What This Site Can Do

This page exists for two audiences. Students: it shows why the notes look the way they do. Teachers: it is a working reference for everything you can put in a page, with the source visible in every example.

Everything below is written in Markdown — plain text with a few marks of punctuation that mean something. If you can write a text message, you can write this.

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Text that carries meaning

You get bold, italic, struck through, and highlighted text. Highlighting is the one worth knowing: it draws the eye better than bold when you want a single key term to stand out in a paragraph.

How that was made:

**bold**, *italic*, ~~struck through~~, ==highlighted==

Arrows written as -> become proper arrows: secant → secant → tangent.

Keyboard keys look like keys: press ⌘ + K to search.

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Mathematics, typeset properly

This is the feature a calculus course lives on. Inline maths sits in a sentence: an average speed is a plain fraction, like $\frac{150\text{ km}}{2\text{ h}}=75$ km/h. Display maths gets its own centred line — and this course’s central definition deserves one:

$$f^{\prime }(x)=\underset{h\to 0}{\lim }\frac{f(x+h)-f(x)}{h}$$

Fractions, limits, vectors, and symbols all come out exactly as they should:

$$\frac{d}{dx}\sin x=\cos x\vec{u}\cdot \vec{v}=|\vec{u}||\vec{v}|\cos \theta \underset{x\to 3}{\lim }\frac{x^2-9}{x-3}=6$$

How that was made: single dollar signs keep it in the sentence, double ones give it a line of its own.

Inline: $\frac{150 \text{ km}}{2 \text{ h}} = 75$
 
Display:
$$
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
$$

No more screenshotting equations out of a document — edit the text and the mathematics re-typesets itself.

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Code (not used in this course — but here if you need it)

This course has no coding expectations, so you will not meet program code in our pages. The site can carry it anyway — coloured, exact, spacing preserved — which matters if you also teach a course that codes:

def height(t):
    return -4.9 * t ** 2 + 20 * t
 
print(height(2))   # 20.4

How that was made: three backticks and the language name, the code, then three backticks to close it.

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Headings, and the table of contents

Every ## heading on a page becomes a link in Navigate this page, over on the right — built automatically from the headings, so it can never fall out of step with the page. Deeper headings nest underneath.

A short page reads better without a contents panel; one frontmatter line (enableToc: false) turns it off. Every class page in All Classes does this — an agenda of six items does not need navigating.

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Callouts

Callouts pull something out of the flow of the page, each kind with its own colour and icon:

Note

Neutral information worth setting apart.

Tip

A shortcut, a habit, or something that makes the work easier.

Important

The one thing to take away if you take away nothing else.

Warning

Where people usually go wrong — the calculator quietly left in degree mode lives in boxes like this one, and so does the inner derivative the chain rule keeps losing.

Question

Something to think about rather than something to know.

At a glance

Used at the top of task pages for format and timing.

How that was made: a blockquote with the kind named in brackets.

> [!warning] Where people usually go wrong
> 
> The text of the callout goes here.

Foldable callouts

Add a - to start a callout collapsed. Every practice set in Exercises hides its worked answers this way — try before you peek, but the peek is always there:

Worked answer

$\frac{d}{dx}\left(x^2\sin x\right)=2x\sin x+x^2\cos x$ — the product rule, each factor’s growth scaled by the other factor’s size. The product of the derivatives, $2x\cos x$, is the answer to a question nobody asked.

> [!success]- Worked answer
> 
> The hidden solution.

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Diagrams

Diagrams are written, not drawn — edited in seconds, never needing a graphics program.

graph LR
    A["Name the quantity to optimize"] --> B["Write it as a function"]
    B --> C["Differentiate and find candidates"]
    C --> D{"Best of all candidates?"}
    D -->|check endpoints too| E["Defend the answer"]
    D -->|a candidate fails| C

How that was made:

```mermaid
graph LR
    A["Name the quantity to optimize"] --> B["Write it as a function"]
    B --> C["Differentiate and find candidates"]
    C --> D{"Best of all candidates?"}
    D -->|check endpoints too| E["Defend the answer"]
    D -->|a candidate fails| C
```

Proportions draw themselves too:

pie title One class period, roughly
    "Number talk" : 15
    "Thinking task" : 45
    "Consolidation" : 20
    "Notes and check-in" : 20

And history fits on a line:

timeline
    title Where this course's ideas came from
    1665 : Newton : works out his "fluxions" in a plague year
    1684 : Leibniz : publishes calculus with the dy/dx notation
    1821 : Cauchy : puts the limit on rigorous footing
    1843 : Hamilton : carves the seed of vector algebra into a Dublin bridge
    1901 : Gibbs : the modern dot and cross products in print

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Tables

How that was made: rows of text separated by |, with a line of dashes under the headings. Mathematics works inside cells, which matters more than it sounds.

Representation	Shows best	Hides
Components $⟨3,4⟩$	Exact arithmetic — adding is just adding	What the arrow looks like
Magnitude and direction — 5 units at $53^{\circ }$	The physical picture: how far, which way	Clean addition
An arrow drawn to scale	Two vectors’ sum, tip to tail, at a glance	Exact values

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Checklists

How that was made: a list where each line starts with - [ ], or - [x] for one already done.

• Estimate before calculating
• Units carried through the whole solution
• Answer sentence written
• Someone else could follow this page

On the site they are read-only — the boxes show what the page says, and clicking one does nothing. Copied into your own notes, they are how Showing Your Thinking turns from advice into habit.

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Links between pages

This is what makes the site more than a pile of documents.

• A plain link: The Chain Rule
• A link with different words: the instant, made precise
• A link to a section: Estimate first, compare after

How that was made: double square brackets.

[[The Chain Rule]]
[[The Limit|different words for the link]]
[[Checking Your Own Work#estimate-first-compare-after|Estimate first, compare after]]

Transclusion — one page inside another

How that was made: ![[Page name]] — a link with an exclamation mark in front of it. Here is the help-session schedule, embedded live rather than copied:

Help Sessions

Extra help

When	Where
Tuesday, lunch	The math room
Thursday, after school until 4:15	The math room

Drop in — no appointment, no need to tell me first. Bring the specific thing you are stuck on: one half-finished problem beats “everything”. The whiteboards are open during these times too, and yes, you may just come to work near other people working.

More: Getting Help

Link to original

Change the source page and every page that embeds it updates. This is how task pages show the curriculum expectations they address, and how one schedule stays correct everywhere it appears, without anyone maintaining duplicates.

Backlinks

Scroll to the bottom of any page and you will find Backlinks — every page that links to this one, gathered automatically. Open The Derivative and its backlinks list every exploration, task, and practice set that leans on it. Nobody maintains that list.

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Hover previews

Hover over Getting Unstuck without clicking. The page appears in a small window. Checking one definition mid-problem does not cost you your place.

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Footnotes

How that was made: [^1] where the marker goes, and a matching [^1]: line anywhere in the page.

The word “calculus” is humbler than the subject.¹

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Tags

How that was made: a tags list in the frontmatter at the very top of the page.

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tags:
  - concepts
  - unit-2
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Every tag becomes a page listing everything filed under it.

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What you cannot see

Two things on this page are invisible in the browser:

1. Comments. Text wrapped in “ never reaches the site. Useful for notes to yourself in a page you are still writing — tomorrow’s hint, next year’s fix.
2. Holding a page back. A page with publish: false in its frontmatter is skipped entirely when the site is built. Write next week’s lesson today and publish it when you are ready.

For teachers reading this

With more than one section, per-section keys like publishForSection1 and publishForSection2 let one shared page be published to one class and held back from another — useful when your two sections sit a few days apart.

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The point of all this

None of it is decoration. Each feature removes a reason for a page to be out of date:

Feature	The problem it solves
Typeset maths	Screenshotted equations nobody can edit
Transclusion	The same text copied into six places, five stale
Backlinks	”Where did we use this again?”
Folded answers	Solutions that spoil the attempt
Holding a page back	Next week’s lesson in a separate file somewhere

Write it once, link to it everywhere.

Footnotes

1. It is Latin for “small pebble” — the counting stones of Roman arithmetic boards. The name stuck to the mathematics of Newton and Leibniz because it, too, was a system for calculating — though its pebbles turned out to be instants. ↩