From the fist page of the lecture, there is a derivation of transconductance of MOSFET using Taylor expansion.
As seen from the picture bellow, drain current is a function of vGS, vDS and vBS. iD is a function of three variables here. However, in Taylor expansion around DC operating point (VGS, VDS, VBS) the author didn't take vDS, vBS as variables. So iD is just like a function of vGS only.
I am wondering why they can do that? This seems to be wrong to me. Could anyone confirm?