|
Week
|
Topics
|
Study Metarials
|
|
1
|
Set theory, metric spaces, complete metric spaces
|
R1. Section 1.1
|
|
2
|
Definition of norm and some basic theorems
|
R1. Section 2.1
|
|
3
|
Banach spaces
|
R1. Section 2.2
|
|
4
|
Finite dimensional spaces
|
R1. Section 2.3
|
|
5
|
Continuous and bounded linear operators
|
R1. Section 3.1
|
|
6
|
Dual space and operator norm
|
R1. Section 3.2
|
|
7
|
Hahn-Banach Theorem
|
R1. Section 3.3
|
|
8
|
Open mapping theorem, Closed graph theorem
|
R1. Section 3.4
|
|
9
|
Dual spaces
|
R1. Section 4.1
|
|
10
|
Dual operators, weak convergence
|
R1. Section 4.2
|
|
11
|
Inner product spaces
|
R1. Section 5.1
|
|
12
|
Orthogonality, Orthogonal complement
|
R1. Section 5.2
|
|
13
|
Hilbert spaces
|
R1. Section 6.1
|
|
14
|
Fourier series
|
R1. Section 7.1
|