In solving first order PDE's with solution $u(x,y)$, when constructing a graph of $u$ as a union of initial curves $C_s$ emanating from the initial curve $\Gamma$. My lecture notes say, for each $s \in (\alpha,\beta) \subset \mathbb{R}$, $$C_s:= \{(x(t;s),y(t;s),z(t;s)) | t \in (-\epsilon_s, \epsilon_s), \epsilon_s >0\}$$ and $$\mathrm{Graph}_u = \bigcup_{s\in (\alpha,\beta)\subset\mathbb{R}}C_s$$
I don't understand this 'semi-colon' notation given when defining $C_s$ as surely $x,y,z$ are functions of only one variable?
I appreciate any help!
