In Homework 2, a hint for problem 1 is that in some sub-problems it could be useful to use the dual version of Lemma 2.39 in Huybrechts (see Lecture 6). That is, for maps in D(A) we don't need to use roofs if the source is a complex of projective objects
Lecture notes from Lecture 8 are available at the course web page.
There is also a list of projects available on the course web page.