Credits: 3 (3-0-0)
Prerequisites: MTL104 and MTL122
Overlaps with: MTL602
Description
Review of some basic concepts in metric spaces and topological spaces; Normed linear spaces and Banach spaces, Examples of Banach spaces, Bounded linear operators and examples, Finite dimensional Banach spaces; Introduction of Lebesgue integration on real line, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem, Lp spaces; Hahn Banach extension theorem, Hahn Banach separation theorem, Uniform boundedness principle, Open mapping theorem, Closed graph theorem; Characterization of dual of certain concrete Banach spaces; Schauder basis and separability, Reflexive Banach spaces, Best approximation in Banach spaces; Hilbert spaces and their geometry; Basic operator theory.
Prerequisite Tree
flowchart TD
MTL411-614[MTL411]
MTL122-614 --> MTL100-614[MTL100]
MTL411-614 --> MTL122-614[MTL122]
MTL104-614 --> MTL101-614[MTL101]
MTL411-614 --> MTL104-614[MTL104]
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