Math 382 (Real Analysis I)

Basic properties of the field of real numbers, completeness axiom, countable sets. Sequences and their convergence, monotone sequence, Bolzano-Weierstrass theorem, Cauchy criterion. Basic topological properties of the real numbers. Limit of a function, continuous functions and properties of continuity, uniform continuity, compact sets. The derivative of a function, mean value theorem, L'Hospital rule, Taylor theorem