Syllabus for |
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TMA401 - Functional analysis
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| Funktionalanalys |
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| Syllabus adopted 2019-02-22 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits
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| Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail |
| Education cycle: Second-cycle |
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Major subject: Mathematics
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: English
Application code: 20140
Open for exchange students: Yes
| Module |
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0101 |
Examination |
7,5 c |
Grading: TH |
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7,5 c
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28 Oct 2020 am J
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05 Jan 2021 pm J
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18 Aug 2021 am J
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In programs
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
Examiner:
Håkan Andreasson
Go to Course Homepage
Eligibility
General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
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 including compulsory elements
Written exam.