Functional Analysis (BSc)

6 EC

Semester 2, period 4, 5

5122FUAN6Y

Owner Bachelor Wiskunde
Coordinator prof. dr. Rob Stevenson
Part of Exchange Programme Faculty of Science, specialisation BSc Mathematics, year 1Bachelor Wiskunde, year 3Dubbele bachelor Wis- en Natuurkunde, year 3Bachelor Bèta-gamma, major Wiskunde, year 3Dubbele bachelor Wiskunde en Informatica, year 3

Course manual 2019/2020

Course content

Functional analysis concerns the analysis of linear spaces and mappings in infinite dimensional spaces. Other than in finite dimensional spaces the topology on these spaces plays a crucial role. So in this sense functional analysis can be viewed as a combination of linear algebra and analysis. The study of differential and integral equations has been the driving force in the development of the abstract functional analysis.

Study materials

Literature

  • Bryan P. Rynne and Martin A. Youngson, 'Linear Functional Analysis', 2nd Edition, Springer.

Objectives

  • The student is familiar with the concepts of normed linear spaces, inner product spaces, and their complete variants, being the Banach and Hilbert spaces, bounded linear mappings, and normed linear spaces of those, in particular dual spaces and reflexivity.
  • The student has knowledge of (orthogonal) bases and (orthogonal) projections in Hilbert spaces, adjoint operators, and the Riesz representation theorem,
  • The student understands the main theorems in functional analysis such as the Hahn-Banach extension theorem, the open mapping theorem, the closed graph theorem, and the uniform boundedness principle,
  • The student is familiar with the concepts of the spectrum of an operator, compact operators, and their spectral theory,
  • The student is able to solve elementary and more advanced exercises about all aforementioned concepts,
  • The student has been introduced to applications of functional analysis for solving integral and differential equations.

Teaching methods

  • Lecture
  • Self-study
  • Lectures
  • Exercise classes

Learning activities

Activiteit

Aantal uur

Lectures

26

Exercise classes

26

Mid-term exam

3

Final exam

 3

Self-study

110

Attendance

Programme's requirements concerning attendance (OER-B):

  • Each student is expected to actively participate in the course for which he/she is registered.
  • If a student can not be present due to personal circumstances with a compulsory part of the programme, he / she must report this as quickly as possible in writing to the relevant lecturer and study advisor.
  • It is not allowed to miss obligatory parts of the programme's component if there is no case of circumstances beyond one's control.
  • In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are stated in advance in the course manual and on Canvas.
  • In the first and second year, a student should be present in at least 80% of the seminars and tutor groups. Moreover, participation to midterm tests and obligatory homework is required. If the student does not comply with these obligations, the student is expelled from the resit of this course. In case of personal circumstances, as described in OER-A Article A-6.4, an other arrangement will be proposed in consultation with the study advisor.

Assessment

Item and weight Details

Final grade

1 (100%)

Tussentoets

Exact information  about the grading of this course can be found on https://staff.fnwi.uva.nl/r.p.stevenson/funcanal2020.html

Inspection of assessed work

The manner of inspection will be communicated via the lecturer's website.

Assignments

Exercises and other information can be found on the website: https://staff.fnwi.uva.nl/r.p.stevenson/funcanal2020.html 

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Weeknummer Onderwerpen Studiestof
1 Normed spaces   Ch. 1,2
2 Inner Product Spaces, Hilbert Spaces  Ch. 3
3 Linear Operators  Ch. 4
4 Linear Operators  Ch. 4
5 Linear Operators Ch. 4
6 Duality and the Hahn–Banach Theorem  Ch. 5
7 Duality and the Hahn–Banach Theorem  Ch. 5
8 Mid-term exam  
9 Duality and the Hahn–Banach Theorem  Ch. 5
10 Duality and the Hahn–Banach Theorem  Ch. 5
11 Linear Operators on Hilbert Spaces   Ch. 6
12 Compact Operators  Ch. 7
13 Integral and Differential Equations  Ch. 8
14 Integral and Differential Equations  Ch. 8
15 Zie website cursus  
16 Final exam  

Timetable

The schedule for this course is published on DataNose.

Honours information

There is no honours extension to this course.

Additional information

Recommended prerequisites: Linear algebra; Analysis 4; Topology; Measure Theory

Processed course evaluations

Below you will find the adjustments in the course design in response to the course evaluations.

Contact information

Coordinator

  • prof. dr. Rob Stevenson