Home »Mathematics »IIT Kharagpur » Functional Analysis

Functional Analysis

Lecture 1: Mod-01 Lec-01 Metric Spaces with Examples

Download:   mp3 download MP4,FLV & 3GP 16792 views

SEE: Guide to Download NPTEL Video Lecture

Lecture Details :

Functional Analysis by Prof. P.D. Srivastava, Department of Mathematics, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

Metric Spaces : Metric spaces with examples,Holder inequality & Minkowski inequality,Various concepts in a metric space,Separable metric space with examples,Convergence, Cauchy sequence , Completeness,Examples of Complete & Incomplete metric spaces,Completion of Metric spaces +Tutorial,Vector spaces with examples

Normed / Banach Spaces : Normed Spaces with examples,Banach Spaces & Schauder Basis,Finite Dimensional Normed Spaces & Subspaces,Compactness of Metric/Normed spaces,Linear Operators-definition & examples,Bounded linear operators in a Normed Space,Bounded linear Functionals in a Normed space,Concept of Algebraic Dual & Reflexive space,Dual Basis & Algebraic Reflexive Space,Dual spaces with examples,Tutorial

Inner-Product Space & Hilbert Space : Inner Product & Hilbert space,Further properties of Inner product spaces,Projection Theorem & Orthonormal Sets & Sequences,Representation of functionals on a Hilbert Spaces,Hilbert Adjoint Operator,Self Adjoint, Unitary & normal Operators,Tutorial,Annihilator in an IPS,Total Orthonormal Sets & Sequences

Fundamental Theorems for Normed & Banach Spaces : Partially Ordered Set & Zornís Lemma,Hahn Banach Theorem for Real Vector Spaces,Hahn Banach Theorem for Complex V.S. & Normed Spaces,Baireís Category & Uniform Boundedness Theorems,Open Mapping Theorem,Closed Graph Theorem,Adjoint Operator,Strong & Weak Convergence,Convergence of Sequence of Operators & Functionals,Tutorial,Banach Fixed Point Theorem

Questions & Worked out answers : Problems on Metric Spaces,Problems on Normed & Banach Spaces,Problems on IPS & Hilbert Spaces - Assignment Sheet & Cumulative Question Papers

Other Resources :

Syllabus | Handouts | Citation |

Other Mathematics Courses

» check out the complete list of Mathematics Video lectures          


Get Your Degree!

Find schools and get information on the program that’s right for you.

Powered by Campus Explorer


Post your Comments