MATH 3243

MATH 3243 (Advanced Calculus). This course is a rigorous undergraduate introduction to analysis. Topics include the Completeness Axiom and applications, sequences and series, the Bolzano-Weierstrass Theorem, Cauchy sequences; basic topology of the real line, open sets, closed sets, and compact sets; functional limits and continuity; algebra of continuous functions; the Extreme Value Theorem; the Intermediate Value Theorem; the derivative; the Mean Value Theorem; Uniform Convergence and its relation to differentiation; series of functions; the Riemann integral; and the Fundamental Theorem of Calculus

The course meets three class hours per week.