Course No.：S070100XJ011
Course Category：Basics course of subject
Period/Credits： 40/2
Prerequisites：undergraduate real analysis or permission of the instructor.
Aims & Requirements：
This is a first-year course for all incoming Master students interested in pursuing research in applied mathematics or analysis and PDEs.
Primary Coverage：
The class will cover the following topics: Hilbert Spaces, Banach Spaces, Finite Dimensional Spaces, Quotients and Products Spaces, Riesz Representation Theorem, Hahn-Banach Theorem and its Geometric Consequence, Open Mapping and Closed Graph Theorems, Principle of Uniform Boundedness, Locally Convex Spaces, Metrizable and Normable Locally Convex Spaces, Weak Topologies, Alaoglu’s Theorem, Krein-Milman Theorem, Reflexive Spaces, Compact Operators, Fredholm Operators, Bananch Algebras and Spectral Theory for Operators on a Banach Space, Riesz-Schauder theory. Secondary topics that we will cover only briefly will be current variational techniques and then find a variety of applications in PDEs.
Textbook：
A Course in Functional Analysis, J.B.Conway GTM96,Springer-Verlag, 2nd Ed.1989.
Author：Yijing Sun (School of Mathematical Sciences, GUCAS)
Date：June, 2009
