A parametric [[Function]] or parametric equation is one whose output is some [[Point]] in space $\vec{\mathbf{x}}$ given some list of [[Free Parameter|Free Parameters]], typically denoted as $t$, $u$, or $v$. $\huge p(u,v) = \mat{ f_{x_{0}}(u, v) \\ f_{x_{1}}(u, v) \\ \vdots } = \vec {\mathbf{x}} $ >[!example] Parametric curves in $\R^{2}$ >![[Pasted image 20251105170504.png|invert_Sepia]] ### [[Partial Derivative]] The [[Partial Derivative]] of a parametric function is one that can be thought of a function that gives a tangeant [[Vector]] to the curve at [[Free Parameter|paramerers]] $(u,v)$.