[kragen]

When I studied the equivalents of calc 1 and 2 (from a textbook), the textbook proved everything, although somewhat informally. I mean, with epsilons and deltas and everything, but with a lot more prose than you see in a math paper on arXiv. The different textbook I later used for calc 3, which I actually did take a class in, also proved everything. As did the professor, in class, on the blackboard. I basically never read the book or did any of the homework for that class; I just rederived things from first principles during the exams, based on my memories of the lectures. I always finished the exams last, but I got an A in the class. This was all in the US. My father's calculus textbook, from which I'd learned calculus to start with, was also from his calculus courses in the US.

I take it my experience was atypical?

[bradleyjg]

No in many US universities rigorous calculus proofs are saved for a class called something like Real Analysis which is typically take as the 4th or 5th class for a math major.

Compare e.g.

Transcendental functions, techniques and applications of integration, indeterminate forms, improper integrals, infinite series.

with

Algebraic and topological structure of the real number system; rigorous development of one-variable calculus including continuous, differentiable, and Riemann integrable functions and the Fundamental Theorem of Calculus; uniform convergence of a sequence of functions; contributions of Newton, Leibniz, Cauchy, Riemann, and Weierstrass.

[RegEx]

Professors at my university do prove things in the classes I mentioned above, but I was attempting to make a distinction between courses where the emphasis is the proof(Abstract/Contemporary algebra) and courses where the emphasis is the process (Matrix methods). Sorry for any confusion.