[thanatropism]

Check out Mattuck's Introduction to Analysis.

Analysis is basically "really rigorous calculus". Basic analysis courses are also usually where you learn to do proofs.

(To some reasonable generality "calculus" stands for "rules of manipulation", while analysis is the mathematical theory of calculus. So I can teach you stochastic calculus in a couple of two-hour sessions but understanding what the hell is going on (stochastic analysis) requires measure theory, some functional analysis and much courage)