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Hochschulmathematik/Mathe Anleitung/bis05.lyx
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1.
Formelumstellungen
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In Technik, Physik und Mathematik sind gegenseitige Beziehungen zwischen
Größen als Formeln bekannt.
Es handelt sich um Gleichungen, die entweder Identitäten sind (für alle
Belegungen der Variablen gelten) oder innerhalb eines bestimmten Definitionsber
eiches die objektive Realität widerspiegeln.
Häufig sind solche Beziehungen ihrër mathematischen Struktur nach gleichartig
aufgebaut.
Die Bearbeitung der völlig: verschiedenen Gebieten entnommenen Gesetzmäßigkeite
n erfolgt deshalb oft analog.
Ein und derselbe Typ einer mathematischen Beziehung beschreibt und charakterisi
ert also dann physikalische oder technische Verhältnisse aus verschiedenen
Sachgebieten.
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\begin_layout Plain Layout
Typ:
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\boldsymbol{A}=\frac{\boldsymbol{B}\cdot\boldsymbol{C}}{\boldsymbol{D}\pm\boldsymbol{E}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\varrho=\frac{\gamma_{\mathrm{F}}\cdot G}{G-G_{\mathrm{F}}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Dichte-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
bestimmung
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $R=\frac{R_{1}\cdot R_{2}}{R_{1}+R_{2}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
KiRchHoFF-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
sches Gesetz
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $f=\frac{a\cdot b}{a+b}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Brennweite
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
beim Spiegel
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $Z=\frac{\omega L_{1}\cdot L_{2}}{L_{1}+L_{2}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Betrag des Wider-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
standsoperators
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Parallelschaltung
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Typ:
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}\frac{\boldsymbol{C}\cdot\boldsymbol{D}}{\boldsymbol{E}^{2}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $F=\gamma\frac{m_{1}\cdot m_{2}}{r^{2}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Anziehung
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
von Massen
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $F=\frac{1}{4\pi\varepsilon}\frac{Q_{1}\cdot Q_{2}}{s^{2}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
CoulomB-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Gesetz
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $F=c\frac{m_{1}\cdot m_{2}}{e^{2}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Magnetisches
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Feld
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $E=\frac{I\cdot\cos\varepsilon}{r^{2}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Beleuchtungs-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
stärke
\begin_inset Formula $\quad$
\end_inset
.
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\mathrm{Typ}:$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\boldsymbol{A}=\boldsymbol{B}(\mathbf{1}+\boldsymbol{C})$
\end_inset
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $l=$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $l_{0}(1+\alpha\Delta t)$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Längen-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
ausdehnung
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $V=$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $V_{0}(1+\gamma\Delta t)$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Volumen-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
ausdehnung
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $R=$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $R_{0}(1+\alpha t)$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Widerstand
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
in Abhängig-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
keit von der
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Temperatur
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $a_{n}-a_{1}=$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $d(n-1)$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
arithmetische
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Folge
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\begin_layout Standard
Die Beziehungen (Gleichungen, Formeln) enthalten in den Termen Variablen,
die voneinander abhängen.
\end_layout
\begin_layout Standard
Die Beziehung
\begin_inset Formula $s\quad v\quad.\quad t$
\end_inset
\begin_inset Formula $($
\end_inset
Weg = Geschwindigkeit
\begin_inset Formula $\cdot$
\end_inset
Zeit
\begin_inset Formula $)$
\end_inset
kann als Funktionsgleichung
\begin_inset Formula
\[
s(t)\quad=\quad v\cdot t\quad[s\text{ und }t\text{ variabel, }v\text{ konstant }]
\]
\end_inset
dargestellt werden.
Bedeutung: Der zurückgelegte Weg
\begin_inset Formula $s$
\end_inset
ist bei gleichförmig geradliniger Bewegung von der Zeit
\begin_inset Formula $t$
\end_inset
abhängig.
Entsprechend kann man schreiben:
\begin_inset Formula $U(R)=I\cdot R$
\end_inset
und
\begin_inset Formula $v(r)=\omega\cdot r$
\end_inset
und
\begin_inset Formula $F_{R}\left(F_{\mathrm{N}}\right)=\mu\cdot F_{\mathrm{N}}$
\end_inset
und
\begin_inset Formula $u(d)=\pi\cdot d$
\end_inset
usw.
Der Typ oiner solchen Abhängigkeit wird mathematisch durch die verallgemeinernd
e Symbolik
\begin_inset Formula $f(x)=\ldots$
\end_inset
beschrieben.
In der Regel ist in einer Formel eine bestimmte Variable gesucht (unbekannt),
die anderen Größen sind gegeben.
Nicht immer ist jedoch die unbekannte Variable in Abhängigkeit von den
anderen explizit dargestellt.
Dann muß die Formel erst nach einer bestimmten (umbekannten) Variablen
aufgelöst werden.
\end_layout
\begin_layout Standard
Das geschieht in folgender Weise:
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="3">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Schritt
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Prinzip
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Muster
\end_layout
\end_inset
</cell>
</row>
<row>
<cell multirow="3" alignment="none" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
t
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Aufgabenstellung
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(sachgebietsbezogen)
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
In einer Batterieschaltung sind
\begin_inset Formula $n$
\end_inset
Ele-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
mente in Reihe (hintereinander) ge-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
schaltet.
Jedes Element hat die Span-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
nung
\begin_inset Formula $U$
\end_inset
und den inneren Widerstand
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $R_{1}$
\end_inset
.
Die Gesamtstromstärke ist
\begin_inset Formula $I$
\end_inset
.
Der
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Außenwiderstand
\begin_inset Formula $R_{\mathrm{a}}$
\end_inset
ist gesucht.
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Aufstellen der Formel
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(bekannt oder gegeben, evtl.
aus
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
der Formelsammlung zu entnehmen)
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $I=\frac{n\cdot U}{n\cdot R_{\mathrm{i}}+R_{\mathrm{a}}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Formulierung der mathema-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
tischen Aufgabe
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(Kennzeichnung der gesuchten
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Größe)
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $I=\frac{n\cdot U}{n\cdot R_{\mathrm{i}}+\boldsymbol{R}_{\mathrm{a}}}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
ist nach
\begin_inset Formula $R_{\mathrm{a}}$
\end_inset
aufzulösen.
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell multirow="3" alignment="none" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
t
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Beschreibung der mathematischen
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Terme
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(Lösungsplan)
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Die gesuchte Variable steht als Sum-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
mand im Nenner eines Bruches.
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Elementare 0perationen zur Verein-
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
fachung
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(falls erforderlich, Wurzeln oder
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Brüche beseitigen - falls unbek.
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Variable innerhalb eines durch
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Klammern eingeschlossenen Terms,
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Auflösen desselben oft zweckmäßig)
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $I\left(n\cdot R_{\mathrm{i}}+R_{\mathrm{a}}\right)=n\cdot U$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $I\cdot n\cdot R_{\mathrm{i}}+I\cdot R_{\mathrm{a}}=n\cdot U$
\end_inset
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\begin_layout Standard
C Isolieren der unbekannten Variablen
\begin_inset Formula $I\cdot R_{\mathrm{a}}=n\cdot U-I\cdot n\cdot R_{1}$
\end_inset
(Ziel: Terme mit der unbekannten Variablen stehen isoliert auf einer Seite
der Beziehung) Division der gesamten Gleichung durch den Koeffizienten
(Beiwert)
\begin_inset Formula $R_{\mathrm{a}}=\frac{n\cdot U-I\cdot n\cdot R_{\mathrm{i}}}{I}$
\end_inset
der unbekannten Variablen (Zuvor ist gegebenenfalls die unbekannte Variable
auszuheben / auszuklammern)
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="1">
<features tabularvalignment="middle">
<column alignment="left" valignment="top">
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
D Bessere Gestaltung der gefundenen
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Formel
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset Formula $R_{\mathrm{a}}=n\frac{U}{I}-nR_{1}$
\end_inset
oder:
\begin_inset Formula
\[
R_{\mathrm{a}}=n\left(\frac{U}{I}-R_{\mathrm{l}}\right)
\]
\end_inset
\end_layout
\begin_layout Standard
Deutung und Diskussion Der Außenwiderstand kann bestimmt werden durch die
mit der Anzahl der Elemente multiplizierten Differenz von Gesamtwiderstand
und Innenwiderstand.
\end_layout
\begin_layout Standard
Beachten Sie: Bei der Umstellung von Formeln gelten die Gesetzmäßigkeiten
des Lösens von Gleichungen.
Es dürfen also nur äquivalente Umformungen vorgenommen werden.
Grundsätzlich darf auf beiden Seiten einer Gleichheitsbeziehung nur die
gleiche Operation ausgeführt werden, und zwar: Addition oder Subtraktion
eines Terms,.
Multiplikation mit einem von Null verschiedenen Term, Division durch einen
von Null verschiedenen Term, Potenzieren mit ungeradzahligem Exponenten,
Radizieren, sofern auf beiden Seiten positive Größen stehen.
Eine Division durch 0 oder durch einen Term, der den Wert 0 annehmen kann,
ist nicht zulässig.
\end_layout
\begin_layout Standard
\end_layout
\end_body
\end_document