Functional Analysis KYF9E9CA37

URI	`m2://res/KYF9E9CA37`
Kind	course
Creators	P.D. Srivastava (instructor)
Date	2012-06-19
Scope	in
Ids	course 03w5sq511:111105037

Expressions

e1: edition

Language	en
Date	2012-06-19

m1: page, IIT Kharagpur (record). nptel 111105037
m2: page, 2012-06-19 (record). nptel 111105037

Contents

part 1: Functional Analysis
session 1: Metric Spaces with Examples
session 2: Holder Inequality and Minkowski Inequality
session 3: Various Concepts in a Metric Space
session 4: Separable Metrics Spaces with Examples
session 5: Convergence, Cauchy Sequence, Completeness
session 6: Examples of Complete and Incomplete Metric Spaces
session 7: Completion of Metric Spaces + Tutorial
session 8: Vector Spaces with Examples
session 9: Normed Spaces with Examples
session 10: Banach Spaces and Schauder Basic
session 11: Finite Dimensional Normed Spaces and Subspaces
session 12: Compactness of Metric/Normed Spaces
session 13: Linear Operators-definition and Examples
session 14: Bounded Linear Operators in a Normed Space
session 15: Bounded Linear Functionals in a Normed Space
session 16: Concept of Algebraic Dual and Reflexive Space
session 17: Dual Basis & Algebraic Reflexive Space
session 18: Dual Spaces with Examples
session 19: Tutorial - I
session 20: Tutorial - II
session 21: Inner Product & Hilbert Space
session 22: Further Properties of Inner Product Spaces
session 23: Projection Theorem, Orthonormal Sets and Sequences
session 24: Representation of Functionals on a Hilbert Spaces
session 25: Hilbert Adjoint Operator
session 26: Self Adjoint, Unitary & Normal Operators
session 27: Tutorial - III
session 28: Annihilator in an IPS
session 29: Total Orthonormal Sets And Sequences
session 30: Partially Ordered Set and Zorns Lemma
session 31: Hahn Banach Theorem for Real Vector Spaces
session 32: Hahn Banach Theorem for Complex V.S. & Normed Spaces
session 33: Baires Category & Uniform Boundedness Theorems
session 34: Open Mapping Theorem
session 35: Closed Graph Theorem
session 36: Adjoint Operator
session 37: Strong and Weak Convergence
session 38: Convergence of Sequence of Operators and Functionals
session 39: LP - Space
session 40: LP - Space (Contd.)

Catalogue records

nptel: 111105037 (manifestation)
nptel_video: 111105037 (manifestation)