transmission line parameters
It looks to me like the slides use primed variables for per length quantities, and unprimed for total, but besides that I think you're right. As The-Photon comments, if you check the units you'll find you need the per length quantities to get m/s. For the propagation delay you can say T' = sqrt(L'C') and T = sqrt(LC) and for the impedance you can use either since you divide out any constants. So if you're calculating L and C from T and Z, you get L' and C' if you use T'.