What should I do when teaching maths for unmotivated undergraduate students? After completing my Phd in an area in pure Maths and going back to my country, I got a job as a math lecturer at a university, where maths is not the main subject for students there. Maths is like school swimming subject that every student at my university has to learn before moving on to other subjects. 

I usually teach 35 hours/week. That sounds a bit crazy for many people, but it is normal here when you are living in a small country with a big population. I love doing reaseach. Spending time quitely, reading papers of other mathematicians, taking note, enjoying the findings, these were what I used to have during my Phd in support from a scholarship. 

The problem is that, I am now teaching students who are really unmotivated. It is understandable because maths is not their main concern.  Even though Maths here is quite basic, for example calculus or linear algebra, it seems that it is a big deal for them. The students always feel like they are forced to learn unnecessary, difficult stuff. So their reaction is to almost ignore the subject. They go to class, sleep or talk, and let whatever happens to their exams for the future. It is quite stressful to teach these students. I admit that many maths stuff like, surface integrals or Green formula, are really hard to teach  for this kind of students. Because they don't like to hear or know how should a theorem be true. On the other hand, if you just tell them that well! this is a theorem, let's imagine it was true and use it. Then the situation isn't better either. Of course, I am not in a position to determine what I have to teach, what not. All the given content in a subject should be taught for students during the course. 

These things are bothering me and take me a lot of time. The students may complain if they don't like me. So I should focus on my teaching duty. However, it is killing me since I cannot have time for my reserach. At the end of the day, I am exhausted and feel guity because I have done nothing.

My question: do we have any way or tricks to teach unmotivated students to make them feel easy, feel smart, so they don't complain, but in the same time we don't spend total energy for the teaching? If I run my work properly, I still have time and mental energy for my reaseach.

Any suggestions, even small, would extremely be appreciated.
Start each session with a quiz.  Have students exchange papers to grade.  Have full hour tests every 1-2 weeks.  Do lots of in class exercises that students work on.  (Put the animals to work.)

Emphasize calculations and problem solving.  Not theorems.

Emphasize efficiency in terms of grading exams.

Follow the text closely and spend minimal time on your lecture prep.