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1 changed files with 18 additions and 2 deletions
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@ -125,7 +125,7 @@
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\raggedright
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\raggedright
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\footnotesize
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\footnotesize
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\begin{multicols*}{4}
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\begin{multicols*}{3}
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% multicol parameters
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% multicol parameters
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@ -153,10 +153,26 @@ $$\frac{dH}{dt} = v_0 - \frac{H(t)}{\tau}$$
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Eine Lösung davon
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Eine Lösung davon
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$$H(t) = (H_0 - v_0\tau)^{\frac{-t}{\tau}} + v_0 \tau$$
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$$H(t) = (H_0 - v_0\tau)^{\frac{-t}{\tau}} + v_0 \tau$$
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\subsection{Fliessgleichgewicht}
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Für eine Funktion $F$, bei
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$$\frac{dF}{dt} = 0$$
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\subsection{Satz von Gauss}
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$$\iint_A \mathrm{div} \, v \, dA = \oint_C \, v \, dr$$
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Flächenintegral der Divergenz von $v$ = Fluss von $v$ durch Rand $C$
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\subsection{Satz von Stokes}
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$$\iint_A \mathrm{rot} \, v \, dA = \iint_A \zeta \, dA = \oint_C \, v \, ds$$
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Flächenintegral der Rotation von $v$ = Linienintegral von $v$ entlang $C$ (Zirkulation)
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\section{Taylor-Reihe}
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\section{Taylor-Reihe}
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An der stelle $a$ einer Funtkion $f(x)$
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$$f(a) + \frac{f'(a)}{1!}(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + ...$$
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\section{Operators}
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\section{Operators}
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$$\mathrm{rot} \ u = \nabla \times \vec{u}$$
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$$\mathrm{div} \, \vec{u} = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}$$
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$$\mathrm{rot} \, \vec{u} = \nabla \times \vec{u} = -\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}$$
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$$\nabla = \begin{pmatrix}
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$$\nabla = \begin{pmatrix}
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\frac{\partial}{\partial x},
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\frac{\partial}{\partial x},
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