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[formelsammlung] ein paar kleine fehlerkorrekturen

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Oliver Groß 2008-07-10 11:49:39 +02:00
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formelsammlung.tex
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@ -24,7 +24,7 @@
Eigenschaft 4 bedeutet, daß die Abbildung $b\mapsto [a,b]$ eine Derivation ist. Eigenschaft 4 bedeutet, daß die Abbildung $b\mapsto [a,b]$ eine Derivation ist.
\subsubsection*{Levi-Civita-Symbol:} \subsubsection*{Levi-Civita-Symbol}
\begin{math} \begin{math}
\varepsilon_{12\dots n} = 1 \\ \varepsilon_{12\dots n} = 1 \\
\varepsilon_{ij\dots u\dots v\dots} = -\varepsilon_{ij\dots v\dots u\dots}\\ \varepsilon_{ij\dots u\dots v\dots} = -\varepsilon_{ij\dots v\dots u\dots}\\
@ -40,17 +40,18 @@
\det A = \levicivita{i_1 i_2 \dots i_n} A_{1i_1} A_{2i_2} \dots A_{ni_n} \det A = \levicivita{i_1 i_2 \dots i_n} A_{1i_1} A_{2i_2} \dots A_{ni_n}
\end{math} \end{math}
\subsubsection*{Kronecker-Delta} \subsubsection*{Kronecker-Delta}
$\krondelta{i,j}= \begin{cases} 1 & \mbox{falls } i=j \\ 0 & \mbox{falls } i \neq j \end{cases}$ \\ \equationblock{\krondelta{i,j} = \begin{cases} 1 & \mbox{falls } i=j \\ 0 & \mbox{falls } i \neq j \end{cases}}
Die $n\times n$-Einheitsmatrix kann als $(\krondelta{ij})_{i,j\in\{1,\ldots,n\}}$ geschrieben werden. Die $n\times n$-Einheitsmatrix kann als $(\krondelta{ij})_{i,j\in\{1,\ldots,n\}}$ geschrieben werden.
\subsubsection*{Reihenentwicklungen} \subsubsection*{Reihenentwicklungen}
\begin{align} \begin{align}
exp(x) = \sum_{n = 0}^{\infty} {\frac{x^n}{n!}} \\ \exp(x) &= \sum_{n = 0}^{\infty} {\frac{x^n}{n!}} \\
sin (x) = \sum_{n=0}^\infty (-1)^n\frac{x^{2n+1}}{(2n+1)!} \\ \sin(x) &= \sum_{n=0}^\infty (-1)^n\frac{x^{2n+1}}{(2n+1)!} \\
cos (x) = \sum_{n=0}^\infty (-1)^n\frac{x^{2n}}{(2n)!} \cos(x) &= \sum_{n=0}^\infty (-1)^n\frac{x^{2n}}{(2n)!}
\end{align} \end{align}
\section{\hypertarget{trans_ft}{Fourier-Transformation}} \section{Fourier-Transformation}
\hypertarget{trans_ft}{}
\subsection*{Fourier-Reihe} \subsection*{Fourier-Reihe}
\subsubsection*{Definitionen:} \subsubsection*{Definitionen:}
\subsubsection*{Eigenschaften:} \subsubsection*{Eigenschaften:}
@ -83,7 +84,8 @@ Hierbei ist $F(\omega)$ das kontinuierliche Spektrum, das die Amplitude jeder Fr
\subsection*{Matrizen-Operationen} \subsection*{Matrizen-Operationen}
\subsubsection*{Spur} \subsubsection*{Spur}
\subsubsection*{Determinatante} \subsubsection*{Determinatante}
\subsubsection*{\hypertarget{fs_linalg_mtrx_inv}{Inversion}} \subsubsection*{Inversion}
\hypertarget{fs_linalg_mtrx_inv}{}
\begin{math} \begin{math}
A^{-1} = \inlinematrix{a & b \\ c & d}^{-1} = \frac{1}{ad - bc} \inlinematrix{d & -b \\ -c & a} A^{-1} = \inlinematrix{a & b \\ c & d}^{-1} = \frac{1}{ad - bc} \inlinematrix{d & -b \\ -c & a}
\end{math} \end{math}