init

UebungenPapula/Aufgabe001.tex

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+\documentclass{book}%
+\usepackage{amsfonts}
+\usepackage{amsmath}%
+\setcounter{MaxMatrixCols}{30}%
+\usepackage{amssymb}%
+\usepackage{graphicx}
+%TCIDATA{OutputFilter=latex2.dll}
+%TCIDATA{Version=5.50.0.2953}
+%TCIDATA{CSTFile=40 LaTeX Book.cst}
+%TCIDATA{Created=Sunday, December 14, 2008 16:28:52}
+%TCIDATA{LastRevised=Sunday, December 14, 2008 16:47:49}
+%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
+%TCIDATA{<META NAME="SaveForMode" CONTENT="1">}
+%TCIDATA{BibliographyScheme=Manual}
+%TCIDATA{<META NAME="DocumentShell" CONTENT="Standard LaTeX\Standard LaTeX Book">}
+%BeginMSIPreambleData
+\providecommand{\U}[1]{\protect\rule{.1in}{.1in}}
+%EndMSIPreambleData
+\newtheorem{theorem}{Theorem}
+\newtheorem{acknowledgement}[theorem]{Acknowledgement}
+\newtheorem{algorithm}[theorem]{Algorithm}
+\newtheorem{axiom}[theorem]{Axiom}
+\newtheorem{case}[theorem]{Case}
+\newtheorem{claim}[theorem]{Claim}
+\newtheorem{conclusion}[theorem]{Conclusion}
+\newtheorem{condition}[theorem]{Condition}
+\newtheorem{conjecture}[theorem]{Conjecture}
+\newtheorem{corollary}[theorem]{Corollary}
+\newtheorem{criterion}[theorem]{Criterion}
+\newtheorem{definition}[theorem]{Definition}
+\newtheorem{example}[theorem]{Example}
+\newtheorem{exercise}[theorem]{Exercise}
+\newtheorem{lemma}[theorem]{Lemma}
+\newtheorem{notation}[theorem]{Notation}
+\newtheorem{problem}[theorem]{Problem}
+\newtheorem{proposition}[theorem]{Proposition}
+\newtheorem{remark}[theorem]{Remark}
+\newtheorem{solution}[theorem]{Solution}
+\newtheorem{summary}[theorem]{Summary}
+\newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
+\begin{document}
+
+\frontmatter
+\title{The Title}
+\author{The Author}
+\date{The Date}
+\maketitle
+\tableofcontents
+
+$y=\left(  5x^{3}-4x\right)  \left(  x^{2}+5x\right)  =\allowbreak
+5x^{5}+25x^{4}-4x^{3}-20x^{2}$
+
+$\bigskip$
+
+$y=uv\Longrightarrow y'$
+
+
+
+\bigskip
+
+\bigskip
+
+
+\end{document} 

UebungenPapula/Differentialrechnung.tex

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+\chapter{Differentialrechnung}
+\section{Ableitungsregeln}
+\subsection{Produktregel}
+\fbox{$y=uv\Longrightarrow y'=u'v+v'u$}
+\subsubsection{A1 $ y= \left( {5x^3  - 4x} \right)\left( {x^2  + 5x} \right),\text{  }y' = ?$}
+Die vorliegende Funktion ist ein \emph{Produkt aus zwei} Faktoren \emph{u} und \emph{v}, die jeweils von der Variablen \emph{x} abh<62>ngen:
+
+\begin{tabbing}
+\tabumg
+
+\>\>$y=\underbrace{\left( {5x^3  - 4x} \right)}_{u}\underbrace{\left( {x^2  + 5x} \right)}_{v}=uv$\\
+
+
+Somit gilt:\\
+\\
+Bem. S.R: gliedweise Differenzierung per $y'=n\cdot x^{n-1}$\\
+\\
+\>\>$u=5x^3-4x,\text{  }v=x^2 + 5x $ und $u'=15x^2-4\text{  }v'=2x+5$\\
+\\
+Die Produktregel liefert dann die gesuchte Ableitung:\\ \\
+\>\>$y'=u'v+v'u=(15x^2 - 4)(x^2 + 5x)$
+
+\end{tabbing}
+
+%http://www.math.montana.edu/frankw/ccp/multiworld/topic.htm#contents
+
+
+

UebungenPapula/UebungenPapula.tex

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+%\documentclass[10pt,german]{article}%
+\documentclass[12pt,a4paper,pagesize, DIVcalc,BCOR1cm, smallheadings, twoside]{scrbook}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{microtype,ellipsis,fixltx2e,mparhack}
+\usepackage{amssymb}
+\usepackage{graphicx}%
+\usepackage[english,german,ngerman]{babel}
+\usepackage[T1,OT1]{fontenc}
+\usepackage{longtable}
+\usepackage[latin1]{inputenc}
+\usepackage{tikz}
+\usetikzlibrary{arrows}
+\usepackage{geometry} %paperwidth=left+width+right   paperheight=top+height+bottom  left = inner
+\geometry{left=25mm, right=25mm, width=160mm}
+
+\usepackage{pstricks,pst-node}
+\usepackage[colorlinks = false,pdfborder={0 0 0}]{hyperref}
+\pdfcompresslevel=9
+
+\usepackage{nameref}
+  \usepackage{hyperref}
+  \usepackage{sidecap}
+
+\definecolor{Red}{rgb}{1,0,0}
+%\setlength{\emergencystretch}{20pt} \emergencystretch=3pt\relax \setlength{\tolerance}{2000}
+\newcommand{\clearemptydoublepage}{\newpage{\pagestyle{empty}\cleardoublepage}}
+\clubpenalty=2500 \widowpenalty=10000
+
+
+\newcommand{\IR}{I\hspace{-1.4mm}R}
+\newcommand{\IN}{I\hspace{-1.4mm}N}
+\newcommand{\tabumg}{\=hspace{5mm}\hspace{5mm}\=hspace{5mm}\=hspace{5mm}\=hspace{5mm}\=hspace{5mm}\kill \\}
+\newcommand{\entspricht}{\stackrel{\scriptscriptstyle\wedge}{=}}
+
+\makeatother
+
+\begin{document}
+
+
+\newrgbcolor{lila}{0.6 0.2 0.5}
+\newrgbcolor{darkyellow}{1 0.9 0}
+
+\setlength{\parindent}{0em}
+
+
+\tableofcontents{}
+\clearemptydoublepage
+
+
+\input{Differentialrechnung.tex}
+\clearemptydoublepage
+
+%\input{Loesungen.tex}
+%\clearemptydoublepage
+
+
+\renewcommand{\appendixname}{Anhang}
+\renewcommand{\bibname}{Literatur}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\begin{appendix}%
+%\input{Anhang.tex}
+
+
+%\end{appendix}%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%\setcounter{section}{0}%
+
+
+\end{document}

UebungenPapula/swp_papula001.tex

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+
+\documentclass{article}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%TCIDATA{OutputFilter=LATEX.DLL}
+%TCIDATA{Version=5.50.0.2953}
+%TCIDATA{<META NAME="SaveForMode" CONTENT="1">}
+%TCIDATA{BibliographyScheme=Manual}
+%TCIDATA{Created=Wednesday, December 17, 2008 21:03:05}
+%TCIDATA{LastRevised=Wednesday, December 17, 2008 21:13:48}
+%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
+%TCIDATA{<META NAME="DocumentShell" CONTENT="Standard LaTeX\Blank - Standard LaTeX Article">}
+%TCIDATA{CSTFile=40 LaTeX article.cst}
+
+\newtheorem{theorem}{Theorem}
+\newtheorem{acknowledgement}[theorem]{Acknowledgement}
+\newtheorem{algorithm}[theorem]{Algorithm}
+\newtheorem{axiom}[theorem]{Axiom}
+\newtheorem{case}[theorem]{Case}
+\newtheorem{claim}[theorem]{Claim}
+\newtheorem{conclusion}[theorem]{Conclusion}
+\newtheorem{condition}[theorem]{Condition}
+\newtheorem{conjecture}[theorem]{Conjecture}
+\newtheorem{corollary}[theorem]{Corollary}
+\newtheorem{criterion}[theorem]{Criterion}
+\newtheorem{definition}[theorem]{Definition}
+\newtheorem{example}[theorem]{Example}
+\newtheorem{exercise}[theorem]{Exercise}
+\newtheorem{lemma}[theorem]{Lemma}
+\newtheorem{notation}[theorem]{Notation}
+\newtheorem{problem}[theorem]{Problem}
+\newtheorem{proposition}[theorem]{Proposition}
+\newtheorem{remark}[theorem]{Remark}
+\newtheorem{solution}[theorem]{Solution}
+\newtheorem{summary}[theorem]{Summary}
+\newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
+\input{tcilatex}
+
+\begin{document}
+
+
+$y=5x^{3}$ Solution: $y^{\prime }=15x^{2}$
+
+\bigskip 
+
+$y=5x^{3}-4x$ Solution: $y^{\prime }=15x^{2}-4$
+
+\end{document}