Functional Analysis is a fundamental course arising from Partial Differential Equations, Optimization ,Control Theory and many other applications. The purpose of this course is give student solid training in analysis. We shall focus on linear functional analysis in the first semester and then nonlinear analysis on the second semester.
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
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

Chapter 7 The Hille-Yosida Theorem

Peter Lax : Functinal Analysis
Eberhard Zeidler : Applied Functional Analysis.

Grading Policy:

(i) Homework 40%
(ii) Midterm 30%
(iii) Final Exam.30%