Mathematics · Avançado · Nível 3

Real analysis I

The completeness of the real numbers — suprema, the approximation property, the Archimedean property and density, and estimating with the triangle inequality; sequences, from the epsilon-N definition through the algebra of limits, monotone convergence, Bolzano-Weierstrass and the Cauchy criterion, and then series and the tests that settle them; limits of functions and continuity, with the intermediate and extreme value theorems and uniform continuity; differentiation, the mean value theorem and what it settles, and Taylor's theorem with remainder; the Riemann integral by Darboux sums, which functions are integrable, and the fundamental theorem; and sequences of functions, where pointwise convergence keeps almost nothing and uniform convergence keeps continuity, the integral and — with care — the derivative.

Ages 18+ 28 lessons about 11 hours in all

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