Im a ChemE from a good school... U of DE. We had to take three high level calc classes, designed expressly for engineers and math majors (though others could take them... and of course most all didnt. These were significant classes, 4 credits each, had at least one meeting every day, so we were always busy doing calc! We then had to take a differential equations class on top of that, plus linear algebra and engineering math with matlab.
You really should have had calc I equivalent in HS, and at the bare minimum precalc. The math classes are a lot of hard work that takes a lot of time, so you need to get them out of the way as much as possible (and learn the stuff as much as possible as it helps you out a lot as you ge to advanced thermo and whatnot), at least the calc classes, before getting hot and havy into the actual engineering topics.
I would suggest you find the hardest calc classes and take them - if you have a choice, stay away from the calc for business majors - its easy but a waste of time. take the one for engineers and or math majors, as youll get better knowledge and less of the riff raff. Get calc I-III done, and maybe some prerequisites out of the way, so then you can really focus on your engineering stuff. DiffEQ was less intense for us then our calc III class, and linear alg. is relatively easy. However, they do take time awya from problem sets and whatnot, so get hem done ASAP also. If you can get a bunch of prereqs done in advance, then in the harder senesters you can lighten your load and excel easier... I wish Id have done that, so I didnt have to waste time in unrealted classeswhrn I had 10 more hours of problems to do...
JMH