The text book we shall use is

Functinal Analysis, Sobolev Space and Partial Differential Equations by Haim Brezis, Springer. We shall cover:

Chapter 1 The Hahn-Banach Theorem .Introduction to Theory of Conjugate Convex

Functions.

Chapter 2 The uniform Boundedness Principleand the closed Graph Thoerem

Chapter 3 Weak Topologies. Reflexive Space, Separable Space, Uniform Convexity.

Chapter 3 L-p Space

Chapter 5 Hilbert Spaces

Chapter 6 Compact Operators, Spectral Decomposition of Self-Adjoint Compact

Operators

Chapter 7 The Hille-Yosida Theorem

Refertence:

Peter Lax : Functinal Analysis

Eberhard Zeidler : Applied Functional Analysis.

Grading Policy:

(i) Homework 40%

(ii) Midterm 30%

(iii) Final Exam.30%