Refactor maths chapter
This commit is contained in:
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@ -40,18 +40,6 @@ Einige Beispiele
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<th>Quelltext</th>
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<th>Ergebnis</th>
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</tr>
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<tr class="fragment">
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<td>`\sqrt{16}`</td>
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<td>$\sqrt{16}$</td>
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</tr>
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<tr class="fragment">
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<td>`\frac{3}{4}`</td>
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<td>$\frac{3}{4}$</td>
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</tr>
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<tr class="fragment">
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<td>`e^{\pi}`</td>
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<td>$e^{\pi}$</td>
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</tr>
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<tr class="fragment">
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<td>`\sum_{i=1}^{n}x^2`</td>
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<td>$\sum_{i=1}^{n} x^2$</td>
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@ -66,13 +54,71 @@ Einige Beispiele
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</tr>
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</table>
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++ Durch `^{…}` und `_{…}` werden die Inhalte in den Klammern hoch- oder tiefgestellt.
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@slide(layout=content-only)
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@slide(layout=content-and-preview)
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@title
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Einige Beispiele
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Ausrichtung von mehreren Gleichungen
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@content
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Die Umgebung `align` erlaubt es, Gleichungen zum Beispiel am › = ‹ auszurichten.
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``` {.lang-tex .hljs}
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\begin{align}
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13 \cdot (4a - 3)^2 &= 13 … \\
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&= 208a^2 - 312a + 117
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\end{align}
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```
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* ++ Ausgerichtet wird am ›`&`‹-Zeichen.
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* ++ Zeilenumbrüche werden mit ›`\\`‹ markiert.
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* ++ Die Nummerierung kann bei `align` und `equation` durch durch ein Sternchen nach dem Umgebungsnamen (z. B. `\begin{align*}` und `\end{align*}`) unterdrückt werden.
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@preview
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@slide(layout=task-without-number)
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@task-number
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9a
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@title
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Formeln setzen
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@content
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Setzt die folgenden Formeln in der Datei `exercises/maths/math-formulas.tex`.
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| Bedeutung | Ergebnis |
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|-----------|----------|
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| Fallbeschleunigung (Deutschland) | $9,81\,\frac{m}{s^2}$ |
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| pq-Formel | $x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$ |
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| Mitternachtsformel | $x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ |
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| Catalansche Zahlen | $C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}$ |
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@slide(layout=task-without-number)
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@task-number
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9b
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@title
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Formeln setzen
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@content
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Setzt die folgenden Formeln in der Datei `exercises/maths/math-formulas.tex`.
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| Bedeutung | Ergebnis |
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|-----------|----------|
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| Definition der Fakultät | $n! = \prod_{i=1}^{n} i$ |
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| Menge aller ungeraden natürlichen Zahlen | $\{ x \mid x \in \mathbb{N}, \mathrm{ungerade}(x) \}$ |
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| Elimination $\neg\exists x$ | $\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$ |
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@slide(layout=extra-content-only)
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@title
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Weitere Beispiele
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@content
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<table>
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@ -110,7 +156,7 @@ Einige Beispiele
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</tr>
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</table>
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@slide(layout=content-only)
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@slide(layout=extra-content-only)
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@title
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Mitwachsende Klammern
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@ -121,29 +167,29 @@ Mitwachsende Klammern
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<th>Quelltext</th>
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<th>Ergebnis</th>
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</tr>
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<tr class="fragment">
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<tr>
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<td>`\left( \frac{1}{2} \right)`</td>
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<td>$\left( \frac{1}{2} \right)$</td>
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</tr>
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<tr class="fragment">
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<tr>
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<td>`\left[ \frac{1}{2} \right]`</td>
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<td>$\left[ \frac{1}{2} \right]$</td>
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</tr>
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<tr class="fragment">
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<tr>
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<td>`\left\lbrace \frac{1}{2} \right\rbrace`</td>
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<td>$\left\lbrace \frac{1}{2} \right\rbrace$</td>
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</tr>
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</table>
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``` {.lang-tex .hljs .fragment}
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``` {.lang-tex .hljs}
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$4 \cdot \left( \frac{1}{2} % …
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```
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<p class="fragment" style="text-align: center;">$4 \cdot \left(\frac{1}{2} +\frac{3}{ 12 \cdot \left( 2 + \frac{1}{86 \cdot \left(\frac{1}{2} + 24 \right)} \right)} \right)$</p>
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<p style="text-align: center;">$4 \cdot \left(\frac{1}{2} +\frac{3}{ 12 \cdot \left( 2 + \frac{1}{86 \cdot \left(\frac{1}{2} + 24 \right)} \right)} \right)$</p>
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@slide(layout=content-and-preview)
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@slide(layout=extra-content-and-preview)
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@title
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Darstellung von Grenzen
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@ -164,29 +210,7 @@ Mit dem Befehl `\limits` lassen sich die Grenzen von Integralen unter und über
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@slide(layout=content-and-preview)
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@title
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Ausrichtung von mehreren Gleichungen
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@content
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Die Umgebung `align` erlaubt es, Gleichungen zum Beispiel am › = ‹ auszurichten.
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``` {.lang-tex .hljs}
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\begin{align}
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13 \cdot (4a - 3)^2 &= 13 … \\
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&= 208a^2 - 312a + 117
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\end{align}
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```
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* ++ Ausgerichtet wird am ›`&`‹-Zeichen.
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* ++ Zeilenumbrüche werden mit ›`\\`‹ markiert.
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* ++ Die Nummerierung kann bei `align` und `equation` durch durch ein Sternchen nach dem Umgebungsnamen (z. B. `\begin{align*}` und `\end{align*}`) unterdrückt werden.
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@preview
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@slide(layout=content-only)
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@slide(layout=extra-content-only)
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@title
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Mengenschreibweise
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@ -197,43 +221,8 @@ Manchmal ist es notwendig, im Zusammenhang mit der Mengenschreibweise Prädikate
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Für diesen Fall gibt es den Befehl `\mathrm{}`.
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<p style="text-align: center;">$\left\lbrace x \mid tiefe(x) \geq 20\right\rbrace$</p>
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<p style="text-align: center;" class="fragment">$\left\lbrace x \mid \mathrm{tiefe}(x) \geq 20\right\rbrace$</p>
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<p style="text-align: center;">$\left\lbrace x \mid \mathrm{tiefe}(x) \geq 20\right\rbrace$</p>
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``` {.lang-tex .hljs .fragment}
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``` {.lang-tex .hljs}
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$\left\lbrace x \mid \mathrm{tiefe}(x) …
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```
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@slide(layout=task-without-number)
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@task-number
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9a
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@title
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Formeln setzen
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@content
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Setzt die folgenden Formeln in der Datei `exercises/maths/math-formulas.tex`.
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| Bedeutung | Ergebnis |
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|-----------|----------|
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| Fallbeschleunigung (Deutschland) | $9,81\,\frac{m}{s^2}$ |
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| pq-Formel | $x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$ |
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| Mitternachtsformel | $x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ |
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| Catalansche Zahlen | $C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}$ |
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@slide(layout=task-without-number)
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@task-number
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9b
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@title
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Formeln setzen
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@content
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Setzt die folgenden Formeln in der Datei `exercises/maths/math-formulas.tex`.
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| Bedeutung | Ergebnis |
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|-----------|----------|
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| Definition der Fakultät | $n! = \prod_{i=1}^{n} i$ |
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| Menge aller ungeraden natürlichen Zahlen | $\{ x \mid x \in \mathbb{N}, \mathrm{ungerade}(x) \}$ |
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| Elimination $\neg\exists x$ | $\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$ |
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@ -42,18 +42,6 @@ Examples
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<th>source code</th>
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<th>result</th>
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</tr>
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<tr class="fragment">
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<td>`\sqrt{16}`</td>
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<td>$\sqrt{16}$</td>
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</tr>
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<tr class="fragment">
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<td>`\frac{3}{4}`</td>
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<td>$\frac{3}{4}$</td>
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</tr>
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<tr class="fragment">
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<td>`e^{\pi}`</td>
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<td>$e^{\pi}$</td>
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</tr>
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<tr class="fragment">
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<td>`\sum_{i=1}^{n}x^2`</td>
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<td>$\sum_{i=1}^{n} x^2$</td>
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@ -68,12 +56,72 @@ Examples
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</tr>
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</table>
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++ `^{…}` and `_{…}` make the content between the braces appear as sub- or superscripted.
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@slide(layout=content-only)
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@slide(layout=content-and-preview)
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@title
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Examples
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Aligning a group of equations
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@content
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The `align` environment permits us to align equations at certain positions like the ‘ = ’ character.
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``` {.lang-tex .hljs}
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\begin{align}
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13 \cdot (4a - 3)^2 &= 13 … \\
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&= 208a^2 - 312a + 117
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\end{align}
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```
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* ++ The equations will be aligned with respect to the ampersands (‘`&`’).
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* ++ We can mark a new line using ‘`\\`’.
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* ++ `align` and `equation` will not be numbered if we add an asterisk after their names (e. g. `\begin{align*}` and `\end{align*}`).
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@preview
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@slide(layout=task-without-number)
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@task-number
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9a
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@title
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Typesetting mathematics
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@content
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Code up the following formulas in the file `exercises/maths/math-formulas.tex`.
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| Meaning | Result |
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|---------|--------|
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| Gravitational acceleration | $9,81\,\frac{m}{s^2}$ |
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| Formula to solve quadratic equations | $x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$ |
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| Another formula to solve quadratic equations | $x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ |
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| Catalan numbers | $C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}$ |
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@slide(layout=task-without-number)
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@task-number
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9b
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@title
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Typesetting mathematics
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@content
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Code up the following formulas in the file `exercises/maths/math-formulas.tex`.
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| Meaning | Result |
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|---------|--------|
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| Definition of factorial | $n! = \prod_{i=1}^{n} i$ |
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| Set of all odd natural numbers | $\{ x \mid x \in \mathbb{N}, \mathrm{odd}(x) \}$ |
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| Elimination $\neg\exists x$ | $\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$ |
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@slide(layout=extra-content-only)
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@title
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More examples
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@content
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<table>
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@ -111,7 +159,7 @@ Examples
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</tr>
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</table>
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@slide(layout=content-only)
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@slide(layout=extra-content-only)
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@title
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Height-adapting braces
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@ -122,29 +170,29 @@ Height-adapting braces
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<th>source code</th>
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<th>result</th>
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</tr>
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<tr class="fragment">
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<tr>
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<td>`\left( \frac{1}{2} \right)`</td>
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<td>$\left( \frac{1}{2} \right)$</td>
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</tr>
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<tr class="fragment">
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<tr>
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<td>`\left[ \frac{1}{2} \right]`</td>
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<td>$\left[ \frac{1}{2} \right]$</td>
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</tr>
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<tr class="fragment">
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<tr>
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<td>`\left\lbrace \frac{1}{2} \right\rbrace`</td>
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<td>$\left\lbrace \frac{1}{2} \right\rbrace$</td>
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</tr>
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</table>
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``` {.lang-tex .hljs .fragment}
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``` {.lang-tex .hljs}
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$4 \cdot \left( \frac{1}{2} % …
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```
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<p class="fragment" style="text-align: center;">$4 \cdot \left(\frac{1}{2} +\frac{3}{ 12 \cdot \left( 2 + \frac{1}{86 \cdot \left(\frac{1}{2} + 24 \right)} \right)} \right)$</p>
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<p style="text-align: center;">$4 \cdot \left(\frac{1}{2} +\frac{3}{ 12 \cdot \left( 2 + \frac{1}{86 \cdot \left(\frac{1}{2} + 24 \right)} \right)} \right)$</p>
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@slide(layout=content-and-preview)
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@slide(layout=extra-content-and-preview)
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@title
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Depicting boundaries
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@ -162,33 +210,12 @@ This is the standard behaviour for sums, products and limits.
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<p data-category="Caution!">Don't use `\limits` inline.</p>
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@preview
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@slide(layout=content-and-preview)
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@title
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Aligning a group of equations
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@content
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The `align` environment permits us to align equations at certain positions like the ‘ = ’ character.
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``` {.lang-tex .hljs}
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\begin{align}
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13 \cdot (4a - 3)^2 &= 13 … \\
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&= 208a^2 - 312a + 117
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\end{align}
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```
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* ++ The equations will be aligned with respect to the ampersands (‘`&`’).
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* ++ We can mark a new line using ‘`\\`’.
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* ++ `align` and `equation` will not be numbered if we add an asterisk after their names (e. g. `\begin{align*}` and `\end{align*}`).
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@preview
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@slide(layout=content-only)
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@slide(layout=extra-content-only)
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@title
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Set-builder notation
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@ -199,44 +226,8 @@ In certain situations, it is more adequate to use textual predicates or long fun
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This is where `\mathrm{}` comes into play.
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<p style="text-align: center;">$\left\lbrace x \mid frequency(x) \geq 20\right\rbrace$</p>
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<p style="text-align: center;" class="fragment">$\left\lbrace x \mid \mathrm{frequency}(x) \geq 20\right\rbrace$</p>
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<p style="text-align: center;">$\left\lbrace x \mid \mathrm{frequency}(x) \geq 20\right\rbrace$</p>
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``` {.lang-tex .hljs .fragment}
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$\left\lbrace x \mid \mathrm{frequency} …
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```
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@slide(layout=task-without-number)
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@task-number
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9a
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@title
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Typesetting mathematics
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@content
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Code up the following formulas in the file `exercises/maths/math-formulas.tex`.
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| Meaning | Result |
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|---------|--------|
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| Gravitational acceleration | $9,81\,\frac{m}{s^2}$ |
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| Formula to solve quadratic equations | $x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$ |
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| Another formula to solve quadratic equations | $x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ |
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| Catalan numbers | $C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}$ |
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@slide(layout=task-without-number)
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@task-number
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9b
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@title
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Typesetting mathematics
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@content
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Code up the following formulas in the file `exercises/maths/math-formulas.tex`.
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| Meaning | Result |
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|---------|--------|
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| Definition of factorial | $n! = \prod_{i=1}^{n} i$ |
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| Set of all odd natural numbers | $\{ x \mid x \in \mathbb{N}, \mathrm{odd}(x) \}$ |
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| Elimination $\neg\exists x$ | $\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$ |
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