Module Code :

MA4211

IVLE

Module Title : 
Functional Analysis 
Module Description : 
This course is for students who are majors in pure mathematics or who need functional analysis in their applied mathematics courses. The objective of the module is to study linear mappings defined on Banach spaces and Hilbert spaces, especially linear functionals (realvalued mappings) on L(p), C[0,1] and some sequence spaces. In particular, the four big theorems in functional analysis, namely, HahnBanach theorem, uniform boundedness theorem, open mapping theorem and BanachSteinhaus theorem will be covered.
Major topics: Normed linear spaces and Banach spaces. Bounded linear operators and continuous linear functionals. Dual spaces. Reflexivity. HanhBanach Theorem. Open Mapping Theorem. Uniform Boundedness Principle. BanachSteinhaus Theorem. The classical Banach spaces : c0, lp, Lp, C(K). Compact operators. Inner product spaces and Hilbert spaces. Orthonormal bases. Orthogonal complements and direct sums. Riesz Representation Theorem. Adjoint operators. 
Module Examinable : 


Exam Date : 
02052018 EVENING

Modular Credits : 
4 
Prerequisite : 
MA3207H or MA3209 
Preclusion : 
Nil 
Module Workload (ABCDE)* : 
31006 
Remarks : 
Nil 
* 
A: no. of lecture hours per week
B: no. of tutorial hours per week
C: no. of laboratory hours per week
D: no. of hours for projects, assignments, fieldwork etc per week
E: no. of hours for preparatory work by a student per week
 
Class  Type  Week Type  Week Day  Start  End  Room 
SL1  LECTURE  EVERY WEEK  TUESDAY  1000  1200  S140619,

SL1  LECTURE  EVERY WEEK  FRIDAY  1000  1200  S140619,


Class  Type  Week Type  Week Day  Start  End  Room 
Iteration 
T01  TUTORIAL  EVERY WEEK  THURSDAY  1300  1400  S170405,

Available in Tutorial Balloting [Iteration 2].


