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.
<br>   The text book we shall use is 
<br>     Functinal Analysis, Sobolev Space and Partial Differential Equations by Haim Brezis, Springer. We shall cover:
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<br>Chapter 1 The Hahn-Banach Theorem .Introduction to Theory of Conjugate Convex
<br>          Functions.
<br>Chapter 2 The uniform Boundedness Principleand the closed Graph Thoerem
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<br>Chapter 3 Weak Topologies. Reflexive Space, Separable Space, Uniform Convexity.
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<br>Chapter 3 L-p Space
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<br>Chapter 5  Hilbert Spaces
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<br>Chapter 6  Compact Operators, Spectral Decomposition of Self-Adjoint Compact 
<br>           Operators
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<br>Chapter 7 The Hille-Yosida Theorem
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<br>Refertence:
<br>   Peter Lax : Functinal Analysis
<br>   Eberhard Zeidler : Applied Functional Analysis.
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<br>Grading Policy:
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<br>   (i) Homework 40%
<br>   (ii) Midterm 30%
<br>    (iii) Final Exam.30%