Normal vector

Gradient

fold/unfold

$$ \begin{flalign*} \nabla f = \frac{\partial f}{\partial x}\hat{i} + \frac{\partial f}{\partial y}\hat{j} + \frac{\partial f}{\partial z}\hat{k} && \end{flalign*} $$

Normal unit vector

fold/unfold

$$ \begin{flalign*} \hat{n} = \frac{\nabla f}{|f|} && \end{flalign*} $$

Differential normal area

fold/unfold

$$ \begin{flalign*} d \vec{A} = dA \cdot \hat{n} && \end{flalign*} $$