Those are practical courses, meant to prep for linear algebra and differential equations — and various STEM tracks. As I recall, there were some proofs (eg, limits showing derivative rules; limits showing sums for integral rules).
We covered all the proofs in real analysis 1 (derivatives; sequences) and 2 (integrals; measure).
1. Derivatives
2. Integrals
3. Applications — function approximation; solids of rotation; vectors; etc.
4. Multivariate — partial derivatives, multiple integrals, etc.
Glancing at a nearby community college’s course catalog, they have similar split.