#LyX 2.0 created this file. For more info see http://www.lyx.org/
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\begin_body

\begin_layout Title
Emneopgave 1
\end_layout

\begin_layout Author
Peter Harremoës
\end_layout

\begin_layout Section
Indledning
\end_layout

\begin_layout Standard
Denne LyX-skabelon kan bruges til at lave emneopgaver på Niels Brock.
 Når man skriver i LyX, skal man først skrive indholdet, og først når indholdet
 er på plads laver man en pdf-version af filen.
 Programmet står som udgangspunkt for sideopsætningen, så man kan fokusere
 tilsvarende mere på indhold frem for layout.
 Skabelonen her er optimeret til emneopgaver, så hvis skabelonen skal bruges
 til andre formål, kan det være nødvendigt at ændre i Document>Settings.
 Ved eventuelle problemer med skabelonen kan man kontakte mig på harremoes@ieee.o
rg .
 
\end_layout

\begin_layout Section
Emneopgaver
\end_layout

\begin_layout Standard
Ved mundtlig eksamen bliver man eksamineret i en tilfældigt udvalgt emneopgave.
 En emneopgave skal derfor indeholde de samme elementer som en god eksamenspræst
ation.
 Det vil i praksis sige, at den skal indeholde elementerne definition, sætning,
 bevis og eksempel.
 Strukturen skal være omtrent som i en lærebog i matematik.
\end_layout

\begin_layout Definition
En definition er en slags erklæring om hvordan man vil fremover vil benytte
 visse ord eller symboler.
 
\end_layout

\begin_layout Theorem
Det vi på dansk kalder en sætning, hedder på engelsk 
\begin_inset Quotes gld
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a theorem
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.
\end_layout

\begin_layout Proof
At en sætning på engelsk hedder a theorem checkes let ved at slå op i en
 dansk-engelsk ordbog.
\end_layout

\begin_layout Example
Dette er et eksempel på et eksempel.
\end_layout

\begin_layout Standard
Af omfang skal en emneopgave svare til ca.
 en dags arbejde.
 
\end_layout

\begin_layout Section
Indtastning af matematik
\end_layout

\begin_layout Standard
Ved at taste Ctrl+m skifter man til matematisk input, og der kommer straks
 værktøjer til indtasting af matematiske udtryk.
 Hvert matematisk symbol har en såkaldt LaTeX kode.
 Hvis man f.eks.
 taster 
\backslash
mp mens er i en formel, vil programmet omforme det til 
\begin_inset Formula $\pm$
\end_inset

.
 Hvis man peger på et symbol med musen, vil der blive vist hvilken LaTeX-kode
 symbolet har, så man hurtigt kan lære de mest almindelige genveje til de
 mest almindelige symboler.
 For mange symboler findes der også særlige LyX-genveje, som også bliver
 vist.
 LyX-genvejene kan i modsætning til LaTeX-genvejene kun bruges i LyX.
 Sidst i dette dokument er der angivet en symbolliste.
 
\end_layout

\begin_layout Standard
Hvis man vil oprette en fritstående formel, tastes Crtl+Shift+m.
 Man kan oprette nye linjer i fritstående formler ved at taste Crtl+Enter.
\end_layout

\begin_layout Section
Indsættelse af grafik
\end_layout

\begin_layout Standard
Der findes flere forskellige metoder til at indsætte figurer LyX.
 Vi tænker os at vi vil indsætte en figur fra Geogebra i et LyX-dokument.
 De to simpleste metoder er:
\end_layout

\begin_layout Enumerate
I Geogebra vælges Filer>Eksporter>Kopier Tegning , hvorefter man klikker
 Crtl+v hvor figuren ønskes indsat i LyX-dokumentet.
\end_layout

\begin_layout Enumerate
I Geogebra vælges Filer>Eksporter>Tegning som billede (png, eps)...
 og som filformat vælges PNG (Portable Network Graphics).
 Filen gives et navn og gemmes.
 Herefter vælger man filen med Insert>Graphics...
 inde fra LyX.
\end_layout

\begin_layout Standard
I LyX er der også mulighed for at sætte grafikken ind som en figur med figurteks
t.
 Dette gøres vha.
 Insert>Float>Figure.
 Programmet vil da selv placere figuren et hensigtsmæssigt sted i teksten.
\end_layout

\begin_layout Section
CAS
\end_layout

\begin_layout Standard
LyX kan arbejde sammen med forskellige andre programmer.
 Programmerne Octave og Maxima er begge gratis og kan få LyX til at lave
 visse typer beregninger.
 Programmerne installeres på almindelig vis.
 Herefter går ind i Tools>Preferences...>Paths>PATH prefix: Her skal man angive
 hvor diverse hjælpeprogrammer er installeret.
 Med min opsætning skulle jeg tilføje strengen C:
\backslash
Program Files
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Maxima-5.22.1
\backslash
bin;C:
\backslash
Octave
\backslash
3.2.4_gcc-4.4.0
\backslash
bin som angiver hvor de to programmers exe-filer er placeret.
 Herefter klikker Tools>Recongigure, hvorefter LyX kan lave beregninger.
 Hvis man ønsker et udtryk beregnet, sætter man curseren sidst i den pågældende
 og vælger Edit>math>Use Computer Algebra system>Octave eller Edit>math>Use
 Computer Algebra system>Maxima alt efter hvilket af de to programmer man
 vil have til at lave beregningen.
\end_layout

\begin_layout Section
Læs mere
\end_layout

\begin_layout Standard
En kort introduktion til LyX på dansk kan findes på: http://jura.hollmen.dk/files/
mikko-lyxintro.pdf .
 Ellers kan man finde diverse oplysninger under help.
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Symbolliste
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\end_inset


\end_layout

\end_inset
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</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

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\backslash
mathbb R
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathbb{R}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
emptyset
\end_layout

\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\emptyset$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
wedge
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\wedge$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
vee
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\vee$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
rightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Rightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
leftrightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Leftrightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
leq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\leq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
geq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\geq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_body
\end_document