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MTH-101.4 Real Analysis

Review of Number System: Dedekinds cut; Topology of ℝ: Weierstrass theorem, Heine-Borel theorem, connectedness, series and sequences, continuous and differentiable functions, mean value theorems and their consequences, maxima, minima and curve tracing, functions of bounded variation, Riemann integration, Riemann-Stieltjes integration in ℝ.

Sequences of functions, uniform convergence, Ascoli-Arzela Theorem, functions of several variables, continuity, differentiation – directional derivatives and Frechet derivatives, mean value theorems, maxima, minima, inverse and implicit function theorems.