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Real Analysis: Sequences and series of functions, uniform convergence, power series, Fourier series, Functions of several variables, maxima, minima, multiple integrals, line, surface and volume integrals, Green’s theorem, Gauss and Stoke’s theorem. Metric spaces, completeness, Weierstrass approximation theorem, compactness, Lebesgue measure, measurable functions, Lebesgue integrals, Fatou’s lemma, Dominated convergence theorem.