TATM85 · 6 credits · Advanced level (A1N) · Matematik, Tillämpad matematik

Functional Analysis

Active · next start HT 2026

100%

passed the latest regular sitting

UPG1 · 12 Dec 2025 · 12 students

100%

passed the regular sittings, all sittings over the last 5 years

UPG1 · 36 students

This module only reports passing results, so the pass rate does not show how many did not pass.

Part of 3 programmes

Master of Science in Applied Physics and Electrical Engineeringsemester 7 · period 1, 2 · compulsory
Master's Programme in Mathematicssemester 1 · period 1, 2 · compulsory
Master of Science in Engineering Mathematicssemester 7 · period 1, 2 · elective

Hand-in or lab

UPG1 Assignments

Main rounds

100% passed · 36 students

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Later rounds

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Get 4 or 5: 83% (36 students)

Show small sittings (36)

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About the course

Aim

To become familiar with the fundamental concepts of functional analysis and build a foundation for further studies in mathematics and related subjects. After successfully completing the course, one should:

Be aware of and be able to use basic concepts within the theory of metric and normed spaces, Banach spaces, Hilbert spaces, and dual spaces, as well as understand the logical relationships between them.
Be aware of and be able to use central theorems within the theory of the aforementioned spaces.
Be able to apply Banach's fixed-point theorem within the theory of differential equations and integral equations.
Be aware of and understand fundamental concepts within spectral theory for compact, self-adjoint operators.
Be able to use the Lebesgue integral and central theorems in integration theory to solve problems.

Content

Elementary metric space theory. Normed spaces, Banach spaces, Hilbert spaces. Linear functionals, dual spaces. Linear operators. Aspects of the Lebesgue integral. Integral equations. Introduction to spectral theory for compact, symmetric operators.

Examiner: Jana Björn
Scheduled hours: 60 h
Main field of study: Matematik, Tillämpad matematik

Syllabus on Studieinfo ↗