1. Be as excited as you can be. Rigorous argument is not necessarily the most enthralling of things, but people pick up on whether you care about something and that can make a big difference in their opinion of the topic.
This is so important. My precalc instructor was boring AF and I remember none of it. My DiffEQ instructor got so carried away that the prof next door would come over and tell him to stop banging on the chalkboard. As a result, I think DiffEQ is the fundamental magic that makes the world go 'round.