It is a first level course on Functional Analysis. The motto is to familiarize the students with basic concepts, principles and methods of Functional analysis and its applications.
Course contents: Metric spaces with example, Complete metric spaces, Separable Metric Space, Compact sets, Normed & Banach spaces, Convergence, Bounded linear functionals and operators, Dual spaces, Refexive Spaces, Adjoint Operator, Inner Product Space and Hilbert Spaces with example, Projection theorem, Orthonormal sets and sequences, Total Orthonormal Sets, Riesz Representation theorem, Self adjoint, Unitary and Normal operators, Hilbert -Adjoint Operator, The Hahn Banach Extension theorem, Uniform boundedness theorem (The Banach Steinhaus theorem), Open mapping theorem and Closed graph theorem.