A LaTeX Course.
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\documentclass[handout]{latexkurs}
\subtitle{Grafiken erstellen mit \LaTeX{}}
\date{\dateSeventhLecture}
\def\TikZ{Ti\emph{k}Z}
\begin{document}
\maketitle
\begin{frame}
\frametitle{Grafiken erstellen in \LaTeX}
\onslide<+->
\LaTeX\ stellt von sich aus Möglichkeiten bereit, Graphiken zu erzeugen:
\begin{itemize}
\item<2-> die \texttt{picture}-Umgebung
\item<2-> \texttt{pict2e}, um die \texttt{picture}-Umgebung zu erweitern
\item<2-> \texttt{epic}, \textit{enhanced picture}
\item<2-> \texttt{eepic}, \textit{enhanced epic}
\item<2-> \texttt{pmgraph}, \textit{poor man graphics}
\item<3-> \alert<3-5>{pstricks}
\begin{itemize}
\item<4-> schnell (nutzt Postscript)
\item<5-> funktioniert nicht mit \texttt{pdftex} und \texttt{luatex}
\end{itemize}
\item<6-> \alert<6->{\TikZ}
\begin{itemize}
\item<7-> portabel
\item<8-> langsamer als \texttt{pstricks}
\item<9-> subjektiv einfacher als \texttt{pstricks}
\end{itemize}
\end{itemize}
\end{frame}
\begin{luacode}
function weierstrass(x0, x1, n, a, b, epsilon)
local dx = (x1 - x0) / n
local x = x0
local out = assert(io.open("tmp.data", "w"))
local y, k, dy
while (x <= x1) do
y = 0
k = 0
repeat
dy = math.pow(a, k) * math.cos(math.pow(b, k) * math.pi * x)
y = y + dy
k = k + 1
until (math.abs(dy) < epsilon)
out:write(x, " ", y, "\string\n")
x = x + dx
end
out:close()
end
\end{luacode}
\directlua{weierstrass(-2,2,500,0.3,5,1.e-12)}
\begin{frame}
\frametitle{Weierstraß-Funktion mit \TikZ\ und Lua}
\begin{equation*}
x \mapsto \sum_{n=0} ^\infty a^n \cos(b^n \pi x)
\end{equation*}
\begin{center}
\begin{tikzpicture}
\begin{axis}[axis lines=middle, ymin=-1.5, ymax=1.75]
\addplot[thin, blue] table {tmp.data};
\end{axis}
\end{tikzpicture}
\end{center}
\end{frame}
\section{Grundlagen von \TikZ}
\begin{frame}[fragile]
\frametitle{Wie? }
\onslide<+->
Um \TikZ\ in \LaTeX\ zu nutzen:
\begin{itemize}
\item<+-> \lstinline!\usepackage{tikz}!
\item<+-> Aller Code zwischen \lstinline!\begin{tikzpicture}! und
\lstinline!\end{tikzpicture}! wird von \LaTeX\ an \TikZ\
abgegeben.
\end{itemize}
\onslide<+->
\begin{block}{\textcolor{red}{\textbf{ACHTUNG!}}}
\TikZ\ ist eine eigene \enquote{Sprache}!
\end{block}
\end{frame}
\begin{frame}[fragile,t]
\frametitle{Die \texttt{tikzpicture} Umgebung.}
\begin{lstlisting}
\begin{tikzpicture}
CODE
\end{tikzpicture}
\end{lstlisting}
\pause
Kann zum Beispiel in \texttt{figure} Umgebung eingebettet werden.
\begin{lstlisting}
\begin{figure}[h]
\centering
\begin{tikzpicture}
CODE
\end{tikzpicture}
\caption{\label{fig:someref} some caption}
\end{figure}
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Ein paar Linien …}
\centering
\pause
\begin{columns}
\begin{column}{0.3\linewidth}
\centering
\tikzexternalenable
\begin{tikzpicture}[step=0.3]
\draw<2->[red] (0,0) -- (2,3);
\draw<3->[thick,blue] (1,1) -- (1,3);
\uncover<4->{\draw[step=0.3] (0,0) grid (3,3);}
\end{tikzpicture}
\tikzexternaldisable
\end{column}
\begin{column}{0.7\linewidth}
\begin{lstlisting}[frame=none]
\begin{tikzpicture}
\draw[red] (0,0) -- (2,3); \pause
\draw[thick,blue] (1,1) -- (1,3); \pause
\draw[step=.3] (0,0) grid (3,3);
\end{tikzpicture}
\end{lstlisting}
\end{column}
\end{columns}
\pause
\medskip
\begin{columns}
\begin{column}{0.3\linewidth}
\centering
\tikzexternalenable
\begin{tikzpicture}[step=0.3]
\draw<5->[red,->] (0,0) -- (2,3);
\draw<6->[blue,dashed] (1,1) -- (1,3);
\uncover<7->{\draw[dotted] (0,0) grid (3,3);}
\end{tikzpicture}
\tikzexternaldisable
\end{column}
\begin{column}{0.7\linewidth}
\begin{lstlisting}[frame=none]
\begin{tikzpicture}[step=0.3]
\draw[red,->] (0,0) -- (2,3); \pause
\draw[blue,dashed] (1,1) -- (1,3); \pause
\draw[dotted] (0,0) grid (3,3);
\end{tikzpicture}
\end{lstlisting}
\end{column}
\end{columns}
\end{frame}
\begin{frame}[fragile,t]
\frametitle{Noch mehr Linien …}
\pause
\begin{columns}
\begin{column}{0.3\linewidth}
\centering
\tikzexternalenable
\begin{tikzpicture}[step=0.4,scale=0.8]
\uncover<2->{\draw[red!50,thick,<<-] (0,0) -- (2,3);}
\draw<3->[line width=4pt,blue] (1,1) -- (0,2);
\uncover<4->{\draw[dotted] (0,0) grid (3,3);}
\end{tikzpicture}
\tikzexternaldisable
\end{column}
\begin{column}{0.7\linewidth}
\begin{lstlisting}[frame=none]
\begin{tikzpicture}[scale=0.8,step=0.4]
\draw[red!50,thick,<<-] (0,0) -- (2,3); \pause
\draw[line width=4pt,blue] (1,1) -- (0,2); \pause
\draw[dotted] (0,0) grid (3,3);
\end{tikzpicture}
\end{lstlisting}
\end{column}
\end{columns}
\pause
\medskip
\begin{columns}
\begin{column}{0.3\linewidth}
\centering
\tikzexternalenable
\begin{tikzpicture}[every node/.style={below}]
\tikzset{step=0.3}
\draw<5->[red] (0,0) -- (2,3) node[above] {a};
\draw<6->[blue,dashed] (1,1) rectangle (2,2);
\uncover<7->{\draw[dotted] (0,0) node {0} grid (3,3);}
\draw<8->[fill,,opacity=0.3] (1,1) circle(.707);
\end{tikzpicture}
\tikzexternaldisable
\end{column}
\begin{column}{0.7\linewidth}
\begin{lstlisting}[frame=none]
\begin{tikzpicture}[step=0.3]
\tikzset{every node/.style={below}}
\draw[red] (0,0) -- (2,3) node[above] {a}; \pause
\draw[blue,dashed] (1,1) rectangle (2,2); \pause
\draw[dotted] (0,0) node {0} grid (3,3); \pause
\draw[fill,opacity=0.3] (1,1) circle(1);
\end{tikzpicture}
\end{lstlisting}
\end{column}
\end{columns}
\end{frame}
\begin{frame}[fragile]
\frametitle{Jetzt wird's kurvig!}
\pause
\begin{columns}
\begin{column}{0.3\linewidth}
\centering
\tikzexternalenable
\begin{tikzpicture}
\coordinate (a) at (0,0);
\coordinate (b) at (0,1);
\coordinate (c) at (1,1);
\coordinate (d) at (3,2);
\draw[blue] (a) -- (d);
\draw<2-> (a)..controls (b) and (c)..(d);
\draw<3->[green,bend left=30] (a) to (d);
\draw<4->[red,out=90, in=-90] (a) to (d);
\draw<5-> ($(a)!0.5!(d)$) ellipse (1 and 0.5);
\end{tikzpicture}
\tikzexternaldisable
\end{column}
\begin{column}{0.7\linewidth}
\begin{lstlisting}[mathescape=false,frame=none]
\usetikzlibrary{calc}
\begin{tikzpicture}
\coordinate (a) at (0,0);
\coordinate (b) at (0,1);
\coordinate (c) at (1,1);
\coordinate (d) at (3,2);
\draw[blue] (a) -- (d);
\draw (a)..controls (b) and (c)..(d); \pause
\draw[green,bend left=30] (a) to (d); \pause
\draw[red,out=90, in=-90] (a) to (d); \pause
\draw ($(a)!0.5!(d)$) ellipse(1 and 0.5);
\end{tikzpicture}
\end{lstlisting}
\end{column}
\end{columns}
\end{frame}
\begin{frame}[fragile]
\frametitle{Zickzack}
\pause
\begin{columns}
\begin{column}{0.3\linewidth}
\centering
\begin{tikzpicture}
\coordinate (a) at (0,0);
\coordinate (b) at (1,1);
\coordinate (c) at (3,2);
\draw<2->[blue] (a) -- (c);
\draw<3-> (a)--(b)--(c);
\begin{scope}[yshift=1cm,dashed,thick]
\coordinate (a) at (0,0);
\coordinate (c) at (3,2);
\uncover<6->{\draw[red] (a)--(b)--(c);}
\node<7->[draw,circle through=(a)] at (b){};
\end{scope}
\end{tikzpicture}
\end{column}
\begin{column}{0.7\linewidth}
\begin{lstlisting}[mathescape=false,frame=none]
\usetikzlibrary{through}
\begin{tikzpicture}
\coordinate (a) at (0,0);
\coordinate (b) at (1,1);
\coordinate (c) at (3,2);
\draw[blue] (a) -- (c);\pause
\draw (a)--(b)--(c);\pause
\begin{scope}[yshift=1cm,dashed,thick] \pause
\coordinate (a) at (0,0);
\coordinate (c) at (3,2);\pause
\draw[red] (a)--(b)--(c);\pause
\node[draw,circle through=(a)] at (b){};
\end{scope}
\end{tikzpicture}
\end{lstlisting}
\end{column}
\end{columns}
\end{frame}
\begin{frame}[fragile]
\frametitle{Eine andere Sicht.}
\pause
\begin{columns}
\begin{column}{0.2\linewidth}
\centering
\begin{tikzpicture}
\tikzset{tomsbox/.style={rectangle, draw, very thick,
minimum size=7mm, rounded corners=2mm}}
\node[tomsbox] (1) at (0,0) {$T_1$};
\node[tomsbox] (2) [below=of 1] {$T_2$};
\node[tomsbox] (3) [below=of 2] {$T_3$};
\node[tomsbox] (4) [below=of 3] {$T_4$};
\draw (1)--(2)--(3)--(4);
\end{tikzpicture}
\end{column}
\begin{column}{0.8\linewidth}
\begin{lstlisting}[mathescape=false,frame=none]
\usetikzlibrary{positioning} % in der Präambel
\begin{tikzpicture}
\tikzset{tomsbox/.style={rectangle, draw,
very thick,minimum size=7mm,
rounded corners=2mm}}
\node[tomsbox] (1) at (0,0) {$T_1$};
\node[tomsbox] (2) [below=of 1] {$T_2$};
\node[tomsbox] (3) [below=of 2] {$T_3$};
\node[tomsbox] (4) [below=of 3] {$T_4$};
\draw (1)--(2)--(3)--(4);
\end{tikzpicture}
\end{lstlisting}
\end{column}
\end{columns}
\end{frame}
\begin{frame}[fragile]
\frametitle{Wiederholungen}
\pause
\begin{columns}
\begin{column}{0.2\linewidth}
\centering
\begin{tikzpicture}
\tikzset{tomsbox/.style={rectangle, draw, very thick,
minimum size=7mm, rounded corners=2mm}}
\node[tomsbox] (1) at (0,0) {$T_1$};
\foreach \i [count=\j] in {2,3,4}{
\node[tomsbox] (\i) [below=of \j] {$T_\i$};
\draw (\j)--(\i);
}
\end{tikzpicture}
\end{column}
\begin{column}{0.82\linewidth}
\begin{lstlisting}[mathescape=false,frame=none]
\begin{tikzpicture}
\tikzset{tomsbox/.style={rectangle, draw,
very thick,minimum size=7mm,
rounded corners=2mm}}
\node[tomsbox] (1) at (0,0) {$T_1$};
\foreach \i [count=\j] in {2,3,4}
{
\node[tomsbox] (\i) [below=of \j] {$T_\i$};
\draw (\j)--(\i);
}
\end{tikzpicture}
\end{lstlisting}
\end{column}
\end{columns}
\end{frame}
\begin{frame}[fragile]
\frametitle{Bibliotheken}
\onslide<+->
Die Funktionalität von \TikZ\ kann durch externe \emph{Bibliotheken} erweitert werden.
\onslide<+->
\begin{Beispiel}
\begin{lstlisting}
\usetikzlibrary{automata}
\end{lstlisting}
\centering
\begin{tikzpicture}[shorten >=1pt,node distance=1cm and 3cm,on grid,
every state/.style={draw=blue!50,very thick,fill=blue!20}]
\node[state,initial] (q_0) {$q_0$};
\node[state] (q_1) [above right=of q_0] {$q_1$};
\node[state] (q_2) [below right=of q_0] {$q_2$};
\path[->] (q_0) edge node [above left] {0} (q_1)
edge node [below left] {1} (q_2)
(q_1) edge [loop above] node {0} ()
(q_2) edge [loop below] node {1} ();
\end{tikzpicture}
\end{Beispiel}
\end{frame}
\begin{frame}
\frametitle{Bibliotheken}
\onslide<+->
\texttt{3d},
\texttt{angles},
\texttt{arrows},
\texttt{automata},
\texttt{babel},
\texttt{backgrounds},
\texttt{bending},
\texttt{calc},
\texttt{calendar},
\texttt{chains},
\texttt{decorations},
\texttt{decorations.footprints},
\texttt{decorations.fractals},
\texttt{decorations.markings},
\texttt{decorations.pathmorphing},
\texttt{decorations.pathreplacing},
\texttt{decorations.shapes},
\texttt{decorations.text},
\texttt{er},
\texttt{fadings},
\texttt{fit},
\texttt{fixedpointarithmetic},
\texttt{folding},
\texttt{fpu},
\texttt{intersections},
\texttt{lindenmayersystems},
\texttt{math},
\texttt{matrix},
\texttt{mindmap},
\texttt{patterns},
\texttt{petri},
\texttt{plothandlers},
\texttt{plotmarks},
\texttt{positioning},
\texttt{quotes},
\texttt{scopes},
\texttt{shadings},
\texttt{shadows},
\texttt{shapes.arrows},
\texttt{shapes.callouts},
\texttt{shapes},
\texttt{shapes.gates.logic.IEC},
\texttt{shapes.gates.logic.US},
\texttt{shapes.geometric},
\texttt{shapes.misc},
\texttt{shapes.multipart},
\texttt{shapes.symbols},
\texttt{snakes},
\texttt{spy},
\texttt{svg.path},
\texttt{through},
\texttt{topaths},
\texttt{trees},
\texttt{turtle}
\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}
\mode<handout>
\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{0.5}{
\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{0.5}{
\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{0.5}{
\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}
\usetikzlibrary{intersections} % in der Präambel
\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{0.5}{
\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{0.5}{
\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{0.5}{
\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{0.5}{
\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{0.5}{
\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{0.5}{
\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}
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