Taylor

the calculus of one real variable, assembled in logical order: limits, then continuity and its two workhorse theorems (ivt, evt), then the derivative and the mean value theorem, taylor’s theorem with an honest error bound, and finally the riemann integral and both parts of the fundamental theorem. everything downstream — multivariable calculus, differential equations, every convergence argument in machine learning — leans on the theorems here. proofs are given where they are short and instructive; the deferred foundations live in real analysis (Courant, Richard, 1996).