/sci/ - Science & Math

>>10641420

What do your various undergrad calc/analysis courses contain?
I see people say that rigor is often spared until later years, so what is left out?
So far we've had to study proofs of most theorems with a few exceptions like the intermediate and extreme value theorems.
In middle of junior year doing engineering physics, here's my calc so far:

>"Introductory mathematical analysis"
>High school reminders like trig&polynomials
>Semi-serious construction of integers, rationals and reals (proof of basic properties was considered too tedious)
>Induction
>Limits and continuity with ε-δ
>Differentiation and antidifferentiation
>The Riemann integral
>Relevant theorems for proof of FTC
>Generalized integrals

>"Real analysis"
>Linear and Euler differential equations
>Taylor polynomials and representations of the rest term
>L'Hospital
>Difference equations
>Iteration, Newton-Raphson
>Banach fixed-point theorem
>Series and convergence tests (integral, direct and limit comparison, ratio and root)
>Absolute convergence, alternating series and Leibniz criterion
>Power series, Taylor series and radius of convergence
>Function sequences and series
>Pointwise vs. uniform convergence
>Uniform limit, limits under integral sign, M-test (Currently here in the course)
>Dominated convergence, changing order of limits
>Sets in R^n
>Limits and continuity for functions of multiple variables

Further courses are multivariable, complex and Fourier analysis.