Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung Nächste Überarbeitung Beide Seiten der Revision | ||
latex_beispiele [2011/01/09 18:51] 188.22.48.250 |
latex_beispiele [2013/05/21 18:49] admin |
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====== Beispiele ====== | ====== Beispiele ====== | ||
+ | |||
+ | Gliederung\\ | ||
<latex> | <latex> | ||
- | \documentclass[14pt]{article} | + | \section{Mathematik} |
- | \usepackage{amsmath} | + | \label{sec:mathematik} |
- | \usepackage{amsfonts} | + | \subsection{Unterstufe} |
- | \usepackage{eurosym} | + | \label{sec:unterstufe} |
- | \usepackage{ucs} | + | \subsection{Oberstufe} |
- | \usepackage[utf8x]{inputenc} | + | \label{sec:oberstufe} |
- | \usepackage{amssymb} | + | |
- | \pagestyle{empty} | + | |
- | \begin{document} | + | |
- | $a^2+b^2=c^2$ | + | |
- | \Latex2e\ ist nett! | + | |
- | \end{document} | + | |
</latex> | </latex> | ||
- | Gliederung\\ | + | <latex> |
+ | I am \LaTeXe! | ||
+ | </latex> | ||
+ | |||
+ | <latex>\setlength{\unitlength}{1mm} | ||
+ | \begin{picture}(93,46) | ||
+ | \put( 0,14){\vector(1,0){60}} | ||
+ | \put(61,13){$x$} | ||
+ | \put(20,4){\vector(0,1){37}} | ||
+ | \put(19,43){$y$} | ||
+ | \put(50,34){\circle*{2}} | ||
+ | \put(52,35){$P$} | ||
+ | \multiput(20,34)(4,0){8}{\line(1,0){2}} | ||
+ | \put(14.5,33.5){$y_P$} | ||
+ | \multiput(50,14)(0,4){5}{\line(0,1){2}} | ||
+ | \put(48,11){$x_P$} | ||
+ | \put( 2,8){\vector(3,1){56}} | ||
+ | \put(59,26.5){$x'$} | ||
+ | \multiput(50,34)(1.9,-5.7){2} | ||
+ | {\line(1,-3){1.2}} | ||
+ | \put(52,22){$x_P'$} | ||
+ | \multiput(50,34)(-5.8,-1.933){6} | ||
+ | {\line(-3,-1){3.6}} | ||
+ | \put(12,21){$y_P'$} | ||
+ | \put(22,8){\vector(-1,3){10.5}} | ||
+ | \put(10,41){$y'$} | ||
+ | \end{picture}</latex> | ||
<latex> | <latex> | ||
Zeile 133: | Zeile 155: | ||
*peer:/usr/local/texlive/2007 | *peer:/usr/local/texlive/2007 | ||
*[[http://www.math.tu-dresden.de/~rudl/latex/LaTeX-LIT-Chemnitz.pdf|Einführung in das Textsatzsystem LaTeX]] | *[[http://www.math.tu-dresden.de/~rudl/latex/LaTeX-LIT-Chemnitz.pdf|Einführung in das Textsatzsystem LaTeX]] | ||
- | <file> | + | <code latex> |
\documentclass[a4paper,10pt]{article} | \documentclass[a4paper,10pt]{article} | ||
- | \usepackage{amsmath} | + | \usepackage{amsmath} %American Mathematical Society |
\usepackage{amsfonts} | \usepackage{amsfonts} | ||
\usepackage{amssymb} | \usepackage{amssymb} | ||
Zeile 152: | Zeile 174: | ||
\end{enumerate} | \end{enumerate} | ||
\end{document} | \end{document} | ||
- | </file> | + | </code> |
+ | |||
+ | <code latex formelheft.tex> | ||
+ | \documentclass[11pt,fleqn]{scrartcl} | ||
+ | \usepackage{ucs} %unicode support | ||
+ | \usepackage[utf8x]{inputenc} | ||
+ | \usepackage{ngerman} | ||
+ | \usepackage{graphicx} | ||
+ | \usepackage{amsmath,amssymb,amstext,bbm} %American Mathematical Society | ||
+ | \usepackage[automark]{scrpage2} | ||
+ | \title{Formelheft} | ||
+ | \author{Helmuth Peer} | ||
+ | \date{\today{}, Weiz} | ||
+ | \begin{document} | ||
+ | \maketitle | ||
+ | \thispagestyle{empty}% weil \maketitle ggf. ein \thispagestyle{plain} enthält | ||
+ | \tableofcontents | ||
+ | %\pagestyle{empty} | ||
+ | %\ifoot[]{Peer} | ||
+ | %\cfoot{} | ||
+ | %\ofoot{} | ||
+ | |||
+ | %Tabellenzwischenräume vergrößern/verändern | ||
+ | %Spaltenzwischenraum zwischen zwei benachbarten Spalten | ||
+ | \setlength{\tabcolsep}{10pt} | ||
+ | %Zeilenabstand innerhalb der Tabelle | ||
+ | \renewcommand{\arraystretch}{2} | ||
+ | |||
+ | \newpage | ||
+ | \section{Potenzen} | ||
+ | $a, b \in \mathbb{R}, r, s \in \mathbb{R}, k \in \mathbb{Z}, m, n \in | ||
+ | \mathbb{N}^{\ast}$\\ | ||
+ | %\vspace{5cm}\\ | ||
+ | \begin{tabular}{|c|c|c|c|c|} | ||
+ | \hline | ||
+ | $a^0 = 1$ & $a^1 = a$ & $a^{- n} = \frac{1}{a^n} = \left( \frac{1}{a} \right)^n$ & $a^{\frac{1}{n}} = \sqrt[n]{a}$& | ||
+ | |||
+ | $a^{\frac{k}{n}} = \sqrt[n]{a^k}$ \\ | ||
+ | |||
+ | \hline | ||
+ | |||
+ | \end{tabular}\\ | ||
+ | \begin{tabular}{|c|c|} | ||
+ | \hline | ||
+ | $a^r \cdot a^s = a^{r + s}$ & $\sqrt[n]{a^k} = \sqrt[n \cdot m]{a^{k \cdot m}}$\\\hline | ||
+ | $a^r : a^s = a^{r - s}$ & $\sqrt[n]{\sqrt[m]a} = \sqrt[n \cdot m]{a}$\\\hline | ||
+ | $(a^r)^s=a^{r \cdot s}$ & $( \sqrt[n]{a})^k = \sqrt[n]{a^k}$\\\hline | ||
+ | $(a \cdot b)^r = a^r \cdot b^r$ & $\sqrt[n]{a \cdot b} = \sqrt[n]{a} \cdot \sqrt[n]{b}$\\\hline | ||
+ | $( \frac{a}{b})^r= \frac{a^r}{b^r}$ & $\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$\\\hline | ||
+ | \end{tabular} | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | $(a \pm b)^2 = a^2 \pm 2 ab + b^2$ | ||
+ | |||
+ | |||
+ | \section{Logarithmen} | ||
+ | |||
+ | \(^{10}\)log a = 1\\ | ||
+ | $a, b \in \mathbbm{R}^+ \backslash \left\{ 1 \right\}, | ||
+ | u, v \in \mathbbm{R}^+, r \in \mathbbm{R}, n \in \mathbbm{N}^{\ast} \bot \in | ||
+ | \backslash$ | ||
+ | |||
+ | \[e = \lim_{n \rightarrow \infty} \left( 1 + \frac{1}{n} \right)^n\] | ||
+ | |||
+ | \[ \lim_{n \rightarrow \infty} \left( 1 + \frac{1}{n} \right)^n = 2, 71828 \dots \] | ||
+ | |||
+ | \section{Quadratische Gleichungen} | ||
+ | |||
+ | \[x^2 + px + q = 0\] | ||
+ | |||
+ | \[x = - \frac{p}{2} \pm \sqrt{\left( \frac{p}{2} \right)^2 - q}\] | ||
+ | |||
+ | \begin{tabular}{|c|c|} | ||
+ | \hline | ||
+ | $x^2 + px + q = 0$ & $ax^2 + bx + c = 0$\\ | ||
+ | \hline | ||
+ | $x = - \frac{p}{2} \pm \sqrt{\left( \frac{p}{2} \right)^2 - q}$ & $x = \frac{- b \pm \sqrt{b^2 - 4 ac}}{2 a}$\\ | ||
+ | \hline | ||
+ | \end{tabular} | ||
+ | |||
+ | \section{Komplexe Zahlen} | ||
+ | |||
+ | \(z = a + bi \in \mathbbm{C} \Leftrightarrow a, b \in \mathbbm{R} | ||
+ | \ \mbox{und} \ i^2 = - 1 ; \sqrt{- a} = i \sqrt{a} \ \mbox{mit} \ a > 0\) \\ | ||
+ | $(a + bi) (a - bi) = a^2 + b^2$ | ||
+ | |||
+ | $\left| z \right| = r = \sqrt{a^2 + b^2}$ | ||
+ | |||
+ | $\arg z = \varphi \in [0^{\circ} ; 360^{\circ} [$ | ||
+ | |||
+ | %\includegraphics{oelta002.png} | ||
+ | |||
+ | \section{Schaltalgebra} | ||
+ | |||
+ | |||
+ | |||
+ | $a \vee b = b \vee a$ | ||
+ | |||
+ | $a \wedge b = b \wedge a$ | ||
+ | \section{Vektoren} | ||
+ | |||
+ | \subsection{Vektorielles Produkt} | ||
+ | |||
+ | $\vec{a} = \left(\begin{array}{c} | ||
+ | a_1\\ | ||
+ | a_2\\ | ||
+ | a_3 | ||
+ | \end{array}\right) \times \left(\begin{array}{c} | ||
+ | b_1\\ | ||
+ | b_2\\ | ||
+ | b_3 | ||
+ | \end{array}\right) = \left(\begin{array}{c} | ||
+ | \left|\begin{array}{c} | ||
+ | a_2 b_2\\ | ||
+ | a_3 b_3 | ||
+ | \end{array}\right|\\ | ||
+ | - \left|\begin{array}{c} | ||
+ | a_1 b_1\\ | ||
+ | a_3 b_3 | ||
+ | \end{array}\right|\\ | ||
+ | \left|\begin{array}{c} | ||
+ | a_1 b_1\\ | ||
+ | a_2 b_2 | ||
+ | \end{array}\right| | ||
+ | \end{array}\right) = \left(\begin{array}{c} | ||
+ | a_2 b_3 - a_3 b_2\\ | ||
+ | a_3 b_1 - a_1 b_3\\ | ||
+ | a_1 b_2 - a_2 b_1 | ||
+ | \end{array}\right)$ | ||
+ | |||
+ | \section{Analytische Geometrie} | ||
+ | |||
+ | $\overrightarrow{\text{AB}} = B - A$ | ||
+ | |||
+ | \subsection{Flächeninhalt Parallelogramm} | ||
+ | |||
+ | $A_p = \sqrt{\vec{a}^2 \cdot \vec{b}^2 - ( \vec{a} \cdot \vec{b})^2}$ | ||
+ | |||
+ | |||
+ | |||
+ | \subsection{Parameterdarstellung einer Geraden} | ||
+ | |||
+ | $\vec{x} = \left(\begin{array}{c} | ||
+ | 1\\ | ||
+ | 2\\ | ||
+ | 3 | ||
+ | \end{array}\right) + t \cdot \left(\begin{array}{c} | ||
+ | 4\\ | ||
+ | 5\\ | ||
+ | 6 | ||
+ | \end{array}\right)$ | ||
+ | |||
+ | \section{Differential- und Integralrechnung} | ||
+ | |||
+ | \subsection{Ableitungs- und Stammfunktionen} | ||
+ | |||
+ | \begin{tabular}{|l|l|l|} | ||
+ | \hline | ||
+ | Funktion & Ableitungsfunktion & Stammfunktionen\\ | ||
+ | \hline | ||
+ | $y = f (x) = k$ & $y' = f' (x) = 0$ & $F (x) = \int \mbox{kdx} = \mbox{kx} + C$\\\hline | ||
+ | $y = f (x) = x^q$ & $y' = f' (x) = q \cdot x^{q - 1}$ & $q \neq - 1 :$ \\\hline | ||
+ | & & $F (x) = \int x^q \mbox{dx} = \frac{x^{q + 1}}{q + 1} + C$\\\hline | ||
+ | \end{tabular} | ||
+ | |||
+ | \subsection{Rauminhalte} | ||
+ | |||
+ | \subsubsection{Drehk\"orper} | ||
+ | |||
+ | Drehung um die x-Achse: | ||
+ | |||
+ | \(V = \pi \int^b_a y^2 \mbox{dx}\) | ||
+ | |||
+ | \subsection{Numerische Integration} | ||
+ | |||
+ | \subsubsection{Rechtecksformel} | ||
+ | |||
+ | $\int^b_a f (x) \mbox{dx} \approx \frac{b - a}{n} \cdot [f (x_0) + f (x_1) + f | ||
+ | (x_2) + \ldots . + f (x_{n - 1})] = \Delta x \cdot \sum^{n - 1}_{i = 0} f | ||
+ | (x_i)$ | ||
+ | \[ \Delta x \cdot \sum_{i = 0}^{i - 1} f (x_i) \] | ||
+ | |||
+ | \subsection{Binomialverteilung} | ||
+ | |||
+ | $P (X = k) = b_{n, p} (k) = \left(\begin{array}{c} | ||
+ | n\\ | ||
+ | k | ||
+ | \end{array}\right) p^k (1 - p)^{n - k}$ | ||
+ | |||
+ | \subsection{Normalverteilung} | ||
+ | |||
+ | $\varphi (x) = \frac{1}{\sqrt{2 \pi}} e^{- \frac{x^2}{2}}$ | ||
+ | |||
+ | |||
+ | \[ \Phi (z) = \int^z_{- \infty} \varphi (x) \text{dx} = \frac{1}{\sqrt{2 \pi}} | ||
+ | \int^z_{- \infty} e^{- \frac{x^2}{2}} \mbox{dx} \] | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | \end{document} | ||
+ | </code> |