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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, Not passed
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students
Block schedule: X

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0101 Examination 7,5c Grading: TH   7,5c   23 Oct 2013 am V,  18 Jan 2014 am V,  30 Aug 2014 am V

In programs

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

Examiner:

Univ lektor  Peter Kumlin



  Go to Course Homepage

Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

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.


Published: Mon 28 Nov 2016.