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