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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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|
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\end{frame} |
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\section{Datenvisualisierung} |
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\begin{frame}[fragile] |
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\frametitle{Datenvisualisierung} |
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\onslide<+-> |
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|
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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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\datavisualization [school book axes, visualize as smooth line] |
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data {x, y |
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-1.5, 2.25 |
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-1, 1 |
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-.5, .25 |
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0, 0 |
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.5, .25 |
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1, 1 |
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1.5, 2.25 |
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}; |
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\end{tikzpicture} |
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\end{column} |
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\begin{column}{0.6\linewidth} |
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\small |
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\begin{lstlisting}[frame=none] |
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\usetikzlibrary{datavisualization} |
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\begin{tikzpicture} |
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\datavisualization [school book axes, |
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visualize as smooth line] |
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data {x, y |
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-1.5, 2.25 |
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-1, 1 |
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-.5, .25 |
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0, 0 |
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.5, .25 |
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1, 1 |
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1.5, 2.25 |
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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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|
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\begin{frame}[fragile] |
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\frametitle{Automatisch} |
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\onslide<+-> |
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|
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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}[baseline] |
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\datavisualization [school book axes, |
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visualize as smooth line] |
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data [format=function] { |
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var x : interval [-1.5:1.5] samples 7; |
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func y = \value x * \value x; |
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}; |
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\end{tikzpicture} |
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\end{column} |
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\begin{column}{0.6\linewidth} |
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\small |
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\begin{lstlisting}[mathescape=false,frame=none] |
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\usetikzlibrary{(*@datavisualization@*), |
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(*@datavisualization@*).formats.functions} |
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\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) -- |
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(*@node@*)[below] {(*@\$@*)\varepsilon(*@\$@*)} (i-2 |- O); |
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\draw[gray] (i-2) -- (i-2 -| xmax); |
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\draw[gray, <->] ([xshift = -0.5cm]i-2 -| xmax) -- |
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(*@node@*)[fill = white] {(*@\$@*)f(x_0 + \varepsilon)(*@\$@*)} |
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([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: |
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%%% mode: latex |
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%%% TeX-master: t |
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%%% TeX-engine: luatex |
|
%%% End: |
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