- Offered for Year: 2021/22
- Module Leader(s): Dr David Seifert
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
|
Semester 1 Credit Value:
|
10
|
|
ECTS Credits:
|
5.0
|
Aims
To introduce students to the basic ideas of functional analysis, an important area of research developed to study integral and differential equations. To introduce students to the notion of convergence and continuous transformations on vector spaces.
Module Summary
At the end of the last century, mathematicians began to realise that the methods used to solve differential equations are quite like those involved in solving simultaneous equations and they began to investigate this similarity and make it rigorous. Thus, this topic grew out of an attempt to provide a framework to explain phenomena in applied mathematics. One needs linear algebra to explain the matrix behaviour, and analysis to explain the calculus. The result is the concept of a Banach space, a place where we have vectors and a notion of size, and operators, which are like matrices. The course develops the general theory, stressing the similarities between vectors and matrices and the new ideas.
Outline Of Syllabus
Norms. Cauchy sequences, completeness, Banach and Hilbert spaces. Examples: l^p spaces, spaces of continuous functions, matrices. Bounded operators on Banach spaces and Hilbert spaces: operator norm, adjoints, inverses, the spectrum.
Teaching Methods
Teaching Activities
| Category |
Activity |
Number |
Length |
Student Hours |
Comment |
|---|
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | 2 Revision Lectures – Synchronous On-Line |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | 5 Problem Classes – Synchronous On-Line |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in course assessments |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | 14 Formal Lectures – Present in Person;
6 Formal Lectures – Synchronous On-line. |
| Guided Independent Study | Independent study | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
| Total | | | | 100:00 | |
Jointly Taught With
| Code |
Title |
|---|
| MAS8702 | Linear analysis |
Teaching Rationale And Relationship
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.
Assessment Methods
The format of resits will be determined by the Board of Examiners
Exams
| Description |
Length |
Semester |
When Set |
Percentage |
Comment |
|---|
| Written Examination | 120 | 1 | A | 80 | N/A |
Exam Pairings
| Module Code |
Module Title |
Semester |
Comment |
|---|
| MAS8702 | Linear analysis | 1 | N/A |
Other Assessment
| Description |
Semester |
When Set |
Percentage |
Comment |
|---|
| Prob solv exercises | 1 | M | 10 | N/A |
| Prof skill assessmnt | 1 | M | 10 | N/A |
Assessment Rationale And Relationship
AA substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.
In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.
Reading Lists
Timetable
