In this part, it is said that dk is the distance from the center, shouldn’t it be that dk = |k-pi/a| ? since if you don’t, then for k=0 the would become E0 -vhpi/a, just the same as the k’-part.
You are right, and “distance” is imprecise, thanks for reporting. I changed the lecture notes to call \delta k the wavevector offset.