diff options
| author | Nao Pross <naopross@thearcway.org> | 2020-04-08 14:29:59 +0200 |
|---|---|---|
| committer | Nao Pross <naopross@thearcway.org> | 2020-04-08 14:30:25 +0200 |
| commit | ebc2ed485e0f5a27904a80a7c722da4e8a4ef84d (patch) | |
| tree | cfd8ad992c1e40baec7ab031d1081b957f2b8acd | |
| parent | Add current work to version control (diff) | |
| download | An2E-ebc2ed485e0f5a27904a80a7c722da4e8a4ef84d.tar.gz An2E-ebc2ed485e0f5a27904a80a7c722da4e8a4ef84d.zip | |
Add references, notation and license, update curve table
Diffstat (limited to '')
| -rw-r--r-- | an2e_zf.pdf | bin | 53843 -> 59600 bytes | |||
| -rw-r--r-- | an2e_zf.tex | 34 |
2 files changed, 28 insertions, 6 deletions
diff --git a/an2e_zf.pdf b/an2e_zf.pdf Binary files differindex 76358e9..0117265 100644 --- a/an2e_zf.pdf +++ b/an2e_zf.pdf diff --git a/an2e_zf.tex b/an2e_zf.tex index 16812c5..fcc1a94 100644 --- a/an2e_zf.tex +++ b/an2e_zf.tex @@ -145,7 +145,7 @@ Alle normale differenziazionsregeln gelten. \section{Ebene \brpage{250} und Raumkurven \brpage{263}} \begin{sideways} \centering -\renewcommand{\arraystretch}{3.5} +\renewcommand{\arraystretch}{1.5} \begin{tabular}{l *{3}{>{\(\displaystyle}l<{\)}} } \toprule \textbf{Ebene Kurven} & \textbf{Explizit} & \textbf{Polar} & \textbf{Parameter} \\ @@ -154,28 +154,29 @@ Bogenl\"ange \brpage{251} & \int\limits_a^b \sqrt{1 + (y')^2} \dd{x} & \int\limits_\alpha^\beta \sqrt{(r')^2 + r^2} \dd{\varphi} & \int\limits_{t_0}^{t_1} \sqrt{\dot{x}^2 + \dot{y}^2} \dd{t} = \int\limits_{t_0}^{t_1} |\vec{c}| \dd{t} -\\ +\\[1cm] Fl\"ache & \int\limits_a^b |f(x)| \dd{x} & \frac{1}{2}\int\limits_\alpha^\beta r(\varphi)^2 \dd{\varphi} & \frac{1}{2}\int\limits_{t_0}^{t_1} x\dot{y} - \dot{x}y \dd{t} = \frac{1}{2}\int\limits_{t_0}^{t_1}\det(\vec{c},\dot{\vec{c}}) \dd{t} -\\ +\\[1cm] Rotationsvolumen um \(x\) & \pi \left|\int\limits_a^b y^2 \dd{x} \right| & \pi \left|\int\limits_{t_0}^{t_1} y \dot{x} \dd{t} \right| & \pi \left|\int\limits_\alpha^\beta r^2 \sin^2 \varphi (r'\cos\varphi - r\sin\varphi) \dd{\varphi} \right| -\\ +\\[1cm] Rotationsoberfl\"ache um \(x\) & 2\pi \int\limits_a^b |y| \sqrt{1 + (y')^2} \dd{x} & 2\pi \int\limits_\alpha^\beta |r\sin(\varphi)| \sqrt{(r')^2 + r^2} \dd{\varphi} & 2\pi \int\limits_{t_0}^{t_1} |y| \sqrt{\dot{x}^2 + \dot{y}^2} \dd{t} -\\ +\\[1cm] % Rotationsvolumen um \(y\) \\ % Rotationsoberfl\"ache um \(y\) \\ \bottomrule \end{tabular} \end{sideways} +\begin{multicols}{2} \subsection{Kr\"ummung} \[ \kappa = \deriv{\alpha}{s} = \frac{\ddot{y}}{(1+\dot{y}^2)^{3/2}} @@ -187,6 +188,27 @@ Rotationsoberfl\"ache um \(x\) |\vec{\dot{c}}\times\vec{\ddot{c}}|\,|\vec{c}|^{-3} \] +\begin{thebibliography}{1} + \bibitem{hsr} + \texttt{An2E} Vorlesungen an der Hochschule f\"ur Technik Rapperswil und der dazugehoerige Skript, + \textit{Dr. Bernhard Zgraggen}, Fr\"uhlingssemester 2020 + \bibitem{bronstein} + Taschenbuch der Mathematik, + 10. \"uberarbeitete Auflage, 2016 (1977), + \textit{Bronstein, Semendjajew, Musiol, M\"uhlig}, + \texttt{ISBN 978-3-8085-5789-1} + \bibitem{mathe2} + Mathematik 2 Lehrbuch für ingenieurwissenschaftliche Studieng\"ange, + 2012, 7. Auflage, XII, Springer Berlin, + \textit{Albert Fetzer, Heiner Fränkel}, + \texttt{ISBN-10 364224114X}, + \texttt{ISBN-13 9783642241147} + +\end{thebibliography} + +\section*{Notation} +Rot markierte Zahlen wie zB \brpage{477} sind Hinweise auf die Seiten in der ``Bronstein'': ``Taschenbuch der Mathematik, 10. \"uberarbeitete Auflage''. \texttt{ISBN 978-3-8085-5789-1} + \section*{License} { \tt An2E-ZF (c) by Naoki Pross @@ -198,5 +220,5 @@ You should have received a copy of the license along with this work. If not, see \url{http://creativecommons.org/licenses/by-sa/4.0/} } - +\end{multicols} \end{document}
\ No newline at end of file |