MTL411: Difference between revisions
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| credits = 3 | | credits = 3 | ||
| credit_structure = 3-0-0 | | credit_structure = 3-0-0 | ||
| pre_requisites = MTL104 and MTL122 | | pre_requisites = [[MTL104]] and [[MTL122]] | ||
| overlaps = MTL602 | | overlaps = [[MTL602]] | ||
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== MTL411 : Functional Analysis == | == MTL411 : Functional Analysis == | ||
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. | 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. | ||
Latest revision as of 16:42, 14 April 2026
| MTL411 | |
|---|---|
| Functional Analysis | |
| Credits | 3 |
| Structure | 3-0-0 |
| Pre-requisites | MTL104 and MTL122 |
| Overlaps | MTL602 |
MTL411 : Functional Analysis
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.