MTL503: Real Analysis

4 Credits (3-1-0)

Elementary set theory, Countable and Uncountable sets, Real number system and its order completeness.

Metric spaces, Continuous and uniformly continuous functions, Homeomorphism and isometry, Completeness, Fixed Points, Baire’s Category Theorem, Totally bounded metrics, Compactness, Connectedness.

Sequences and series of functions, Pointwise and uniform convergence of sequences of functions, Equicontinuity, Arzelà-Ascoli Theorem, Dini’s Theorem, Stone-Weierstrass Theorems (Lattice and algebra versions).

Functions of several variables, Linear transformations, Differentiation, Inverse function theorem, Implicit Function theorem, Derivatives of higher order