One of my professors is quite enthusiastic about teaching the subject. He often derives from the main content and gets lost in details vastly beside or beyond the matter at hand - which is interesting, though not immediately helpful.
Effectively, this means that he regularly fails to complete the day's chapter. To compensate, he always overruns on time (15 minutes are not unusual at all).
Despite that, he failed to finish several chapters that (according to him) were intended to be taught (and indeed have been in the year before), and did not discuss or even provide solutions to previous homework due to lack of time in class.
I'm looking for advice how to deal with this situation. How can we make him stick to relevant content?
My fear is that the students will a) lack knowledge from missing several chapters, leading to future problems in subsequent courses and b) have worse conditions to succeed in this course's exam, as they lack relevant information and experience.
I'm baffled how he is able to continue like this - he clearly noticed the problem and also apologized to the students about it several times, but did not yet change his habits at all.
As I have already talked to him about other problems before, which he is attempting to fix now, I do not want to "complain" to him again if possible. I'm also a bit unsure what that would accomplish, seeing that he appears to be completely unable to keep his lectures on point.
If the students were to talk to the department head, is he likely to take action, or is this rather within the professors individual judgement? If they do, I'm clueless to imagine how he would take it.
Regarding the missing homework solutions, I considered requesting written solutions to the tasks we failed to look at in class. However, this kind of exercise does not benefit from just solutions and instead requires explanations.