Compare commits
7 commits
1bc6a09cb0
...
3c31741db7
Author | SHA1 | Date | |
---|---|---|---|
3c31741db7 | |||
8bf473e564 | |||
826fd7486d | |||
1eaccc234f | |||
9e21c49fc4 | |||
49c4b456da | |||
3c1af1ccb9 |
1 changed files with 18 additions and 2 deletions
|
@ -125,7 +125,7 @@
|
|||
|
||||
\raggedright
|
||||
\footnotesize
|
||||
\begin{multicols*}{4}
|
||||
\begin{multicols*}{3}
|
||||
|
||||
|
||||
% multicol parameters
|
||||
|
@ -153,10 +153,26 @@ $$\frac{dH}{dt} = v_0 - \frac{H(t)}{\tau}$$
|
|||
Eine Lösung davon
|
||||
$$H(t) = (H_0 - v_0\tau)^{\frac{-t}{\tau}} + v_0 \tau$$
|
||||
|
||||
\subsection{Fliessgleichgewicht}
|
||||
Für eine Funktion $F$, bei
|
||||
$$\frac{dF}{dt} = 0$$
|
||||
|
||||
\subsection{Satz von Gauss}
|
||||
$$\iint_A \mathrm{div} \, v \, dA = \oint_C \, v \, dr$$
|
||||
Flächenintegral der Divergenz von $v$ = Fluss von $v$ durch Rand $C$
|
||||
|
||||
\subsection{Satz von Stokes}
|
||||
$$\iint_A \mathrm{rot} \, v \, dA = \iint_A \zeta \, dA = \oint_C \, v \, ds$$
|
||||
Flächenintegral der Rotation von $v$ = Linienintegral von $v$ entlang $C$ (Zirkulation)
|
||||
|
||||
\section{Taylor-Reihe}
|
||||
An der stelle $a$ einer Funtkion $f(x)$
|
||||
$$f(a) + \frac{f'(a)}{1!}(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + ...$$
|
||||
|
||||
\section{Operators}
|
||||
$$\mathrm{rot} \ u = \nabla \times \vec{u}$$
|
||||
$$\mathrm{div} \, \vec{u} = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}$$
|
||||
|
||||
$$\mathrm{rot} \, \vec{u} = \nabla \times \vec{u} = -\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}$$
|
||||
|
||||
$$\nabla = \begin{pmatrix}
|
||||
\frac{\partial}{\partial x},
|
Loading…
Reference in a new issue