikzlibrary{positioning} % in der Präambel
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\begin{tikzpicture}
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\tikzset{tomsbox/.style={rectangle, (*@draw@*),
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very thick,minimum size=7mm,
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rounded corners=2mm}}
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\node[tomsbox] (1) at (0,0) {$T_1$};
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\node[tomsbox] (2) [below=of 1] {$T_2$};
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\node[tomsbox] (3) [below=of 2] {$T_3$};
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\node[tomsbox] (4) [below=of 3] {$T_4$};
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\draw (1)--(2)--(3)--(4);
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\end{tikzpicture}
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\end{lstlisting}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{for many times}
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\pause
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\begin{columns}
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\begin{column}{0.2\linewidth}
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\centering
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\begin{tikzpicture}
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\tikzset{tomsbox/.style={rectangle, draw, very thick,
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minimum size=7mm, rounded corners=2mm}}
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\node[tomsbox] (1) at (0,0) {$T_1$};
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\foreach \i [count=\j] in {2,3,4}{
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\node[tomsbox] (\i) [below=of \j] {$T_\i$};
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\draw (\j)--(\i);
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}
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\end{tikzpicture}
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\end{column}
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\begin{column}{0.82\linewidth}
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\begin{lstlisting}[mathescape=false,frame=none]
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\begin{tikzpicture}
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\tikzset{tomsbox/.style={rectangle, (*@draw@*),
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very thick,minimum size=7mm,
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rounded corners=2mm}}
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\node[tomsbox] (1) at (0,0) {$T_1$};
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\foreach \i [count=\j] in {2,3,4}
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{
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\node[tomsbox] (\i) [below=of \j] {$T_\i$};
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\draw (\j)--(\i);
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}
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\end{tikzpicture}
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\end{lstlisting}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Bibliotheken}
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\onslide<+->
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Die Funktionalität von \TikZ\ kann durch externe \emph{Bibliotheken} erweitert werden.
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\onslide<+->
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\begin{Beispiel}
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\begin{lstlisting}
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\usetikzlibrary{automata}
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\end{lstlisting}
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\centering
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\begin{tikzpicture}[shorten >=1pt,node distance=1cm and 3cm,on grid,
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every state/.style={draw=blue!50,very thick,fill=blue!20}]
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\node[state,initial] (q_0) {$q_0$};
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\node[state] (q_1) [above right=of q_0] {$q_1$};
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\node[state] (q_2) [below right=of q_0] {$q_2$};
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\path[->] (q_0) edge node [above left] {0} (q_1)
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edge node [below left] {1} (q_2)
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(q_1) edge [loop above] node {0} ()
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(q_2) edge [loop below] node {1} ();
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\end{tikzpicture}
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\end{Beispiel}
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\end{frame}
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\begin{frame}
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\frametitle{Bibliotheken}
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\onslide<+->
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\texttt{3d},
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\texttt{angles},
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\texttt{arrows},
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\texttt{automata},
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\texttt{babel},
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\texttt{backgrounds},
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\texttt{bending},
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\texttt{calc},
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\texttt{calendar},
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\texttt{chains},
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\texttt{decorations},
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\texttt{decorations.footprints},
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\texttt{decorations.fractals},
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\texttt{decorations.markings},
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\texttt{decorations.pathmorphing},
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\texttt{decorations.pathreplacing},
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\texttt{decorations.shapes},
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\texttt{decorations.text},
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\texttt{er},
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\texttt{fadings},
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\texttt{fit},
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\texttt{fixedpointarithmetic},
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\texttt{folding},
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\texttt{fpu},
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\texttt{intersections},
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\texttt{lindenmayersystems},
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\texttt{math},
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\texttt{matrix},
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\texttt{mindmap},
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\texttt{patterns},
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\texttt{petri},
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\texttt{plothandlers},
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\texttt{plotmarks},
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\texttt{positioning},
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\texttt{quotes},
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\texttt{scopes},
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\texttt{shadings},
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\texttt{shadows},
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\texttt{shapes.arrows},
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\texttt{shapes.callouts},
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\texttt{shapes},
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\texttt{shapes.gates.logic.IEC},
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\texttt{shapes.gates.logic.US},
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\texttt{shapes.geometric},
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\texttt{shapes.misc},
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\texttt{shapes.multipart},
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\texttt{shapes.symbols},
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\texttt{snakes},
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\texttt{spy},
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\texttt{svg.path},
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\texttt{through},
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\texttt{topaths},
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\texttt{trees},
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\texttt{turtle}
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|
|
\end{frame}
|
|
|
|
\section{Datenvisualisierung}
|
|
|
|
\begin{frame}[fragile]
|
|
\frametitle{Datenvisualisierung}
|
|
\onslide<+->
|
|
|
|
\begin{columns}
|
|
\begin{column}{0.3\linewidth}
|
|
\centering
|
|
\begin{tikzpicture}
|
|
\datavisualization [school book axes, visualize as smooth line]
|
|
data {x, y
|
|
-1.5, 2.25
|
|
-1, 1
|
|
-.5, .25
|
|
0, 0
|
|
.5, .25
|
|
1, 1
|
|
1.5, 2.25
|
|
};
|
|
\end{tikzpicture}
|
|
\end{column}
|
|
\begin{column}{0.6\linewidth}
|
|
\small
|
|
\begin{lstlisting}[frame=none]
|
|
\usetikzlibrary{datavisualization}
|
|
\begin{tikzpicture}
|
|
\datavisualization [school book axes,
|
|
visualize as smooth line]
|
|
data {x, y
|
|
-1.5, 2.25
|
|
-1, 1
|
|
-.5, .25
|
|
0, 0
|
|
.5, .25
|
|
1, 1
|
|
1.5, 2.25
|
|
};
|
|
\end{tikzpicture}
|
|
\end{lstlisting}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}[fragile]
|
|
\frametitle{Automatisch}
|
|
|
|
\onslide<+->
|
|
|
|
\begin{columns}
|
|
\begin{column}{0.3\linewidth}
|
|
\centering
|
|
\begin{tikzpicture}[baseline]
|
|
\datavisualization [school book axes,
|
|
visualize as smooth line]
|
|
data [format=function] {
|
|
var x : interval [-1.5:1.5] samples 7;
|
|
func y = \value x * \value x;
|
|
};
|
|
\end{tikzpicture}
|
|
\end{column}
|
|
\begin{column}{0.6\linewidth}
|
|
\small
|
|
\begin{lstlisting}[mathescape=false,frame=none]
|
|
\usetikzlibrary{(*@datavisualization@*),
|
|
(*@datavisualization@*).formats.functions}
|
|
\begin{tikzpicture}
|
|
\datavisualization
|
|
[school book axes,
|
|
visualize as smooth line]
|
|
data [format=function] {
|
|
var x : interval [-1.5:1.5]
|
|
samples 7;
|
|
func y = \value x * \value x;
|
|
};
|
|
\end{tikzpicture}
|
|
\end{lstlisting}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}[fragile]
|
|
\frametitle{Achsen}
|
|
|
|
\onslide<+->
|
|
|
|
\begin{columns}
|
|
\begin{column}{0.3\linewidth}
|
|
\centering
|
|
\begin{tikzpicture}[baseline]
|
|
\datavisualization [scientific axes=clean,
|
|
x axis={length=.7\linewidth, ticks=few},
|
|
visualize as smooth line]
|
|
data [format=function] {
|
|
var x : interval [-1.5:1.5] samples 7;
|
|
func y = \value x * \value x;
|
|
};
|
|
\end{tikzpicture}
|
|
\end{column}
|
|
\begin{column}{0.6\linewidth}
|
|
\small
|
|
\begin{lstlisting}[mathescape=false,frame=none]
|
|
\begin{tikzpicture}
|
|
\datavisualization
|
|
[scientific axes=clean,
|
|
x axis={length=.7\linewidth,
|
|
ticks=few},
|
|
visualize as smooth line]
|
|
data [format=function] {
|
|
var x : interval [-1.5:1.5]
|
|
samples 7;
|
|
func y = \value x * \value x;
|
|
};
|
|
\end{tikzpicture}
|
|
\end{lstlisting}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}[fragile]
|
|
\frametitle{Darstellung}
|
|
|
|
\onslide<+->
|
|
|
|
\begin{columns}
|
|
\begin{column}{0.3\linewidth}
|
|
\centering
|
|
\begin{tikzpicture}[baseline]
|
|
\datavisualization [scientific axes=clean,
|
|
x axis={length=.7\linewidth, ticks=few},
|
|
visualize as scatter]
|
|
data [format=function] {
|
|
var x : interval [-1.5:1.5] samples 7;
|
|
func y = \value x * \value x;
|
|
};
|
|
\end{tikzpicture}
|
|
\end{column}
|
|
\begin{column}{0.6\linewidth}
|
|
\small
|
|
\begin{lstlisting}[mathescape=false,frame=none]
|
|
\begin{tikzpicture}
|
|
\datavisualization
|
|
[scientific axes=clean,
|
|
x axis={length=.7\linewidth,
|
|
ticks=few},
|
|
visualize as scatter]
|
|
data [format=function] {
|
|
var x : interval [-1.5:1.5]
|
|
samples 7;
|
|
func y = \value x * \value x;
|
|
};
|
|
\end{tikzpicture}
|
|
\end{lstlisting}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}[fragile]
|
|
\frametitle{Legenden}
|
|
|
|
\onslide<+->
|
|
|
|
\begin{columns}
|
|
\begin{column}{0.3\linewidth}
|
|
\centering
|
|
\begin{tikzpicture}[baseline]
|
|
\datavisualization [scientific axes=clean,
|
|
x axis={length=.7\linewidth, ticks=few},
|
|
legend={below},
|
|
visualize as smooth line/.list={square},
|
|
square={label in legend={text=$x^2$}}]
|
|
data [format=function,set=square] {
|
|
var x : interval [-1.5:1.5] samples 7;
|
|
func y = \value x * \value x;
|
|
};
|
|
\end{tikzpicture}
|
|
\end{column}
|
|
\begin{column}{0.6\linewidth}
|
|
\small
|
|
\begin{lstlisting}[mathescape=false,frame=none]
|
|
\begin{tikzpicture}
|
|
\datavisualization
|
|
[scientific axes=clean,
|
|
x axis={length=.7\linewidth,
|
|
ticks=few},
|
|
legend={below},
|
|
visualize as smooth
|
|
line/.list={sq},
|
|
sq={label in legend={text=$x^2$}}]
|
|
data [format=function,set=sq] {
|
|
var x : interval [-1.5:1.5]
|
|
samples 7;
|
|
func y = \value x * \value x;
|
|
};
|
|
\end{tikzpicture}
|
|
\end{lstlisting}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
|
|
|
|
\section{Ein Tutorial}
|
|
|
|
\begin{frame}[t]
|
|
|
|
\begin{block}{Ziel}
|
|
\begin{center}
|
|
\begin{tikzpicture}[
|
|
thick,
|
|
>=stealth',
|
|
dot/.style = {
|
|
draw,
|
|
fill = white,
|
|
circle,
|
|
inner sep = 0pt,
|
|
minimum size = 4pt
|
|
}
|
|
]
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
|
|
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
|
|
\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\begin{scope}[name intersections = {of = x and y, name = i}]
|
|
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
|
|
\draw (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\draw (i-1) node[dot, label = {above:$P$}] (i-1) {} -- node[left,yshift=-3pt]
|
|
{$f(x_0)$} (i-1 |- O) node[dot, label = {below:$x_0$}] {};
|
|
\path (i-2) node[dot, label = {above:$Q$}] (i-2) {} -- (i-2 |- i-1)
|
|
node[dot] (i-12) {};
|
|
\draw (i-12) -- (i-12 |- O) node[dot,
|
|
label = {below:$x_0 + \varepsilon$}] {};
|
|
\draw[blue, <->] (i-2) -- node[right] {$f(x_0 + \varepsilon) - f(x_0)$}
|
|
(i-12);
|
|
\draw[blue, <->] (i-1) -- node[below] {$\varepsilon$} (i-12);
|
|
\path (i-1 |- O) -- node[below] {$\varepsilon$} (i-2 |- O);
|
|
\draw[gray] (i-2) -- (i-2 -| xmax);
|
|
\draw[gray, <->] ([xshift = -0.5cm]i-2 -| xmax) -- node[fill = white]
|
|
{$f(x_0 + \varepsilon)$} ([xshift = -0.5cm]xmax);
|
|
\end{scope}
|
|
\end{tikzpicture}
|
|
\end{center}
|
|
\end{block}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}[t,fragile]
|
|
|
|
\onslide<+->
|
|
|
|
\begin{center}
|
|
\scalebox{0.6}[0.6]{
|
|
\begin{tikzpicture}
|
|
\coordinate (O) at (0,0); \draw[->] (-0.3,0) -- (8,0) coordinate[label =
|
|
{below:$x$}] (xmax); \draw[->] (0,-0.3) -- (0,5) coordinate[label =
|
|
{right:$f(x)$}] (ymax);
|
|
\end{tikzpicture}
|
|
}
|
|
\end{center}
|
|
|
|
\small
|
|
|
|
\begin{lstlisting}
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) (*@coordinate@*)[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) (*@coordinate@*)[label = {right:$f(x)$}] (ymax);
|
|
\end{lstlisting}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}[t,fragile]
|
|
|
|
\begin{center}
|
|
\scalebox{0.6}[0.6]{
|
|
\begin{tikzpicture}
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
|
|
\draw (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\end{tikzpicture}
|
|
}
|
|
\end{center}
|
|
|
|
\small
|
|
|
|
\begin{lstlisting}
|
|
\draw (0.3,0.5) -- (6.7,4.7) (*@node@*)[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\end{lstlisting}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}[t,fragile]
|
|
|
|
\onslide<+->
|
|
|
|
\begin{center}
|
|
\scalebox{0.6}[0.6]{
|
|
\begin{tikzpicture}
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
|
|
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
|
|
\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\begin{scope}[name intersections = {of = x and y, name = i}]
|
|
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
|
|
\draw (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\end{scope}
|
|
\end{tikzpicture}
|
|
}
|
|
\end{center}
|
|
|
|
\small
|
|
|
|
\begin{lstlisting}
|
|
\path[name (*@path@*)=x] (0.3,0.5) -- (6.7,4.7);
|
|
\path[name (*@path@*)=y] plot[smooth]
|
|
coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\begin{scope}[name intersections = {of = x and y, name = i}]
|
|
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
|
|
\draw (0.3,0.5) -- (6.7,4.7) (*@node@*)[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth]
|
|
coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\end{scope}
|
|
\end{lstlisting}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}[t,fragile]
|
|
|
|
\begin{center}
|
|
\scalebox{0.6}[0.6]{
|
|
\begin{tikzpicture}
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
|
|
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
|
|
\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\begin{scope}[name intersections = {of = x and y, name = i}]
|
|
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
|
|
\draw (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\draw (i-1) node[label = {above:$P$}] {} -- node[left,yshift=-3pt]
|
|
{$f(x_0)$} (i-1 |- O) node[label = {below:$x_0$}] {};
|
|
\end{scope}
|
|
\end{tikzpicture}
|
|
}
|
|
\end{center}
|
|
|
|
\small
|
|
|
|
\begin{lstlisting}
|
|
\begin{scope}[name intersections = {$\dots$}]
|
|
$\dots\quad (\textsl{Wie vorher})$
|
|
\draw (i-1) (*@node@*)[label = {above:$\text{\$P\$}$}] {}
|
|
-- (*@node@*)[left,yshift=-3pt] {$\text{\$f(x\_0)\$}$}
|
|
(i-1 |- O) (*@node@*)[label = {below:$\text{\$x\_0\$}$}] {};
|
|
\end{scope}
|
|
\end{lstlisting}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}[t,fragile]
|
|
|
|
\onslide<+->
|
|
|
|
\begin{center}
|
|
\scalebox{0.6}[0.6]{
|
|
\begin{tikzpicture}
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
|
|
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
|
|
\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\begin{scope}[name intersections = {of = x and y, name = i}]
|
|
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
|
|
\draw (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\draw (i-1) node[label = {above:$P$}] {} -- node[left,yshift=-3pt]
|
|
{$f(x_0)$} (i-1 |- O) node[label = {below:$x_0$}] {};
|
|
\path (i-2) node[label = {above:$Q$}] {} -- (i-2 |- i-1) node (i-12) {};
|
|
\end{scope}
|
|
\end{tikzpicture}
|
|
}
|
|
\end{center}
|
|
|
|
\small
|
|
|
|
\begin{lstlisting}
|
|
\begin{scope}[$\dots$]
|
|
$\dots\quad (\textsl{Wie vorher})$
|
|
\path (i-2) (*@node@*)[label = {above:$\text{\$Q\$}$}] {}
|
|
-- (i-2 |- i-1) (*@node@*) (i-12) {};
|
|
\end{scope}
|
|
\end{lstlisting}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}[t,fragile]
|
|
|
|
\begin{center}
|
|
\scalebox{0.6}[0.6]{
|
|
\begin{tikzpicture}
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
|
|
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
|
|
\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\begin{scope}[name intersections = {of = x and y, name = i}]
|
|
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
|
|
\draw (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\draw (i-1) node[label = {above:$P$}] {} -- node[left,yshift=-3pt]
|
|
{$f(x_0)$} (i-1 |- O) node[label = {below:$x_0$}] {};
|
|
\path (i-2) node[label = {above:$Q$}] {} -- (i-2 |- i-1) node (i-12) {};
|
|
\draw (i-12) -- (i-12 |- O) node[label = {below:$x_0 + \varepsilon$}] {};
|
|
\end{scope}
|
|
\end{tikzpicture}
|
|
}
|
|
\end{center}
|
|
|
|
\small
|
|
|
|
\begin{lstlisting}
|
|
\begin{scope}[$\dots$]
|
|
$\dots\quad(\textsf{Wie vorher})$
|
|
\draw (i-12) -- (i-12 |- O)
|
|
(*@node@*)[label = {below:(*@\$@*)x_0 + \varepsilon(*@\$@*)}] {};
|
|
\end{scope}
|
|
\end{lstlisting}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}[t,fragile]
|
|
|
|
\begin{center}
|
|
\scalebox{0.6}[0.6]{
|
|
\begin{tikzpicture}
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
|
|
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
|
|
\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\begin{scope}[name intersections = {of = x and y, name = i}]
|
|
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
|
|
\draw (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\draw (i-1) node[label = {above:$P$}] {} -- node[left,yshift=-3pt]
|
|
{$f(x_0)$} (i-1 |- O) node[label = {below:$x_0$}] {};
|
|
\path (i-2) node[label = {above:$Q$}] {} -- (i-2 |- i-1) node (i-12) {};
|
|
\draw (i-12) -- (i-12 |- O) node[label = {below:$x_0 + \varepsilon$}] {};
|
|
\draw[blue, <->] (i-2) -- node[right] {$f(x_0 + \varepsilon) - f(x_0)$} (i-12);
|
|
\draw[blue, <->] (i-1) -- node[below] {$\varepsilon$} (i-12);
|
|
\end{scope}
|
|
\end{tikzpicture}
|
|
}
|
|
\end{center}
|
|
|
|
\small
|
|
|
|
\begin{lstlisting}
|
|
\begin{scope}[$\dots$]
|
|
$\dots\quad(\textsl{Wie vorher})$
|
|
\draw[blue, <->] (i-2) --
|
|
(*@node@*)[right] {(*@\$@*)f(x_0 + \varepsilon) - f(x_0)(*@\$@*)} (i-12);
|
|
\draw[blue, <->] (i-1) --
|
|
(*@node@*)[below] {(*@\$@*)\varepsilon(*@\$@*)} (i-12);
|
|
\end{scope}
|
|
\end{lstlisting}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}[t,fragile]
|
|
|
|
\begin{center}
|
|
\scalebox{0.6}[0.6]{
|
|
\begin{tikzpicture}
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
|
|
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
|
|
\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\begin{scope}[name intersections = {of = x and y, name = i}]
|
|
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
|
|
\draw (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\draw (i-1) node[label = {above:$P$}] {} -- node[left,yshift=-3pt]
|
|
{$f(x_0)$} (i-1 |- O) node[label = {below:$x_0$}] {};
|
|
\path (i-2) node[label = {above:$Q$}] {} -- (i-2 |- i-1) node (i-12) {};
|
|
\draw (i-12) -- (i-12 |- O) node[label = {below:$x_0 + \varepsilon$}] {};
|
|
\draw[blue, <->] (i-2) -- node[right] {$f(x_0 + \varepsilon) - f(x_0)$} (i-12);
|
|
\draw[blue, <->] (i-1) -- node[below] {$\varepsilon$} (i-12);
|
|
\path (i-1 |- O) -- node[below] {$\varepsilon$} (i-2 |- O);
|
|
\draw[gray] (i-2) -- (i-2 -| xmax);
|
|
\draw[gray, <->] ([xshift = -0.5cm]i-2 -| xmax) -- node[fill = white]
|
|
{$f(x_0 + \varepsilon)$} ([xshift = -0.5cm]xmax);
|
|
\end{scope}
|
|
\end{tikzpicture}
|
|
}
|
|
\end{center}
|
|
|
|
\small
|
|
|
|
\begin{lstlisting}
|
|
\begin{scope}[$\dots$]
|
|
$\dots\quad (\textsl{Wie vorher})$
|
|
\path (i-1 |- O) --
|
|
(*@node@*)[below] {(*@\$@*)\varepsilon(*@\$@*)} (i-2 |- O);
|
|
\draw[gray] (i-2) -- (i-2 -| xmax);
|
|
\draw[gray, <->] ([xshift = -0.5cm]i-2 -| xmax) --
|
|
(*@node@*)[fill = white] {(*@\$@*)f(x_0 + \varepsilon)(*@\$@*)}
|
|
([xshift = -0.5cm]xmax);
|
|
\end{scope}
|
|
\end{lstlisting}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}[t,fragile]
|
|
|
|
\begin{center}
|
|
\scalebox{0.6}[0.6]{
|
|
\begin{tikzpicture}[
|
|
thick,
|
|
>=stealth',
|
|
dot/.style = {
|
|
draw,
|
|
fill = white,
|
|
circle,
|
|
inner sep = 0pt,
|
|
minimum size = 4pt
|
|
}
|
|
]
|
|
\coordinate (O) at (0,0);
|
|
\draw[->] (-0.3,0) -- (8,0) coordinate[label = {below:$x$}] (xmax);
|
|
\draw[->] (0,-0.3) -- (0,5) coordinate[label = {right:$f(x)$}] (ymax);
|
|
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
|
|
\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\begin{scope}[name intersections = {of = x and y, name = i}]
|
|
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
|
|
\draw (0.3,0.5) -- (6.7,4.7) node[pos=0.8, below right] {Sekante};
|
|
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
|
|
\draw (i-1) node[dot, label = {above:$P$}] (i-1) {} -- node[left,yshift=-3pt]
|
|
{$f(x_0)$} (i-1 |- O) node[dot, label = {below:$x_0$}] {};
|
|
\path (i-2) node[dot, label = {above:$Q$}] (i-2) {} -- (i-2 |- i-1)
|
|
node[dot] (i-12) {};
|
|
\draw (i-12) -- (i-12 |- O) node[dot,
|
|
label = {below:$x_0 + \varepsilon$}] {};
|
|
\draw[blue, <->] (i-2) -- node[right] {$f(x_0 + \varepsilon) - f(x_0)$}
|
|
(i-12);
|
|
\draw[blue, <->] (i-1) -- node[below] {$\varepsilon$} (i-12);
|
|
\path (i-1 |- O) -- node[below] {$\varepsilon$} (i-2 |- O);
|
|
\draw[gray] (i-2) -- (i-2 -| xmax);
|
|
\draw[gray, <->] ([xshift = -0.5cm]i-2 -| xmax) -- node[fill = white]
|
|
{$f(x_0 + \varepsilon)$} ([xshift = -0.5cm]xmax);
|
|
\end{scope}
|
|
\end{tikzpicture}
|
|
}
|
|
\end{center}
|
|
|
|
\small
|
|
|
|
\begin{lstlisting}
|
|
\begin{tikzpicture}[thick, >=stealth',
|
|
dot/.style = {
|
|
(*@draw@*),
|
|
fill = white,
|
|
circle,
|
|
inner sep = 0pt,
|
|
minimum size = 4pt
|
|
}]
|
|
$\dots$
|
|
\end{lstlisting}
|
|
\end{frame}
|
|
\end{document}
|
|
|
|
%%% Local Variables:
|
|
%%% mode: latex
|
|
%%% TeX-master: t
|
|
%%% TeX-engine: luatex
|
|
%%% End:
|
|
|
|
|