Search course

Use the search function to find more information about the study programmes and courses available at Chalmers. When there is a course homepage, a house symbol is shown that leads to this page.

Graduate courses

Departments' graduate courses for PhD-students.

​​​​
​​

Syllabus for

Academic year
TMA401 - Functional analysis  
 
Syllabus adopted 2012-02-22 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0101 Examination 7,5c Grading: TH   7,5c   25 Oct 2017 am SB,  04 Jan 2018 pm SB   01 Sep 2018 am SB_MU  

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory)
MPPAS PHYSICS AND ASTRONOMY, MSC PROGR, Year 2 (elective)

Examiner:

Univ lektor  Peter Kumlin



  Go to Course Homepage

Eligibility:


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Linear algebra and multivariable analysis.

Aim

To introduce functional analysis, a fundamental tool for i.e. ordinary and differential equations, mathematical statistics and numerical analysis.

Learning outcomes (after completion of the course the student should be able to)

-State and explain the concepts vector space, normed space, Banach and Hilbert space
-State and explain the theory for linear operators on Hilbert spaces in particular for compact and self-adjoint operators.
-Apply the spectral theorem for compact, self-adjoint operators.
-Apply fixed point theorems to differential- and integral equations.
-Communicate, both in writing and orally, the logical connections between the different concepts that appear in the course.

Content

Normed Spaces. Banach and Hilbert Spaces. Basics facts on Lebesgue Integrals. Contractions. Fixed Point Theorems.
Compactness. Operators on Hilbert Spaces. Spectral Theory for
Compact Self Adjoint Operators. Fredholm's Alternative. Applications to Integral and Differential Equations. Sturm-Liouville theory.

Organisation

See the course homepage.

Literature

L.Debnath/P.Mikusinski: Introduction to HilbertSpaces with
Applications, 2nd ed, Academic Press 1999.


P.Kumlin: Lecture Notes  (see the course homepage)

Examination

Written exam.


Page manager Published: Thu 04 Feb 2021.