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Refactor maths chapter

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Knoch 2022-10-11 20:56:54 +02:00
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155
slides/chapter-09.de.md
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@ -40,18 +40,6 @@ Einige Beispiele
<th>Quelltext</th> <th>Quelltext</th>
<th>Ergebnis</th> <th>Ergebnis</th>
</tr> </tr>
<tr class="fragment">
<td>`\sqrt{16}`</td>
<td>$\sqrt{16}$</td>
</tr>
<tr class="fragment">
<td>`\frac{3}{4}`</td>
<td>$\frac{3}{4}$</td>
</tr>
<tr class="fragment">
<td>`e^{\pi}`</td>
<td>$e^{\pi}$</td>
</tr>
<tr class="fragment"> <tr class="fragment">
<td>`\sum_{i=1}^{n}x^2`</td> <td>`\sum_{i=1}^{n}x^2`</td>
<td>$\sum_{i=1}^{n} x^2$</td> <td>$\sum_{i=1}^{n} x^2$</td>
@ -66,13 +54,71 @@ Einige Beispiele
</tr> </tr>
</table> </table>
++ Durch `^{…}` und `_{…}` werden die Inhalte in den Klammern hoch- oder tiefgestellt.
@slide(layout=content-and-preview)
@slide(layout=content-only)
@title @title
Einige Beispiele Ausrichtung von mehreren Gleichungen
@content
Die Umgebung `align` erlaubt es, Gleichungen zum Beispiel am ›&hairsp;=&hairsp;‹ auszurichten.
``` {.lang-tex .hljs}
\begin{align}
13 \cdot (4a - 3)^2 &= 13 … \\
&= 208a^2 - 312a + 117
\end{align}
```
* ++ Ausgerichtet wird am ›`&`‹-Zeichen.
* ++ Zeilenumbrüche werden mit ›`\\`‹ markiert.
* ++ Die Nummerierung kann bei `align` und `equation` durch durch ein Sternchen nach dem Umgebungsnamen (z.&thinsp;B. `\begin{align*}` und `\end{align*}`) unterdrückt werden.
@preview
![](svg/chapter-09/alignment-crop.svg)
@slide(layout=task-without-number)
@task-number
9a
@title
Formeln setzen
@content
Setzt die folgenden Formeln in der Datei `exercises/maths/math-formulas.tex`.
| Bedeutung | Ergebnis |
|-----------|----------|
| Fallbeschleunigung (Deutschland) | $9,81\,\frac{m}{s^2}$ |
| pq-Formel | $x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$ |
| Mitternachtsformel | $x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ |
| Catalansche Zahlen | $C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}$ |
@slide(layout=task-without-number)
@task-number
9b
@title
Formeln setzen
@content
Setzt die folgenden Formeln in der Datei `exercises/maths/math-formulas.tex`.
| Bedeutung | Ergebnis |
|-----------|----------|
| Definition der Fakultät | $n! = \prod_{i=1}^{n} i$ |
| Menge aller ungeraden natürlichen Zahlen | $\{ x \mid x \in \mathbb{N}, \mathrm{ungerade}(x) \}$ |
| Elimination $\neg\exists x$ | $\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$ |
@slide(layout=extra-content-only)
@title
Weitere Beispiele
@content @content
<table> <table>
@ -110,7 +156,7 @@ Einige Beispiele
</tr> </tr>
</table> </table>
@slide(layout=content-only) @slide(layout=extra-content-only)
@title @title
Mitwachsende Klammern Mitwachsende Klammern
@ -121,29 +167,29 @@ Mitwachsende Klammern
<th>Quelltext</th> <th>Quelltext</th>
<th>Ergebnis</th> <th>Ergebnis</th>
</tr> </tr>
<tr class="fragment"> <tr>
<td>`\left( \frac{1}{2} \right)`</td> <td>`\left( \frac{1}{2} \right)`</td>
<td>$\left( \frac{1}{2} \right)$</td> <td>$\left( \frac{1}{2} \right)$</td>
</tr> </tr>
<tr class="fragment"> <tr>
<td>`\left[ \frac{1}{2} \right]`</td> <td>`\left[ \frac{1}{2} \right]`</td>
<td>$\left[ \frac{1}{2} \right]$</td> <td>$\left[ \frac{1}{2} \right]$</td>
</tr> </tr>
<tr class="fragment"> <tr>
<td>`\left\lbrace \frac{1}{2} \right\rbrace`</td> <td>`\left\lbrace \frac{1}{2} \right\rbrace`</td>
<td>$\left\lbrace \frac{1}{2} \right\rbrace$</td> <td>$\left\lbrace \frac{1}{2} \right\rbrace$</td>
</tr> </tr>
</table> </table>
``` {.lang-tex .hljs .fragment} ``` {.lang-tex .hljs}
$4 \cdot \left( \frac{1}{2} % … $4 \cdot \left( \frac{1}{2} % …
``` ```
<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> <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>
@slide(layout=content-and-preview) @slide(layout=extra-content-and-preview)
@title @title
Darstellung von Grenzen Darstellung von Grenzen
@ -164,29 +210,7 @@ Mit dem Befehl `\limits` lassen sich die Grenzen von Integralen unter und über
![](svg/chapter-09/limits-crop.svg) ![](svg/chapter-09/limits-crop.svg)
@slide(layout=content-and-preview) @slide(layout=extra-content-only)
@title
Ausrichtung von mehreren Gleichungen
@content
Die Umgebung `align` erlaubt es, Gleichungen zum Beispiel am ›&hairsp;=&hairsp;‹ auszurichten.
``` {.lang-tex .hljs}
\begin{align}
13 \cdot (4a - 3)^2 &= 13 … \\
&= 208a^2 - 312a + 117
\end{align}
```
* ++ Ausgerichtet wird am ›`&`‹-Zeichen.
* ++ Zeilenumbrüche werden mit ›`\\`‹ markiert.
* ++ Die Nummerierung kann bei `align` und `equation` durch durch ein Sternchen nach dem Umgebungsnamen (z.&thinsp;B. `\begin{align*}` und `\end{align*}`) unterdrückt werden.
@preview
![](svg/chapter-09/alignment-crop.svg)
@slide(layout=content-only)
@title @title
Mengenschreibweise Mengenschreibweise
@ -197,43 +221,8 @@ Manchmal ist es notwendig, im Zusammenhang mit der Mengenschreibweise Prädikate
Für diesen Fall gibt es den Befehl `\mathrm{}`. Für diesen Fall gibt es den Befehl `\mathrm{}`.
<p style="text-align: center;">$\left\lbrace x \mid tiefe(x) \geq 20\right\rbrace$</p> <p style="text-align: center;">$\left\lbrace x \mid tiefe(x) \geq 20\right\rbrace$</p>
<p style="text-align: center;" class="fragment">$\left\lbrace x \mid \mathrm{tiefe}(x) \geq 20\right\rbrace$</p> <p style="text-align: center;">$\left\lbrace x \mid \mathrm{tiefe}(x) \geq 20\right\rbrace$</p>
``` {.lang-tex .hljs .fragment} ``` {.lang-tex .hljs}
$\left\lbrace x \mid \mathrm{tiefe}(x) … $\left\lbrace x \mid \mathrm{tiefe}(x) …
``` ```
@slide(layout=task-without-number)
@task-number
9a
@title
Formeln setzen
@content
Setzt die folgenden Formeln in der Datei `exercises/maths/math-formulas.tex`.
| Bedeutung | Ergebnis |
|-----------|----------|
| Fallbeschleunigung (Deutschland) | $9,81\,\frac{m}{s^2}$ |
| pq-Formel | $x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$ |
| Mitternachtsformel | $x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ |
| Catalansche Zahlen | $C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}$ |
@slide(layout=task-without-number)
@task-number
9b
@title
Formeln setzen
@content
Setzt die folgenden Formeln in der Datei `exercises/maths/math-formulas.tex`.
| Bedeutung | Ergebnis |
|-----------|----------|
| Definition der Fakultät | $n! = \prod_{i=1}^{n} i$ |
| Menge aller ungeraden natürlichen Zahlen | $\{ x \mid x \in \mathbb{N}, \mathrm{ungerade}(x) \}$ |
| Elimination $\neg\exists x$ | $\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$ |

155
slides/chapter-09.en.md
View File

@ -42,18 +42,6 @@ Examples
<th>source code</th> <th>source code</th>
<th>result</th> <th>result</th>
</tr> </tr>
<tr class="fragment">
<td>`\sqrt{16}`</td>
<td>$\sqrt{16}$</td>
</tr>
<tr class="fragment">
<td>`\frac{3}{4}`</td>
<td>$\frac{3}{4}$</td>
</tr>
<tr class="fragment">
<td>`e^{\pi}`</td>
<td>$e^{\pi}$</td>
</tr>
<tr class="fragment"> <tr class="fragment">
<td>`\sum_{i=1}^{n}x^2`</td> <td>`\sum_{i=1}^{n}x^2`</td>
<td>$\sum_{i=1}^{n} x^2$</td> <td>$\sum_{i=1}^{n} x^2$</td>
@ -68,12 +56,72 @@ Examples
</tr> </tr>
</table> </table>
++ `^{…}` and `_{…}` make the content between the braces appear as sub- or superscripted.
@slide(layout=content-only) @slide(layout=content-and-preview)
@title @title
Examples Aligning a group of equations
@content
The `align` environment permits us to align equations at certain positions like the ‘&hairsp;=&hairsp;’ character.
``` {.lang-tex .hljs}
\begin{align}
13 \cdot (4a - 3)^2 &= 13 … \\
&= 208a^2 - 312a + 117
\end{align}
```
* ++ The equations will be aligned with respect to the ampersands (‘`&`’).
* ++ We can mark a new line using ‘`\\`’.
* ++ `align` and `equation` will not be numbered if we add an asterisk after their names (e.&thinsp;g. `\begin{align*}` and `\end{align*}`).
@preview
![](svg/chapter-09/alignment-crop.svg)
@slide(layout=task-without-number)
@task-number
9a
@title
Typesetting mathematics
@content
Code up the following formulas in the file `exercises/maths/math-formulas.tex`.
| Meaning | Result |
|---------|--------|
| Gravitational acceleration | $9,81\,\frac{m}{s^2}$ |
| Formula to solve quadratic equations | $x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$ |
| Another formula to solve quadratic equations | $x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ |
| Catalan numbers | $C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}$ |
@slide(layout=task-without-number)
@task-number
9b
@title
Typesetting mathematics
@content
Code up the following formulas in the file `exercises/maths/math-formulas.tex`.
| Meaning | Result |
|---------|--------|
| Definition of factorial | $n! = \prod_{i=1}^{n} i$ |
| Set of all odd natural numbers | $\{ x \mid x \in \mathbb{N}, \mathrm{odd}(x) \}$ |
| Elimination $\neg\exists x$ | $\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$ |
@slide(layout=extra-content-only)
@title
More examples
@content @content
<table> <table>
@ -111,7 +159,7 @@ Examples
</tr> </tr>
</table> </table>
@slide(layout=content-only) @slide(layout=extra-content-only)
@title @title
Height-adapting braces Height-adapting braces
@ -122,29 +170,29 @@ Height-adapting braces
<th>source code</th> <th>source code</th>
<th>result</th> <th>result</th>
</tr> </tr>
<tr class="fragment"> <tr>
<td>`\left( \frac{1}{2} \right)`</td> <td>`\left( \frac{1}{2} \right)`</td>
<td>$\left( \frac{1}{2} \right)$</td> <td>$\left( \frac{1}{2} \right)$</td>
</tr> </tr>
<tr class="fragment"> <tr>
<td>`\left[ \frac{1}{2} \right]`</td> <td>`\left[ \frac{1}{2} \right]`</td>
<td>$\left[ \frac{1}{2} \right]$</td> <td>$\left[ \frac{1}{2} \right]$</td>
</tr> </tr>
<tr class="fragment"> <tr>
<td>`\left\lbrace \frac{1}{2} \right\rbrace`</td> <td>`\left\lbrace \frac{1}{2} \right\rbrace`</td>
<td>$\left\lbrace \frac{1}{2} \right\rbrace$</td> <td>$\left\lbrace \frac{1}{2} \right\rbrace$</td>
</tr> </tr>
</table> </table>
``` {.lang-tex .hljs .fragment} ``` {.lang-tex .hljs}
$4 \cdot \left( \frac{1}{2} % … $4 \cdot \left( \frac{1}{2} % …
``` ```
<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> <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>
@slide(layout=content-and-preview) @slide(layout=extra-content-and-preview)
@title @title
Depicting boundaries Depicting boundaries
@ -162,33 +210,12 @@ This is the standard behaviour for sums, products and limits.
<p data-category="Caution!">Don't use `\limits` inline.</p> <p data-category="Caution!">Don't use `\limits` inline.</p>
@preview @preview
![](svg/chapter-09/limits-crop.svg) ![](svg/chapter-09/limits-crop.svg)
@slide(layout=content-and-preview) @slide(layout=extra-content-only)
@title
Aligning a group of equations
@content
The `align` environment permits us to align equations at certain positions like the ‘&hairsp;=&hairsp;’ character.
``` {.lang-tex .hljs}
\begin{align}
13 \cdot (4a - 3)^2 &= 13 … \\
&= 208a^2 - 312a + 117
\end{align}
```
* ++ The equations will be aligned with respect to the ampersands (‘`&`’).
* ++ We can mark a new line using ‘`\\`’.
* ++ `align` and `equation` will not be numbered if we add an asterisk after their names (e.&thinsp;g. `\begin{align*}` and `\end{align*}`).
@preview
![](svg/chapter-09/alignment-crop.svg)
@slide(layout=content-only)
@title @title
Set-builder notation Set-builder notation
@ -199,44 +226,8 @@ In certain situations, it is more adequate to use textual predicates or long fun
This is where `\mathrm{}` comes into play. This is where `\mathrm{}` comes into play.
<p style="text-align: center;">$\left\lbrace x \mid frequency(x) \geq 20\right\rbrace$</p> <p style="text-align: center;">$\left\lbrace x \mid frequency(x) \geq 20\right\rbrace$</p>
<p style="text-align: center;" class="fragment">$\left\lbrace x \mid \mathrm{frequency}(x) \geq 20\right\rbrace$</p> <p style="text-align: center;">$\left\lbrace x \mid \mathrm{frequency}(x) \geq 20\right\rbrace$</p>
``` {.lang-tex .hljs .fragment} ``` {.lang-tex .hljs .fragment}
$\left\lbrace x \mid \mathrm{frequency} … $\left\lbrace x \mid \mathrm{frequency} …
``` ```
@slide(layout=task-without-number)
@task-number
9a
@title
Typesetting mathematics
@content
Code up the following formulas in the file `exercises/maths/math-formulas.tex`.
| Meaning | Result |
|---------|--------|
| Gravitational acceleration | $9,81\,\frac{m}{s^2}$ |
| Formula to solve quadratic equations | $x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$ |
| Another formula to solve quadratic equations | $x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ |
| Catalan numbers | $C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}$ |
@slide(layout=task-without-number)
@task-number
9b
@title
Typesetting mathematics
@content
Code up the following formulas in the file `exercises/maths/math-formulas.tex`.
| Meaning | Result |
|---------|--------|
| Definition of factorial | $n! = \prod_{i=1}^{n} i$ |
| Set of all odd natural numbers | $\{ x \mid x \in \mathbb{N}, \mathrm{odd}(x) \}$ |
| Elimination $\neg\exists x$ | $\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$ |