Band 2

Band2/B2.1.tex

@@ -0,0 +1,74 @@
+%!tikz editor 1.0
+\documentclass{article}
+\usepackage{tikz}
+\usepackage[graphics, active, tightpage]{preview}
+\usepackage{circuitikz}
+\PreviewEnvironment{tikzpicture}
+
+%!tikz preamble begin
+\usepackage{pgfplots}
+%!tikz preamble end
+
+
+\begin{document}
+%!tikz source begin
+\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm,scale=3]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-2.5,
+xmax=2.5,
+ymin=-0.5,
+ymax=4,
+%ytick={1,2},
+%yticklabels={1,2},
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks={0.5},
+    extra x tick style={
+        tick label style={anchor=north}},
+    extra x tick labels={$\frac{1}{2}$},
+extra y ticks={0.25},
+     extra y tick style={
+        tick label style={anchor=east}},
+    extra y tick labels={$\frac{1}{4}$},
+enlargelimits = true,
+]
+
+
+
+\draw [thick, dashed] (axis cs: -0.05,1) -- (axis cs: 0.5,1);
+\draw [thick, dashed] (axis cs: 0.5,-0.05) -- (axis cs: 0.5,1);
+
+
+\addplot[domain=-2:2, blue, line width=1,samples=2000] {x^2};
+
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(0.5,2)};
+
+\draw [ultra thin, dashed] (axis cs: -.05,1/4) -- (axis cs: 1/2,1/4);
+\draw [thick, dashed] (axis cs: 0.5,1) -- (axis cs: 0.5,2);
+
+
+
+\scriptsize{ \node () at (axis cs:2.4,1.8) {$\displaystyle y=\left\{ \begin{array}{rl}
+\frac{x^2-\frac{1}{4}}{x-\frac{1}{2}} & \text{für}\; x \neq \frac{1}{2}\\ \\
+2 & \text{für}\; x = \frac{1}{2}\\
+\end{array}
+\right .$};}
+
+% \draw[] (axis cs:1.3, 0.1) -- (axis cs:1.3, -0.1);
+% \node () at (axis cs:1.3,-0.25) {$x_0$};
+
+% \draw[] (axis cs:1.14,-0.05) -- (axis cs:1.14, 0.05);
+% \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};
+
+\end{axis}
+\end{tikzpicture}
+%!tikz source end
+
+\end{document}

Band2/B2.10.tikz

@@ -0,0 +1,37 @@
+\begin{tikzpicture}
+
+\begin{axis}[
+ x=1cm,y=1cm,
+axis lines=middle,
+      axis x line=middle,
+        axis y line=middle,
+        %enlarge x limits=0.15,
+        %enlarge y limits=0.15,
+        every axis x label/.style={at={(current axis.right of origin)},anchor=north east},
+        every axis y label/.style={at={(current axis.above origin)},anchor=north east},
+xmin=-0.5,
+xmax=6.,
+ymin=-0.5,
+ymax=5,
+ytick={1,...,2},
+xtick={3},
+xlabel=$x$,
+ylabel=$y$,
+]
+
+\addplot[domain=0.75:3, blue!80!black, line width=1,samples=50] {3/x};
+\addplot[domain=3:5, blue!80!black, line width=1,samples=50] {x-1};
+\addplot[color=blue!80!black, only marks, style={mark=*, fill=white}] coordinates {(3,2)};
+\addplot[color=blue!80!black, only marks, style={mark=*	}] coordinates {(3,1)};
+
+\draw [dashed, draw=black] (axis cs: -0.05,1) -- (axis cs: 3,1);
+\draw [dashed, draw=black] (axis cs: -0.05,2) -- (axis cs: 3,2);
+\draw [dashed, draw=black] (axis cs: 3,-0.05) -- (axis cs: 3,2);
+
+\node[] at (axis cs:4.5,4.5) {\footnotesize$y=\left\{\begin{array}{l}
+\frac{3}{x} \text { für } 0<x \leq 3 \\
+x-1 \text { für } x>3
+\end{array}\right.$};
+
+\end{axis}
+\end{tikzpicture}

Band2/B2.11.tikz

@@ -0,0 +1,33 @@
+\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=1.5cm,y=1.5cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.25,
+xmax=4.2,
+ymin=-0.25,
+ymax=3,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra y ticks={1.5},
+ extra y tick style={
+        tick label style={anchor=east}},
+    extra y tick labels={$\displaystyle g$},
+enlargelimits = true,
+]
+\draw [thick, draw=blue!50!black] 
+        (axis cs: -0.05,1.5) -- (axis cs: 5.2,1.5);
+\node[] at (axis cs:2.5,2.5) {$y=f(x)$};
+
+\addplot[domain=1.1:4.4, green!50!black	, line width=1,samples=200] {1.5+(5*e^(-x))*(cos(deg(2*pi*x)))};
+
+\end{axis}
+
+
+
+\end{tikzpicture}

Band2/B2.12.tikz

@@ -0,0 +1,24 @@
+\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
+\begin{axis}[
+x=1cm,y=1cm,
+axis lines=middle,
+xmin=-5,
+xmax=5,
+ymin=-1.4,
+ymax=5,
+ytick={-1,...,4},
+xtick={-3,...,3},
+xlabel=$x$,
+ylabel=$y$,
+]
+
+
+\addplot[domain=0.5:4, blue, line width=1,samples=50] {1/(x^2)};
+\addplot[domain=-4:-0.5, blue, line width=1,samples=50] {1/(x^2)};
+
+\node[] at (axis cs:2.5,2.5) {$\displaystyle y=\frac{1}{x^2}\; (x \neq 0)$};
+\end{axis}
+
+
+
+\end{tikzpicture}

Band2/B2.3.tikz

@@ -0,0 +1,27 @@
+\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.5},}
+\begin{axis}[
+        axis x line=middle,
+        x=3cm,
+        width=40mm,
+        height=20mm,
+        xmin=0.5,
+        xmax=3.5,
+        xtick = \empty,
+        x axis line style={thick,-latex},
+        xlabel style={anchor=north west},
+        axis y line=none,
+        anchor=left of origin,
+xlabel=$x$,
+extra x ticks={1, 2, 3},
+extra x tick labels={$x_0 - C$, $x_0$, $x_0+C$},
+]
+\draw [line width=2] (axis cs: 1,0) -- (axis cs: 3,0);
+\addplot[only marks, fill=white, thick] coordinates {(1,0)};
+\addplot[only marks, fill=white, thick] coordinates {(2,0)};
+\addplot[only marks, fill=white, thick] coordinates {(3,0)};
+\end{axis}
+
+\end{tikzpicture}

Band2/B2.4.tikz

@@ -0,0 +1,53 @@
+\begin{tikzpicture}
+[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.75,
+xmax=3.75,
+ymin=-0.5,
+ymax=3.5,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks={0.75, 2, 2.5,2.8},
+extra x tick labels={$x_1$, $x_3$, $x_0$, $x_2$},
+extra y ticks={0.64, 1.5, 2.0625, 2.46},
+extra y tick labels={$f(x_1)$, $f(x_3)$, $g$ , $f(x_2)$},
+]
+
+\addplot[domain=0.5:3.1, blue, line width=1,samples=500] {0.25*(x^2)+0.5};
+
+
+\draw [line width=0.1] (axis cs: 0.75,-0.05) -- (axis cs: 0.75,0.640625);
+\draw [line width=0.1] (axis cs: -0.05,0.640625) -- (axis cs: 0.75,0.640625);
+
+\draw [ultra thin] (axis cs: 2,-0.05) -- (axis cs: 2,1.5);
+\draw [ultra thin] (axis cs: -0.05,1.5) -- (axis cs: 2,1.5);
+
+\draw [loosely dashed, ultra thin] (axis cs: 2.5,-0.05) -- (axis cs: 2.5,2.0625);
+\draw [loosely dashed, thin] (axis cs: -0.05,2.0625) -- (axis cs: 2.5,2.0625);
+
+\draw [ultra thin] (axis cs: 2.8,-0.05) -- (axis cs: 2.8,2.46);
+\draw [ultra thin] (axis cs: -0.05,2.46) -- (axis cs: 2.8,2.46);
+
+
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(0.75,0.640625)};
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(2,1.5)};
+
+\addplot[color=blue, only marks, fill=white] coordinates {(2.5,2.0625)};
+
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(2.8,2.46)};
+
+
+\node () at (axis cs:2.5,2.8) {$\displaystyle y=\left(x\right)$};
+
+\end{axis}
+
+
+\end{tikzpicture}

Band2/B2.5.tikz

@@ -0,0 +1,58 @@
+\begin{tikzpicture}
+[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-1,
+xmax=3,
+ymin=-0.5,
+ymax=2,
+ytick={1,2},
+yticklabels={1,2},
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks={0.5},
+    extra x tick style={
+        tick label style={anchor=north}},
+    extra x tick labels={$\frac{1}{2}$},
+enlargelimits = true,
+]
+
+
+
+\draw [thick, dashed] (axis cs: -0.05,1) -- (axis cs: 0.5,1);
+\draw [thick, dashed] (axis cs: 0.5,-0.05) -- (axis cs: 0.5,1);
+
+
+\addplot[domain=-1:0.5, blue, line width=1,samples=2000] {((x^2)-(1/4))/(x-(1/2)};
+\addplot[color=blue!80!black, only marks, style={mark=*, fill=white}] coordinates {(0.5,1)};
+\addplot[domain=0.51:1.5, blue, line width=1,samples=2000] {((x^2)-(1/4))/(x-(1/2)};
+
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(0.5,2)};
+
+\draw [thick, dashed] (axis cs: -0.05,2) -- (axis cs: 0.5,2);
+\draw [thick, dashed] (axis cs: 0.5,1) -- (axis cs: 0.5,2);
+
+
+
+\scriptsize{ \node () at (axis cs:2.4,1.8) {$\displaystyle y=\left\{ \begin{array}{rl}
+\frac{x^2-\frac{1}{4}}{x-\frac{1}{2}} & \text{für}\; x \neq \frac{1}{2}\\ \\
+2 & \text{für}\; x = \frac{1}{2}\\
+\end{array}
+\right .$};}
+
+% \draw[] (axis cs:1.3, 0.1) -- (axis cs:1.3, -0.1);
+% \node () at (axis cs:1.3,-0.25) {$x_0$};
+
+% \draw[] (axis cs:1.14,-0.05) -- (axis cs:1.14, 0.05);
+% \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};
+
+\end{axis}
+
+
+\end{tikzpicture}

Band2/B2.6.tikz

@@ -0,0 +1,33 @@
+\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
+\begin{axis}[
+x=5cm,y=1.5cm,
+axis lines=middle,
+xmin=-1.2,
+xmax=1.2,
+ymin=-1.4,
+ymax=1.4,
+ytick={-1,...,1},
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+]
+
+
+\addplot[domain=0.05:3.8, red, line width=1,samples=5000] {sin(deg(1/(x)))};
+\addplot[domain=-3.8:-0.05, red,  line width=1,samples=5000] {sin(deg(1/(x)))};
+
+%\draw (-0.32,0.1) node[anchor=north west] {$-\frac{1}{\pi}$};
+%\draw (0.32,0.1) node[anchor=north west] {$\frac{1}{\pi}$};
+ \draw[] (axis cs:-0.32, 0.1) -- (axis cs:-0.32, -0.1);
+ \node () at (axis cs:-0.35,-0.45) {$-\frac{1}{\pi}$};
+
+  \draw[] (axis cs:0.32, 0.1) -- (axis cs:0.32, -0.1);
+ \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};
+%\node[color=red, font=\footnotesize] at (-1,-0.25) {$f(x)=3x^3 - x^2 - 10x$};
+%\node[color=blue, font=\footnotesize] at (axis cs: 1.1,2.2) {$g(x)=- x^2 + 2x$};
+
+\end{axis}
+
+
+
+\end{tikzpicture}

Band2/B2.8.tikz

@@ -0,0 +1,56 @@
+\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.5,
+xmax=3,
+ymin=-0.5,
+ymax=2,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks={1.3},
+    extra x tick style={
+        tick label style={anchor=north}},
+    extra x tick labels={$x_0$},
+ extra y ticks={1.14},
+ extra y tick style={
+        tick label style={anchor=east}},
+    extra y tick labels={$\displaystyle \sqrt{x_0}$},
+enlargelimits = true,
+]
+  \draw [thick, dashed] 
+        (axis cs: -0.05,1.14) -- (axis cs: 1.3,1.14);
+  \draw [thick, dashed] 
+        (axis cs: 1.3,-0.05) -- (axis cs: 1.3,1.14);
+\node[label={180:{}},circle,fill,inner sep=1.5] at (axis cs:1.3,1.14) {};
+\node[label={300:{$0$}},circle,fill,inner sep=1.5] at (axis cs:0,0) {};
+ %       node[pos=0.5, above] {$y=12$};
+ %  \addplot coordinates { (0,1.14) (1.3,1.14) };
+ %   \addplot coordinates { (1,4) (2,6) };
+  %  \draw (axis cs:2,3) -- node[left]{Text} (axis cs:2,6);
+
+\addplot[domain=0:2, blue, line width=1,samples=5000] {sqrt(x)};
+%\addplot[domain=-3.8:-0.05, red,  line width=1,samples=5000] {sin(deg(1/(x)))};
+
+
+\begin{scriptsize}
+ \node () at (axis cs:2.2,1.7) {$\displaystyle y=\sqrt{x}\;(x \neq 0)$};
+\end{scriptsize}
+
+% \draw[] (axis cs:1.3, 0.1) -- (axis cs:1.3, -0.1);
+% \node () at (axis cs:1.3,-0.25) {$x_0$};
+
+% \draw[] (axis cs:1.14,-0.05) -- (axis cs:1.14, 0.05);
+% \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};
+
+\end{axis}
+
+
+
+\end{tikzpicture}

Band2/B2.9.tex

@@ -0,0 +1,79 @@
+%!tikz editor 1.0
+\documentclass{article}
+\usepackage{tikz}
+\usepackage[graphics, active, tightpage]{preview}
+\usepackage{circuitikz}
+\PreviewEnvironment{tikzpicture}
+
+%!tikz preamble begin
+\usepackage{pgfplots}
+%!tikz preamble end
+
+
+%%%%%%%%%
+%%   convert -density 300 GW001.pdf -quality 100 GW001.png
+%%%%%%%%%
+
+\begin{document}
+%!tikz source begin
+\begin{tikzpicture}
+[line cap=round,line join=round,x=1cm,y=1cm,scale=1]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.5,
+xmax=3,
+ymin=-0.1,
+ymax=2.5,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks  = {0.75, 1.25,1.75,2.25},
+extra x tick labels= {$x_0$,  $x_3$, $x_2$, $x_1$},
+extra y ticks  = {0.71232, 1.22314, 1.55962, 1.81093},
+extra y tick labels= {$g_r$,  $f(x_3)$, $f(x_2)$, $f(x_1)$}
+]
+
+%\addplot[domain=-2.7:-1.1, blue, line width=1,samples=500] {1/(x^2-1)}; 
+%\addplot[domain=1.1:2.7, blue, line width=1,samples=500] {1/(x^2-1)}; 
+\addplot[domain=0.75:2.65, blue, line width=1,samples=500] {1+ln(x)}; 
+
+
+\addplot[color=blue, only marks, fill=white] coordinates {(0.75,0.71232)};
+
+\draw [dashed, blue] (axis cs: 0.75,-0.05) -- (axis cs: 0.75,0.71232);
+
+\draw [dashed, blue] (axis cs: -0.05,0.71232) -- (axis cs: 0.75,0.71232);
+
+\addplot[color=blue, only marks] coordinates {(1.25,1.22314)};
+
+
+\draw [ blue, thin] (axis cs: 1.25,0) -- (axis cs: 1.25,1.22314);
+
+\draw [ blue, thin] (axis cs: 0, 1.22314) -- (axis cs: 1.25,1.22314);
+
+\addplot[color=blue, only marks] coordinates {(1.75,1.55962)};
+
+\draw [ blue, thin] (axis cs: 1.75,0) -- (axis cs: 1.75,1.55962);
+
+\draw [ blue, thin] (axis cs: 0, 1.55962) -- (axis cs: 1.75,1.55962);
+
+\addplot[color=blue, only marks] coordinates {(2.25,1.81093)};
+
+
+\draw [ blue, thin] (axis cs: 2.25,0) -- (axis cs: 2.25,1.81093);
+
+\draw [ blue, thin] (axis cs: 0, 1.81093) -- (axis cs: 2.25,1.81093);
+
+\end{axis}
+
+
+\end{tikzpicture}
+%!tikz source end
+
+\end{document}

Band2/B2.9.tikz

@@ -0,0 +1,56 @@
+\begin{tikzpicture}
+[line cap=round,line join=round,x=1cm,y=1cm,scale=1]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.5,
+xmax=3,
+ymin=-0.1,
+ymax=2.5,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks  = {0.75, 1.25,1.75,2.25},
+extra x tick labels= {$x_0$,  $x_3$, $x_2$, $x_1$},
+extra y ticks  = {0.71232, 1.22314, 1.55962, 1.81093},
+extra y tick labels= {$g_r$,  $f(x_3)$, $f(x_2)$, $f(x_1)$}
+]
+
+%\addplot[domain=-2.7:-1.1, blue, line width=1,samples=500] {1/(x^2-1)}; 
+%\addplot[domain=1.1:2.7, blue, line width=1,samples=500] {1/(x^2-1)}; 
+\addplot[domain=0.75:2.65, blue, line width=1,samples=500] {1+ln(x)}; 
+
+
+\addplot[color=blue, only marks, fill=white] coordinates {(0.75,0.71232)};
+
+\draw [dashed, blue] (axis cs: 0.75,-0.05) -- (axis cs: 0.75,0.71232);
+
+\draw [dashed, blue] (axis cs: -0.05,0.71232) -- (axis cs: 0.75,0.71232);
+
+\addplot[color=blue, only marks] coordinates {(1.25,1.22314)};
+
+
+\draw [ blue, thin] (axis cs: 1.25,-0.05) -- (axis cs: 1.25,1.22314);
+
+\draw [ blue, thin] (axis cs: -0.05, 1.22314) -- (axis cs: 1.25,1.22314);
+
+\addplot[color=blue, only marks] coordinates {(1.75,1.55962)};
+
+\draw [ blue, thin] (axis cs: 1.75,-0.05) -- (axis cs: 1.75,1.55962);
+
+\draw [ blue, thin] (axis cs: -0.05, 1.55962) -- (axis cs: 1.75,1.55962);
+
+\addplot[color=blue, only marks] coordinates {(2.25,1.81093)};
+
+
+\draw [ blue, thin] (axis cs: 2.25,-0.05) -- (axis cs: 2.25,1.81093);
+
+\draw [ blue, thin] (axis cs: -0.05, 1.81093) -- (axis cs: 2.25,1.81093);
+
+\end{axis}
+\end{tikzpicture}

Band2/Band2.tex

@@ -0,0 +1,49 @@
+\documentclass[german,9.5pt,final,twoside,titlepage]{scrbook}
+
+
+
+\input{Definitions.tex}
+
+
+
+\begin{document}
+	
+\maketitle
+
+\input{Vorwort.tex}
+
+\tableofcontents
+
+\part{Differentialrechnung}
+
+\input{Problemstellung_und_Historisches.tex}
+
+\input{Grenzwert.tex}
+
+%\input{Tests.tex}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%idx extra erzeugen
+%
+%Ä\index{Ae@""A}
+%Ö\index{Oe@""O}
+%Ü\index{Ue@""U}
+
+
+% Index soll Stichwortverzeichnis heissen
+\newpage
+\renewcommand{\indexname}{Stichwortverzeichnis}
+
+% Stichwortverzeichnis soll im Inhaltsverzeichnis auftauchen
+\addcontentsline{toc}{section}{Stichwortverzeichnis}
+
+% Stichwortverzeichnis endgueltig anzeigen
+\printindex
+
+
+
+\end{document}
+

Band2/Definitions.tex

@@ -0,0 +1,271 @@
+%!TEX root=Band2.tex
+
+\usepackage[paperheight=240mm,paperwidth=170mm,left=2.1cm,right=1.9cm,top=20mm,bottom=20mm,heightrounded]{geometry}
+
+\usepackage{babel}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+
+
+\usepackage{tikz}
+\usetikzlibrary{arrows.meta,bending,positioning,matrix,fit,arrows,backgrounds}
+\usepackage{circuitikz}
+\usetikzlibrary{circuits.ee.IEC.relay}
+%\usepackage{sanitize-umlaut}
+
+% fuer Stichwortverzeichnis
+\usepackage{makeidx}
+
+% Stichwortverzeichnis erstellen
+\makeindex
+
+
+\usepackage{graphicx}
+%\usepackage{fancyhdr}
+\usepackage{makecell}
+
+%\reversemarginpar
+
+% ref packages
+%\usepackage{nameref}
+% folowing  must be in this order
+%\usepackage{varioref}
+\usepackage[colorlinks=true,urlcolor=blue,linkcolor=blue]{hyperref}
+%\usepackage{cleveref}
+
+\usepackage[parfill]{parskip}
+%\newcommand{\anf}[1]{"`#1"'}
+
+\newcommand{\anf}[1]{\glqq#1\grqq}
+
+%\usepackage{showframe}
+\usepackage[most]{tcolorbox}
+\usepackage{amsmath,amssymb}
+
+
+\usepackage{scrlayer-scrpage}
+\pagestyle{scrheadings} 	
+
+%https://www.grund-wissen.de/informatik/latex/seitenlayout.html
+\automark[section]{chapter}
+\clearscrheadfoot
+\ohead{\pagemark}
+\ihead{\headmark}
+
+\newcommand{\einrueckungm}[2]{\begin{addmargin}[#1pt]{0pt}
+		#2\end{addmargin}
+}
+
+\newcommand{\einrueckung}[1]{\begin{addmargin}[45pt]{0pt}
+		#1\end{addmargin}
+}
+
+%%%%Leerseite
+\usepackage{afterpage}
+\newcommand\myemptypage{
+	\null
+	\thispagestyle{empty}
+	\addtocounter{page}{-1}
+	\newpage
+}	
+
+%%%%Zahl linker Rand
+
+\newcommand{\liRa}[1]{\marginpar[\raggedleft\Huge{\textbf{#1}}]{\textbf{\Huge{#1}}}}
+
+%%%%Farbbox
+\newtcolorbox{mybox}[1][]{%
+	%enhanced,
+	%boxed title style={colback=red, sharp corners},
+	colframe = orange!20,
+	colback = orange!20,  
+	%	overlay = {\node[text=white, fill=red] at (frame.east) 
+		%		{$\clubsuit$};},
+	#1}
+
+%\usepackage{enumitem,calc}
+%\SetLabelAlign{myparleft}{\parbox[t]\textwidth{#1\par\mbox{}}}
+
+\usepackage{calc}
+\usepackage{enumitem} % für liste mit Klammern siehe 3.4
+%\setlist[description]{leftmargin=\parindent,labelindent=\parindent}\usepackage{enumitem}
+%\setlist[description]{leftmargin=\parindent,labelindent=\parindent}
+
+\newlength{\mylength}
+
+\newcommand{\ausrichtung}[1]{ % Befehl zur Berechnung der Wortlänge
+	\settowidth{\mylength}{#1} % Breite des Wortes berechnen und in Längenvariable speichern
+	\hspace{\mylength}} % wird die Klammer eine Zeile tiefer gesetzt, dann rutscht das nachfolgende um ? nach rechts
+
+
+%%%%%%%%%%%%%%%%%%%%%
+\usepackage{amsthm}
+%\newtheorem{thm}{Theorem}[chapter]
+%\newtheorem{defn}[thm]{Definition}
+%
+%\newtheoremstyle{theorem}
+%{10pt}
+%{0pt}
+%{}
+%{}
+%{\bfseries}
+%{}
+%{\newline}
+%{}
+%\theoremstyle{theorem}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%
+%1. Beispiel
+%\newtheoremstyle{break}
+%{\topsep}{\topsep}%
+%{\itshape}{}%
+%{\bfseries}{}%
+%{\newline}{}%
+%\theoremstyle{break}
+%\newtheorem{theorem}{Theorem}
+%
+%\begin{document}
+%	
+%	\begin{theorem}[Some note]
+	%		\lipsum*[2]
+	%	\end{theorem}
+%	
+%\end{document}
+
+%2. Beispiel
+%\newtheoremstyle{side}{}{}{\advance\leftskip3cm\relax\itshape}{}
+%{\bfseries}{}{0pt}{%
+	%	\makebox[0pt][r]{%
+		%		\smash{\parbox[t]{2.5cm}{\raggedright\thmname{#1}%
+				%				\thmnumber{\space #2}\thmnote{\newline (#3)}}}%
+		%		\hspace{.5cm}}}
+%
+%\theoremstyle{side}
+%\newtheorem{theorem}{Theorem}[section]
+%
+%\theoremstyle{definition}
+%\newtheorem{definition}[theorem]{Definition}
+%
+%\begin{document}
+%	
+%	\lipsum[1]
+%	
+%	\begin{theorem}
+	%		\lipsum[1]
+	%	\end{theorem}
+%	
+%	\begin{theorem}[Euclid]
+	%		\lipsum[2]
+	%	\end{theorem}
+%	
+%	\begin{theorem}[Very long name]
+	%		\lipsum[3]
+	%	\end{theorem}
+%	
+%	\begin{definition}
+	%		\lipsum[1]
+	%	\end{definition}
+%	
+%\end{document}
+
+
+
+
+\usepackage{pgfplots}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\newtheorem{thb}{Theorem}[chapter]
+\newtheorem{bsp}[thb]{Beispiel}
+
+%https://tex.stackexchange.com/questions/338209/remove-dot-after-theorem-with-amsthm-and-hyperref
+
+\usepackage{xpatch}
+\makeatletter
+\AtBeginDocument{\xpatchcmd{\@thm}{\thm@headpunct{.}}{\thm@headpunct{}}{}{}}
+\makeatother
+
+\numberwithin{equation}{chapter} %Numerierung der Formeln mit Kapitelnummer 
+
+%%%%%%%%%%%%%%%%%%%%%Tabellenbreite
+
+\usepackage{tabulary}
+
+%%%%%%%%%%%%%%%%%%%%%
+
+
+
+
+%%%%%%Neues Enviroment für Defintion
+%% https://tex.stackexchange.com/questions/43495/defining-a-custom-environment-with-per-section-numbering
+
+\newcounter{mydefcount}
+\newcounter{mybspcount}
+\newcounter{myaufgcount}
+\newcounter{mysatzcount}
+
+\newenvironment{definition}{%      define a custom environment
+%	\bigskip\noindent%         create a vertical offset to previous material
+	\refstepcounter{mydefcount}% increment the environment's counter
+	\textbf{Definition \themydefcount}: }{}  
+\numberwithin{mydefcount}{chapter}
+
+
+\newenvironment{satz}{%      define a custom environment
+	%	\bigskip\noindent%         create a vertical offset to previous material
+	\refstepcounter{mysatzcount}% increment the environment's counter
+	\textbf{Satz \themysatzcount}: }{}  
+\numberwithin{mysatzcount}{chapter}
+
+%%%%%%Neues Enviroment für Definition Ende
+
+\newenvironment{beispiel}{%      define a custom environment
+	\bigskip\noindent%         create a vertical offset to previous material
+	\refstepcounter{mybspcount}% increment the environment's counter
+	\textbf{Beispiel \themybspcount}:}{}
+\numberwithin{mybspcount}{chapter}
+
+
+\newenvironment{aufgabe}{%      define a custom environment
+	\bigskip\noindent%         create a vertical offset to previous material
+	\refstepcounter{myaufgcount}% increment the environment's counter
+	\textbf{* Aufgabe \themyaufgcount}\mbox{}
+	\vspace*{-\baselineskip}
+	\newline
+	
+}{\par\bigskip}  %          create a vertical offset to following material
+\numberwithin{myaufgcount}{chapter}
+
+\title{Differential- und Integralrechnung für Funktionen mit einer Variablen}
+
+%%%Pfeile
+\pgfdeclarelayer{background}
+\pgfsetlayers{background,main}
+\newcommand{\bglayer}[1]{%
+	\begin{pgfonlayer}{background}
+		\begin{scope}[every picture]
+			#1
+		\end{scope}
+	\end{pgfonlayer}
+}
+%%%Pfeile
+
+\everymath{\displaystyle}
+
+\usepackage[figurewithin=chapter,labelsep=space]{caption}
+
+%\usepackage[font=small,labelfont=bf,figurewithin=section,labelsep=space]{caption}
+
+%%%Caption in tabelle auch links
+%\usepackage[singlelinecheck=false % <-- important
+%]{caption}
+
+\usepackage{booktabs} 
+%\usepackage{floatrow} % um die caption nach rechts zu setzen
+
+%Abbildung nach Bild umbenennen
+\renewcaptionname{german}{\figurename}{Bild}
+
+\newcommand{\hhlline}[3]{\draw (#1-#2-1.south west) -- (#1-#2-#3.south east);}

Band2/Horner01.tikz

@@ -0,0 +1,203 @@
+%!TEX root=Band2.tex
+
+%\begin{tikzpicture}[>=latex]
+%
+%\draw[cyan, densely dotted] (-2,0) grid (12,14);
+%\useasboundingbox (-2,0) rectangle (12,14);
+%
+%%nodes=draw,
+%\matrix (m1) [anchor=west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 6/.style={anchor=base west}, left delimiter=\{ ] at (1, 12)
+%{
+%\phantom{a} & $3$  & $0$\footnotemark & $1$ & $-5 $ & $2$ \\
+%\phantom{a}  & \phantom{a} & $6$ & $12$ & $26$ & $42$\\
+%$2$ & $3$ & $6$ & $13$ & $21$ & $44=g(2)$\\
+%};
+%
+%\matrix (m2) [anchor=west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 5/.style={anchor=base west}, left delimiter=\{ ] at (1, 9)
+%	{
+%\phantom{a} & \phantom{a} & $6$ & $24$ & $74$\\
+%	$2$ & $3$ &	$12$ & $37$ & $95=g'(2)$ \\
+%};
+%
+%\matrix (m3) [anchor= west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 4/.style={anchor=base west} , left delimiter=\{] at (1, 6.5)
+%{
+%\phantom{a} & \phantom{a} & $6$ & $36$\\
+%	$2$ & $3$ &	$18$ &  $73=\frac{g''(2)}{2!}$ \phantom{a}\\
+%};
+%
+%\matrix (m4) [anchor= west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 3/.style={anchor=base west} , left delimiter=\{] at (1, 4)
+%{
+%\phantom{a} & \phantom{a} & $6$\\
+%	$2$ & $3$ &	  $24=\frac{g'''(2)}{3!}$ \phantom{a}\\
+%};
+%
+%\matrix (m5) [anchor= west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 4/.style={anchor=base west} , left delimiter=\{] at (1, 2)
+%{
+%\phantom{a} &$3=\frac{g^{4}(2)} {4!}$ \\
+%};
+%
+%\draw ([xshift=.1cm]m1-1-1.north east) -- ([xshift=.1cm,yshift=-0.3cm]m5-1-1.south east);
+%
+%\draw ([yshift=-.25cm]m1-2-1.south west) -- ([yshift=-.25cm,xshift=1.2cm]m1-2-6.south east);
+%
+%\draw ([yshift=-.25cm]m2-1-1.south west) -- ([yshift=-.25cm,xshift=1.3cm]m2-1-5.south east);
+%
+%\draw ([yshift=-.25cm]m3-1-1.south west) -- ([yshift=-.25cm,xshift=16mm]m3-1-4.south east);
+%
+%\draw ([yshift=-.25cm]m4-1-1.south west) -- ([yshift=-.25cm,xshift=18mm]m4-1-3.south east);
+%
+%%\draw ([yshift=-.25cm]m5-1-1.south west) -- ([yshift=-.25cm,xshift=3mm]m5-1-2.south east);
+%%\draw ([yshift=2mm]m1-3-6.north west) -- ([yshift=-1mm]m1-3-6.south west);
+%	
+%	%\draw ([yshift=-.25cm]m1-2-6.south west) -- ([yshift=-.25cm,xshift=4mm]m1-2-6.south east);
+%	
+%%	\draw ([yshift=-.15cm]m1-3-6.south west) -- 	([yshift=-.15cm]m1-3-6.south east);
+%	
+%
+%\node[circle,draw] (del-left-1) at ($0.5*(m1-3-1.south west)+0.5*(m1-1-1.north west)$){};
+%\node[circle,draw] (del-left-2) at ($0.5*(m2-2-1.south west)+0.5*(m2-1-1.north west)$){};
+%\node[circle,draw] (del-left-3) at ($0.5*(m3-2-1.south west)+0.5*(m3-1-1.north west)$){};
+%\node[circle,draw] (del-left-4) at ($0.5*(m4-2-1.south west)+0.5*(m4-1-1.north west)$){};
+%\node[circle,draw] (del-left-5) at ($0.5*(m5-1-1.south west)+0.5*(m5-1-1.north west)$){};
+%\node[left=10pt] at (del-left-1.west) {1. Schritt};
+%\node[left=10pt] at (del-left-2.west) {2. Schritt};
+%\node[left=10pt] at (del-left-3.west) {3. Schritt};
+%\node[left=10pt] at (del-left-4.west) {4. Schritt};
+%\node[left=10pt] at (del-left-5.west) {5. Schritt};
+%
+%%\draw ($(m1-2-5.north east)!0.5!(m1-2-5.north west)$) -- ($(m1-2-5.south east)!0.5!(m2-2-2.south west)$);
+%%\draw($(m1-2-5.north east)!50!(m1-2-6.north west)$)--($(m1-3-5.south east)!50!(m1-3-6.south west)$);
+%%\draw([yshift=3mm]m1-3-6.north west)--(m1-3-6.south west);
+%
+%\hhlline{m5}{1}{2};
+%
+%%	\node[rectangle,draw] (del-left-2) at ($(m2-2-1)-(m2-1-1)$) {\tikz{\path (m2-2-2.north east) rectangle (m2-2-1.south west);}};
+%
+%
+%
+% %\mymatrixbracetop{2}{6}{$E'$}
+%
+%%\node[font=\color{red}] at (m2.center){X};
+%
+%%\foreach \xy in {$1*(m2-1-1)$, $1*(m2-2-1)$}{
+%%    \node at (\xy) {\xy};
+%%}
+%
+%\end{tikzpicture} \footnotetext{Man beachte, ...}
+
+\begin{tikzpicture}[>=latex]
+	
+%\draw[cyan, densely dotted] (-2,0) grid (8.5,9.5);
+\useasboundingbox (-2,0) rectangle (8.5,9.5);
+	
+%nodes=draw,
+\matrix (m1) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 6/.style={anchor=base west}, left delimiter=\{ ] at (1, 8.4)
+{
+	\phantom{a} & 3  & 0\footnotemark & 1 & -5  & 2 \\
+	\phantom{a}  & \phantom{a} & 6 & 12 & 26 & 42\\
+	2 & 3 & 6 & 13 & 21 & 44=g(2)\\
+};
+	
+\matrix (m2) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes, column 5/.style={anchor=base west}, left delimiter=\{ ] at (1, 6.4)
+{
+	\phantom{a} & \phantom{a} & 6 & 24 & 74\\
+	2 & 3 &	12 & 37 & 95=g'(2) \\
+};
+	
+\matrix (m3) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 4/.style={anchor=base west}, left delimiter=\{ ] at (1, 4.5)
+{
+	\phantom{a} & \phantom{a} & 6 & 36\\
+	2 & 3 &	18 &  73=\frac{g''(2)}{2!} \\
+};
+	
+\matrix (m4) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 3/.style={anchor=base west}, left delimiter=\{ ] at (1, 2.4)
+{
+	\phantom{a} & \phantom{a} & 6\\
+	2 & 3 &	 24=\frac{g'''(2)}{3!} \\
+};
+
+\matrix (m5) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 2/.style={anchor=base west}, left delimiter=\{ ] at (1, 0.7)
+{
+	\phantom{a} &  3=\frac{g^{(4)}(2)}{4!} \\
+};
+	
+\node[circle] (del-left-1) at ($0.5*(m1-3-1.south west)+0.5*(m1-1-1.north west)$){};
+\node[left=10pt] at (del-left-1.west) {1. Schritt};
+	
+	%\draw ($(m1-2-5.north east)!0.5!(m1-2-5.north west)$) -- ($(m1-2-5.south east)!0.5!(m2-2-2.south west)$);
+	%\draw($(m1-2-5.north east)!50!(m1-2-6.north west)$)--($(m1-3-5.south east)!50!(m1-3-6.south west)$);
+	%\draw([yshift=3mm]m1-3-6.north west)--(m1-3-6.south west);
+%\draw ([yshift=-3mm]m1-2-1.south west) -- ([yshift=-3mm,xshift=10mm]m1-2-6.south east);
+
+\draw ($0.5*(m1-2-1.south west)+0.5*(m1-3-1.north west)$) -- ([xshift=5mm]$0.5*(m1-2-6.south east)+0.5*(m1-3-6.north east)$);
+
+\draw ([yshift=1mm]m1-3-6.north west) -- (m1-3-6.south west);
+\draw (m1-3-6.south west) -- (m1-3-6.south east);
+
+\draw ($0.5*(m2-1-1.south west)+0.5*(m2-2-1.north west)$) -- ([xshift=5mm]$0.5*(m2-1-5.south east)+0.5*(m2-2-5.north east)$);
+
+%Ende Zeile 2 
+%vert
+\draw ([yshift=1mm]m2-2-5.north west) -- (m2-2-5.south west);
+%horiz
+\draw (m2-2-5.south west) -- (m2-2-5.south east);
+
+
+%Trennlinie
+\draw ([yshift=1.5mm]$0.5*(m3-1-1.south west)+0.5*(m3-2-1.north west)$) -- ([xshift=5mm]$0.5*(m3-1-4.south east)+0.5*(m3-2-4.north east)$);
+\node[circle] (del-left-2) at ($0.5*(m2-2-1.south west)+0.5*(m2-1-1.north west)$){};
+\node[left=10pt] at (del-left-2.west) {2. Schritt};
+
+\node[circle] (del-left-3) at ([yshift=-1mm]$0.5*(m3-1-1.south west)+0.5*(m3-2-1.north west)$){};
+\node[left=10pt] at (del-left-3.west) {3. Schritt};
+
+\draw ([yshift=1mm]m3-2-4.north west) -- (m3-2-4.south west);
+\draw (m3-2-4.south west) -- (m3-2-4.south east);
+
+%\draw ([yshift=-3mm,thick]m2-1-1.south west) -- ([yshift=-3mm,xshift=10mm]m2-1-5.south east);	
+
+\draw ([yshift=1.5mm]$0.5*(m4-1-1.south west)+0.5*(m4-2-1.north west)$) -- ([xshift=5mm]$0.5*(m4-1-3.south east)+0.5*(m4-2-3.north east)$);
+
+\draw ([yshift=1mm]m4-2-3.north west) -- (m4-2-3.south west);
+\draw (m4-2-3.south west) -- (m4-2-3.south east);
+
+
+\node[circle] (del-left-4) at ([yshift=-1mm]$0.5*(m4-1-1.south west)+0.5*(m4-2-1.north west)$){};
+\node[left=10pt] at (del-left-4.west) {4. Schritt};
+
+\draw ($0.5*(m1-2-1.south west)+0.5*(m1-3-1.north west)$) -- ([xshift=5mm]$0.5*(m1-2-6.south east)+0.5*(m1-3-6.north east)$);
+
+\draw ([yshift=1mm]m1-3-6.north west) -- (m1-3-6.south west);
+\draw (m1-3-6.south west) -- (m1-3-6.south east);
+
+\draw ($0.5*(m2-1-1.south west)+0.5*(m2-2-1.north west)$) -- ([xshift=5mm]$0.5*(m2-1-5.south east)+0.5*(m2-2-5.north east)$);
+
+
+\draw ([yshift=1mm]m3-2-4.north west) -- (m3-2-4.south west);
+\draw (m3-2-4.south west) -- (m3-2-4.south east);
+
+%\draw ([yshift=-3mm,thick]m2-1-1.south west) -- ([yshift=-3mm,xshift=10mm]m2-1-5.south east);	
+
+\node[circle] (del-left-5) at ([yshift=1mm]$0.5*(m5-1-1.south west)+0.5*(m5-1-1.north west)$){};
+\node[left=10pt] at (del-left-5.west) {5. Schritt};
+
+	
+\draw (m5-1-2.north west) -- (m5-1-2.south west);
+\draw (m5-1-2.south west) -- (m5-1-2.south east);
+	
+	
+\draw ([yshift=5.5mm]m5-1-1.north west)-- ([yshift=1mm]m5-1-2.north east);
+
+\draw(m1-1-1.north east)--([yshift=-2mm]m5-1-1.south east);
+
+	%\mymatrixbracetop{2}{6}{$E'$}
+	
+	%\node[font=\color{red}] at (m2.center){X};
+	
+	%\foreach \xy in {$1*(m2-1-1)$, $1*(m2-2-1)$}{
+		%    \node at (\xy) {\xy};
+		%}
+	
+\end{tikzpicture} \footnotetext{Man beachte, ...}
+
+\newpage

Band2/Horner02.tikz

@@ -0,0 +1,56 @@
+%!TEX root=Band2.tex
+\begin{tikzpicture}[>=latex]
+	
+%\draw[cyan, densely dotted] (-2,0) grid (12,14);
+\useasboundingbox (-2,0) rectangle (12,14);
+	
+%nodes=draw,
+\matrix (m1) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 7/.style={anchor=base west}] at (1, 12)
+	{
+		\phantom{a} & 1  & 3 & 5 & 7  & 6 & 2 \\
+		\phantom{a}  & \phantom{a} & -1 & -2 & -3 & -4 & -2\\
+		-1 & 1 & 2 & 3 & 4 & 2 & 0=g(-1)\\
+	};
+	
+\matrix (m2) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes, column 6/.style={anchor=base west}] at (1, 10)
+	{
+		\phantom{a} & \phantom{a} & -1 & -1 & -2 & -2\\
+		-1 & 1 & 1 & 2 & 2 & 0=g'(-1) \\
+	};
+	
+\matrix (m3) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 5/.style={anchor=base west}] at (1, 8.1)
+{
+	\phantom{a} & \phantom{a} & -1 & 0 & -2\\
+	-1 & 1 & 0 & 2 & 0=\frac{g''(-1)}{2!} \\
+};
+	
+\matrix (m4) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 4/.style={anchor=base west}] at (1, 6)
+{
+	\phantom{a} & \phantom{a} & -1 & 1\\
+	-1 & 1 & -1 &	 3=\frac{g'''(-1)}{3!} \neq 0 \\
+};
+
+
+\draw ($0.5*(m1-2-1.south west)+0.5*(m1-3-1.north west)$) -- ([xshift=5mm]$0.5*(m1-2-7.south east)+0.5*(m1-3-7.north east)$);
+
+\draw ([yshift=1mm]m1-3-7.north west) -- (m1-3-7.south west);
+\draw (m1-3-7.south west) -- (m1-3-7.south east);
+
+\draw ($0.5*(m2-1-1.south west)+0.5*(m2-2-1.north west)$) -- ([xshift=5mm]$0.5*(m2-1-6.south east)+0.5*(m2-2-6.north east)$);
+
+\draw ([yshift=1mm]m2-2-6.north west) -- (m2-2-6.south west);
+\draw (m2-2-6.south west) -- (m2-2-6.south east);
+
+\draw ([yshift=1.5mm]$0.5*(m3-1-1.south west)+0.5*(m3-2-1.north west)$) -- ([xshift=5mm]$0.5*(m3-1-5.south east)+0.5*(m3-2-5.north east)$);
+
+\draw ([yshift=1mm]m3-2-5.north west) -- (m3-2-5.south west);
+\draw (m3-2-5.south west) -- (m3-2-5.south east);
+
+\draw ([yshift=1.5mm]$0.5*(m4-1-1.south west)+0.5*(m4-2-1.north west)$) -- ([xshift=12mm]$0.5*(m4-1-4.south east)+0.5*(m4-2-4.north east)$);
+
+\draw ([yshift=1mm]m4-2-4.north west) -- (m4-2-4.south west);
+\draw (m4-2-4.south west) -- (m4-2-4.south east);
+
+\draw([xshift=2mm]m1-1-1.north east)--([xshift=2mm,yshift=-2mm]m4-2-1.south east);
+
+\end{tikzpicture}

Band2/Problemstellung_und_Historisches.tex

@@ -0,0 +1,11 @@
+\chapter{Problemstellung und Historisches}
+
+Zur mathematischen Beschreibung von Naturvorgängen, aber auch von technischen und ökonomischen Prozessen ist die Differentialrechnung ein unentbehrliches Hilfsmittel. Es ist daher nicht verwunderlich, daß gerade von Naturforschern entscheidende Anstöße zu ihrer Entwicklung ausgingen. Wichtige Vorarbeiten wurden im 16. und 17. Jahrhundert geleistet. Die eigentlichen Urheber dieser Disziplin sind aber Isaac Newton (1643-1727) und Gottfried Wilhelm Leibniz (1646-1716), die die Differential- (und Integral-) Rechnung etwa gleichzeitig und voneinander unabhängig zu einem Kalkül entwickelten. Newton schuf seine ,,Fluxionsrechnung“ bei der Ableitung des Gravitationsgesetzes aus den Keplerschen Gesetzen der Planetenbewegung. Leibniz, der auch das Symbol $\frac{\mathrm{d} y}{\mathrm{~d} x}$ einführte, ging von dem Problem aus, an eine Kurve in einem vorgegebenen Kurvenpunkt die Tangente zu legen (,,Tangentenproblem“). Die Arbeiten dieser genialen Forscher lösten eine außerordentlich rasche Entwicklung der Mathematik aus, die ihrerseits in hohem Maße befruchtend auf andere Wissenschaften wirkte. Entscheidenden Anteil an dieser Entwicklung hatten die Brüder Jakob und Johann Bernoulli (1654-1705 bzw. 1667-1748), auf deren Vorlesungen auch das erste, 1696 erschienene Lehrbuch der Differential- und Integralrechnung des Marquis de l'Hospital (1661-1704) basiert.
+
+Wie wir noch sehen werden, beruht die Differentialrechnung, ebenso wie die Integralrechnung, auf dem Begriff des \textit{Grenzwertes}. Zeitlich ging jedoch die kalkülmäßige Entwicklung der Differential- und Integralrechnung der strengen Begriffsdefinition voran. Daraus entstanden immer häufiger Schwierigkeiten und Unstimmigkeiten, die sich zunächst nicht überwinden ließen. Schließlich führte Jean le Rond d'Alembert (1717-1783) den Grenzwertbegriff in die Mathematik ein. Doch erst Bernard Bolzano (1781-1848) und Augustin Louis Cauchy (1789-1857) wendeten diesen Begriff konsequent an und stellten damit die Infinitesimalrechnung (zu der man neben der Differential- und Integralrechnung auch die Theorie der unendlichen Reihen zählt) auf ein solides Fundament.
+
+Vor einem Aufbau der Differentialrechnung ist also der Grenzwertbegriff für Funktionen zu behandeln. Zwangsläufig wird man damit zum Begriff der \textit{Stetigkeit} geführt. Die eigentliche Differentialrechnung beginnt mit der Definition der \textit{Ableitung} einer Funktion.
+
+Alle drei Begriffe werden zur exakten Beschreibung bestimmter Sachverhalte in den unterschiedlichsten Gebieten herangezogen. So kann man mit dem Grenzwertbegriff z. B. das Verhalten einer zeitabhängigen Größe, ,, nach sehr langer Zeit " charakterisieren, mit dem Begriff der Stetigkeit bzw. Unstetigkeit den ,,kontinuierlichen“ bzw. ,,sprunghaften“ Ablauf eines Vorgangs erfassen und mit der Ableitung die ,,Änderungsgeschwindigkeit" eines Prożesses beschreiben.
+
+Die mathematischen Möglichkeiten reichen jedoch über die unmittelbare Anwendbarkeit dieser Begriffe weit hinaus. So werden wir unter Verwendung der Differentialrechnung u. a. Näherungsformeln für (nichtrationale) Funktionen herleiten, Methoden zur Ermittlung von Extremwerten angeben und Verfahren zur numerischen Lösung von Gleichungen behandeln. Dem „Praktiker" werden damit Hilfsmittel zur Verfügung gestellt, auf die er fortlaufend zurückgreifen muß.

Band2/Tests.tex

@@ -0,0 +1,60 @@
+
+
+\begin{tikzpicture}[>=latex]
+
+\draw[cyan, densely dotted] (-5,-5) grid (5,5);
+	\useasboundingbox (-5,5) rectangle (5,5);
+	\matrix (m1) [row sep=6mm,column sep=5mm,matrix of nodes,column 6/.style={anchor=base west}, left delimiter=\{ ]
+	{\phantom{a} & $3$  & $0$ & $1$ & $-5 $ & $2$ & \phantom{a}\\
+		\phantom{a}  & \phantom{a} & $6$ & $12$ & $26$ & $42$ & \phantom{a}\\
+		$2$ & $3$ & $6$ & $13$ & $21$ & $44=g(2)$\\
+};
+
+
+	\matrix (m2) [below=of m1.south west, anchor= north west,yshift=6mm, row sep=6mm,column sep=5mm,matrix of nodes,column 5/.style={anchor=base west} , left delimiter=\{]
+	{
+
+	\phantom{a} & \phantom{a} & $6$ & $24$ & $74$ & \phantom{a}\\
+	$2$ & $3$ &	$12$ & $37$ & $95=g'(2)$ \phantom{a}\\
+};
+
+	\matrix (m3) [below=of m2.south west, anchor= north west,yshift=6mm, row sep=6mm,column sep=5mm,matrix of nodes,column 4/.style={anchor=base west} , left delimiter=\{]
+	{
+\phantom{a} & \phantom{a} & $6$ & $36$ &  \phantom{a}\\
+	$2$ & $3$ &	$18$ &  $73=g''(2)$ \phantom{a}\\
+};
+
+
+	\draw ([xshift=.1cm]m1-1-1.north east) -- ([xshift=.1cm]m2-2-1.south east);
+
+	\draw ([yshift=-.25cm]m1-2-1.south west) -- ([yshift=-.25cm,xshift=1cm]m1-2-6.south east);
+	
+	\draw ([yshift=2mm]m1-3-6.north west) -- ([yshift=-1mm]m1-3-6.south west);
+	
+	%\draw ([yshift=-.25cm]m1-2-6.south west) -- ([yshift=-.25cm,xshift=4mm]m1-2-6.south east);
+	
+	\draw ([yshift=-.15cm]m1-3-6.south west) -- 
+	([yshift=-.15cm]m1-3-6.south east);
+	
+
+	\node[circle] (del-left-1) at ($0.5*(m1-3-1.south west)+0.5*(m1-1-1.north west)$){};
+%	\node[draw,rectangle,left delimiter=\{] (del-left-1) at (m1-2-1) {\tikz{\path (m1-1-1.north east) rectangle (m1-3-1.south west);}};
+	\node[left=10pt] at (del-left-1.west) {1. Schritt};
+
+%\draw ($(m2-1-1.north east)!0.5!(m2-1-2.north west)$) -- ($(m2-2-1.south east)!0.5!(m2-2-2.south west)$);
+
+	\node[circle] (del-left-2) at ($0.5*(m2-2-1.south west)+0.5*(m2-1-1.north west)$){};
+
+\node[left=10pt] at (del-left-2.west) {2. Schritt};
+
+%	\node[rectangle,draw] (del-left-2) at ($(m2-2-1)-(m2-1-1)$) {\tikz{\path (m2-2-2.north east) rectangle (m2-2-1.south west);}};
+%	\node[left=10pt] at (del-left-2.west) {2. Schritt};
+ %\mymatrixbracetop{2}{6}{$E'$}
+
+%\node[font=\color{red}] at (m2.center){X};
+
+%\foreach \xy in {$1*(m2-1-1)$, $1*(m2-2-1)$}{
+%    \node at (\xy) {\xy};
+%}
+
+\end{tikzpicture}

Band2/Vorwort.tex

@@ -0,0 +1,28 @@
+\chapter*{Vorwort}
+
+Dem vorliegenden Band 2 dieser Lehrbuchreihe kommt ebenso wie dem Band 1 insofern eine besondere Bedeutung innerhalb des gesamten Lehrwerkes zu, als nahe$\mathrm{zu}$ alle anderen Bände darauf auf bauen.
+
+Ein Teil der in diesem Buch behandelten Gegenstände ist auch im Lehrplan unserer Oberschulen enthalten. Ein Weglassen des dort bereits Dargebotenen hätte aber zu einer unzusammenhängenden Darstellung des Gebietes geführt; außerdem wäre nicht gewährleistet, daß alle Leser mit den gleichen Voraussetzungen die weiteren Bände studieren können.
+
+Eine korrekte Anwendung mathematischer Methoden setzt die genaue Kenntnis der zugrunde liegenden Begriffe voraus. Es muß dem Leser daher dringend nahegelegt werden, sich um ein volles Verständnis der eingeführten Begriffe zu bemühen. Anhand von vielen Beispielen wird gezeigt, wie mathematische Begriffe in den Anwendungen zu interpretieren sind. Ein gründliches Studium des Textes und das selbständige Lösen der über 100 Übungsaufgaben sollte den Leser in die Lage versetzen, die spezifische Anwendbarkeit der behandelten Begriffe und Methoden in seinem Fachgebiet selbst zu erkennen.
+
+Im Interesse einer straffen Darstellung mußte auf eine Reihe von Beweisen verzichtet werden. Alle Aussagen werden aber erläutert und - soweit möglich - geometrisch interpretiert.
+
+Für wertvolle Hinweise danken wir vor allem dem Herausgeber, Herrn Prof. Dr. O. Greuel (Mittweida), den Gutachtern, Herrn Prof. Dr. W. Dück (Berlin) und Herrn Prof. Dr. H. Goering (Magdeburg), sowie Herrn Prof. Dr. G. Opitz (Dresden). Besonderer Dank gebührt Frau I. Kamenz für das sorgfältige Schreiben des Manuskripts. Dem Verlag sei für die gute Zusammenarbeit herzlich gedankt.
+
+
+Dresden, Januar 1973\hfill E. A. Pforr
+
+\hfill W. Schirotzek
+
+\chapter*{Vorwort zur 6. Auflage}
+In dieser Auflage wurden gegenüber der vorangegangenen an zwei Stellen inhaltliche Veränderungen größeren Umfangs vorgenommen. Im Hinblick auf den Einsatz von elektronischen Rechnern, insbesondere auch von Taschenrechnern, war die Darstellung der Näherungsverfahren (Abschnitt 7.7.) zu überarbeiten. Der algorithmische Aspekt wurde stärker herausgearbeitet, auf die Formulierung von Algorithmen in einer Programmiersprache jedoch verzichtet. Außerdem wurde der Abschnitt über elliptische Integrale (9.3.5.) erweitert.
+
+Für die wertvolle Unterstützung bei der Überarbeitung von Abschnitt 7.7. sei Herrn Dr. sc. nat. S. Dietze (Dresden) herzlich gedankt.
+
+Dresden, Juli 1985\hfill E. A. Pforr
+
+\hfill W. Schirotzek
+
+
+