Are you going into math or engineering? Math majors are highly recommended to take the integrated theoretical series 2230-2240. They cover the topics in far more depth than you are likely to have done. Most students in those classes have also taken at least 2 semesters of calc and often more. They are considered demanding classes. In general, the registration system won’t stop you from registering for something beyond your abilities. However, you may be sorry. Engineers don’t need those math courses in as much depth and don’t really need so many of them, anyway.
http://www.math.cornell.edu/m/Courses/Catalog/lowerlevel.html
http://www.math.cornell.edu/m/Courses/Catalog/upperlevel.html