Real Analysis II

Topics covered include: Continuous functions by the epsilon-delta definition, topological characterization of continuity, continuity and compactness, fixed points, uniform continuity, Lipschitz functions, monotone functions and discontinuities, construction of monotone functions with prescribed discontinuities, inverse functions, derivatives, Rolle’s theorem, mean value theorem, Cauchy mean value theorem with their proofs and applications, inverse function theorem, proof of L’Hospital’s rule, upper and lower sums of the Riemann integral, integrability of continuous and monotone functions, Lebesgue theorem, properties of the Riemann integral and fundamental theorem of calculus, uniform convergence and continuity. Credit cannot be held for both this course and 62:330.