Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MTH310
Module Title: Functional Analysis
Module Level: Level 3
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: MTH118
   
Aims
To introduce the theory of infinite-dimensional normed vector spaces, the linear mappings between them.
Learning outcomes 
A. Work effectively with the notions of metric, normed and inner product spaces.

B. State and prove theorems about Banach spaces and Hilbert spaces.

C. State and prove fundamental results about bounded linear operators and self-adjoint operators.

D. Apply the essential concepts and theorems of functional analysis to simple examples.


Method of teaching and learning 
This module will be delivered using formal lectures.
Syllabus 
Metric Spaces: Definition of Metric Spaces, Point Set Topology, Completion of Metric Spaces.


Normed and Banach Spaces: Definitions of Normed and Banach Spaces, Finite Dimensional Normed Spaces, Linear Operators,

Bounded and Continuous Linear Operators, Linear Functionals, Linear Functionals on Finite Dimensional Spaces.


Normed Spaces of Operators, Dual Space.


Inner Product and Hilbert Spaces: Definitions of Inner Product and Hilbert Spaces, Properties of Inner Product Spaces, Orthonormal Sets and Sequences.


Representation of functionals on Hilbert Spaces, Adjoint Operators.


Self-Adjoint, Unitary and normal Operators.


Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 52           98  150 

Assessment

Sequence Method % of Final Mark
1 Final Exam 85.00
2 Coursework 15.00

Module Catalogue generated from SITS CUT-OFF: 12/10/2019 12:11:45 AM