## Real Analysis

Real Analysis. Instructor: Prof. S.H. Kulkarni, Department of Mathematics, IIT Madras. This course discusses the fundamental concepts in real analysis. Real number system and its order completeness, sequences and series of real numbers. Metric spaces: basic concepts, continuous functions, completeness, contraction mapping theorem, connectedness, intermediate value theorem, compactness, Heine-Borel theorem. Differentiation, Taylor's theorem, Riemann integral, improper integrals, sequences and series of functions, uniform convergence, power series, Weierstrass approximation theorem, equicontinuity, Arzela-Ascoli theorem.
(from **nptel.ac.in**)

Lecture 30 - Characterizations of Compact Sets |

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