Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. P.D. Srivastava
NPTEL Co-ordinating Institute : IIT Kharagpur
NPTEL Lecture Count : 40
NPTEL Course Size : 19 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Metric Spaces with Examples
Lecture 2 - Holder Inequality and Minkowski Inequality
Lecture 3 - Various Concepts in a Metric Space
Lecture 4 - Separable Metrics Spaces with Examples
Lecture 5 - Convergence, Cauchy Sequence, Completeness
Lecture 6 - Examples of Complete and Incomplete Metric Spaces
Lecture 7 - Completion of Metric Spaces + Tutorial
Lecture 8 - Vector Spaces with Examples
Lecture 9 - Normed Spaces with Examples
Lecture 10 - Banach Spaces and Schauder Basic
Lecture 11 - Finite Dimensional Normed Spaces and Subspaces
Lecture 12 - Compactness of Metric/Normed Spaces
Lecture 13 - Linear Operators-definition and Examples
Lecture 14 - Bounded Linear Operators in a Normed Space
Lecture 15 - Bounded Linear Functionals in a Normed Space
Lecture 16 - Concept of Algebraic Dual and Reflexive Space
Lecture 17 - Dual Basis & Algebraic Reflexive Space
Lecture 18 - Dual Spaces with Examples
Lecture 19 - Tutorial - I
Lecture 20 - Tutorial - II
Lecture 21 - Inner Product & Hilbert Space
Lecture 22 - Further Properties of Inner Product Spaces
Lecture 23 - Projection Theorem, Orthonormal Sets and Sequences
Lecture 24 - Representation of Functionals on a Hilbert Spaces
Lecture 25 - Hilbert Adjoint Operator
Lecture 26 - Self Adjoint, Unitary & Normal Operators
Lecture 27 - Tutorial - III
Lecture 28 - Annihilator in an IPS
Lecture 29 - Total Orthonormal Sets And Sequences
Lecture 30 - Partially Ordered Set and Zorns Lemma
Lecture 31 - Hahn Banach Theorem for Real Vector Spaces
Lecture 32 - Hahn Banach Theorem for Complex V.S. & Normed Spaces
Lecture 33 - Baires Category & Uniform Boundedness Theorems
Lecture 34 - Open Mapping Theorem
Lecture 35 - Closed Graph Theorem
Lecture 36 - Adjoint Operator
Lecture 37 - Strong and Weak Convergence
Lecture 38 - Convergence of Sequence of Operators and Functionals
Lecture 39 - LP - Space
Lecture 40 - LP - Space (Continued.)