214 lines
5.3 KiB
Markdown
214 lines
5.3 KiB
Markdown
@slide(layout=chapter-slide)
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@title
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Typesetting mathematics
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@slide(layout=content-and-preview)
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@title
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Formula environments 🧮
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@content
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``` {.lang-tex .hljs}
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$2 \sqrt{\frac{\pi^2}{3} \cdot c_2}$
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```
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Mathematic formulas are only accepted in the so-called **math mode**.
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Inline-formulas must therefore be guarded by two dollar signs.
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We can also use the `equation` environment.
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``` {.lang-tex .hljs}
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\begin{equation}
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2 \sqrt{\frac{\pi^2}{3} \cdot c_2}
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\end{equation}
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```
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Packages: `amsmath`, `amsthm`, `amssymb`, `mathtools`
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@preview
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@slide(layout=content-only)
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@title
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Examples (1)
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@content
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<table>
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<tr>
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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><code>\sqrt{16}</code></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><code>\frac{3}{4}</code></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><code>e^{\pi}</code></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><code>\sum_{i=1}\^{n}x^2</code></td>
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<td>$\sum_{i=1}^{n} x^2$</td>
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</tr>
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<tr class="fragment">
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<td><code>12 \leq 4 x^2 + 13</code></td>
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<td>$12 \leq 4 x^2 + 13$</td>
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</tr>
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</table>
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++ `^{…}` and `_{…}` make the content between the braces appear as super- or subscript.
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@slide(layout=content-only)
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@title
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Examples (2)
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@content
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<table>
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<tr>
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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>
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<td><code>(x), [x], \lbrace x\rbrace, \lvert x\rvert</code></td>
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<td>$(x), [x], \lbrace x\rbrace, \lvert x\rvert$</td>
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</tr>
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<tr>
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<td><code>\exists, \forall, \in, \notin, \infty</code></td>
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<td>$\exists,\forall,\in,\notin,\infty$</td>
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</tr>
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<tr>
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<td><code>\alpha, \beta, \Gamma, \Delta, \varepsilon, \pi</code></td>
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<td>$\alpha, \beta, \Gamma, \Delta, \varepsilon, \pi$</td>
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</tr>
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<tr>
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<td><code>\rightarrow, \leftarrow, \Rightarrow, \Leftarrow, \Leftrightarrow</code></td>
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<td>$\rightarrow, \leftarrow, \Rightarrow, \Leftarrow, \Leftrightarrow$</td>
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</tr>
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<tr>
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<td><code>(A \cup B) \cap C</code></td>
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<td>$(A \cup B) \cap C$</td>
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</tr>
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<tr>
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<td><code>(A \lor B) \land C</code></td>
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<td>$(A \lor B) \land C$</td>
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</tr>
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<tr>
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<td><code>(A \cdot B) \times C</code></td>
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<td>$(A \cdot B) \times C$</td>
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</tr>
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</table>
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@slide(layout=content-only)
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@title
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Height-adapting braces
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@content
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<table>
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<tr>
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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><code>\left( \frac{1}{2} \right)</code></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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<td><code>\left\lbrace \frac{1}{2} \right\rbrace</code></td>
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<td>$\left\lbrace\frac{1}{2} \right\rbrace$</td>
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</tr>
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<tr class="fragment">
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<td><code>\left[ \frac{1}{2} \right]</code></td>
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<td>$\left[\frac{1}{2} \right]$</td>
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</tr>
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</table>
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``` {.lang-tex .hljs .fragment}
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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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@slide(layout=content-and-preview)
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@title
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Depicting boundaries
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@content
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The bounds of an integral can be enforced to appear above and below the integral symbol using the `\limits` command.
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This is the standard behaviour for sums, products and limits.
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``` {.lang-tex .hljs}
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\sum_{i=1}^{n^2}(x+2)
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\prod_{j=1}^{100}(3 \cdot x)
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\lim_{x \rightarrow \infty}(14x^3 - 12)
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\int\limits_{-12}^{4}(14x^3 - 12)
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```
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Caution: Don't use `\limits` inline.
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@preview
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@todo
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Caution-Label
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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 »=«.
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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 regard to the ampersands (»&«).
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* ++ We can mark a new line using two »\«.
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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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@title
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Set-builder notation
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@content
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In certain situations, it is more adequate to use textual predicates or long function names within the set builder notation.
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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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``` {.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)
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@task-number
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8
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@title
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Typesetting mathematics
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@content
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* Reinclude `eingabefile.tex`, `textsatz.tex`, and `mathematik.tex` by adjusting the `\includeonly` command in `l2kurz.tex`.
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* Compile the entire project once again.
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* Have a look at chapter 4: Insert **your personal favourite formula** in section 4.5. |