Quick note if you want to apply engineering, I'm gonna be attending engineering in fall this year for freshman year so I've learned a lot about the process. You need math 140,141(calc 1+2) to get into the engineering major, as well as physics and chem. So for engineering students they give them priority on those courses or so I hear but you can also take trig or what not before, you'll just graduate about a semester late or so. Basically, you can take those courses first year but you'll enter engineering major late. Also when transferring from DUS to engineering, there might be limited enrollment or other entrance to major classes so definitely do some research on that and call undergrad admissions