| name | notation | traditional notation |
|---|---|---|
| function | \( z \mathrel{\overset{f}{\leftarrow}} (x, y) \) | \( f : \mathbb{R}^2 \to \mathbb{R} \) |
| dependence | \( z \depends (x, y) \) | \( (x, y) \mapsto z \) |
| differential | \( \diff z \) | \( d z \) |
| derivative | \( \overset{x}{\diff} z \) | \( {\displaystyle \frac{d z}{d x} } \) |
| slope | \( \operatorname{\overset{\mathit{x}}{\slope}} z \) | |
| bend | \( \operatorname{\overset{\mathit{x}}{\bend}} z \) | |
| natural base | \( \naturalbase \) | \( e \) |
| natural exponential | \( \exp \) | |
| natural logarithm | \( \log \) | \( \ln \) |
| partials | \( \overset{x}{\diff} z \andSpaced \overset{y}{\diff} z \) | \( {\displaystyle \frac{\partial z}{\partial x} \andSpaced \frac{\partial z}{\partial y} } \) |
| slopes | \( \operatorname{\overset{\mathit{x}}{\slope}} z \andSpaced \operatorname{\overset{\mathit{y}}{\slope}} z \) | |
| bends | \( \operatorname{\overset{\mathit{x}}{\bend}} z \andSpaced \operatorname{\overset{\mathit{y}}{\bend}} z \) | |
| warp | \( \warp z \) | |
| standard metrics | \( \hat{\standard}_{x} \andSpaced \hat{\standard}_{y} \) | |
| metric differential | \( \hat{\diff} z \) | |
| tangent metric | \( \tangent z \) | |
| Hessian polymetric | \( \hessian z \) | |
| saddle discriminant | \( \discriminant z \) | |
| standard vectors | \( \vec{\standard}_{x} \andSpaced \vec{\standard}_{y} \) | \( {\displaystyle \begin{bmatrix}1 \\ 0\end{bmatrix} \andSpaced \begin{bmatrix}0 \\ 1\end{bmatrix} } \) |
| standard rulers | \( \bar{\standard}_{x} \andSpaced \bar{\standard}_{y} \) | \( {\displaystyle \begin{bmatrix}1 & 0\end{bmatrix} \andSpaced \begin{bmatrix}0 & 1\end{bmatrix} } \) |
| measurement | \( \langle{r}\mathbin{|}{v}\rangle \) | \( {\displaystyle \begin{bmatrix}x_r & y_r\end{bmatrix} \begin{bmatrix}x_v \\ y_v\end{bmatrix} } \) |
| magnitude | \( \magnitude v \) | \( \lVert v \rVert \) |
| transpose | \( \transpose r \) | |
| ruler differential | \( \bar{\diff} z \) | |
| directional slope | \( \operatorname{\overset{\mathit{v}}{\directional}} z \) | |
| gradient | \( \gradient z \) | \( \lVert \nabla z \rVert \) |
| blip | \( [x_0]_{x} \) | |
| interval | \( [x_1, x_2]_{x} \) | \( [x_1, x_2] \) |
| boundary | \( \boundary b \) | |
| integral | \( {\displaystyle \biggl\langle{a \mult \bar{\diff} x}\mathrel{\displaystyle{\int}}{[x_1, x_2]_{x}}\biggr\rangle } \) | \( {\displaystyle \int_{x_1}^{x_2} a \, d x } \) |
| position vector | \( \position p \) | |
| velocity vector | \( \velocity z \) | |
| speed | \( \speed z \) | |
| one revolution | \( \revolution \) | \( 2 \pi \) |