Course code

MLM7001.DT

old course code

MLM7001

Course title in Estonian

Funktsionaalanalüüs

Course title in English

Functional Analysis

ECTS credits

5.0

Assessment form

Examination

lecturer of 2023/2024 Spring semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

lecturer of 2024/2025 Autumn semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

Course aims

Core subject of the master level mathematics programme. The course completes and generalizes the series of courses in mathematical analysis and looks at the earlier courses from a unified point of view. The main idea of the course is to provide students with basic knowledge in the theory of metric and normed spaces and continuous operators.

Brief description of the course

Metric spaces. Continuous operators in metric spaces. Complete metric space. Banachs fixed point theorem and its applications. Normed space. Banach space. Linear continuous operators in normed spaces. Limit, derivative and integral of a function as linear continuous operators. Main theorems of linear functional analysis: uniform boundedness principle, open mapping principle, Hahn-Banach extension principle.

Learning outcomes in the course

Upon completing the course the student:
Student knows mathematical facts and is able to use methods in volume of the subject.

Teacher

prof Anne Tali

The course is a prerequisite

Study programmes containing that course

Teacher of Mathematics (MLMOM/15.DT)
Teacher of Mathematics (MLMOM/14.DT)
Mathematics (MLMM/14.DT)
Teacher of Mathematics (MLMOM/13.DT)
Mathematics (MLMM/13.DT)
Teacher of Mathematics (MLMOM/12.DT)
Mathematics (MLMM/12.DT)
Teacher of Mathematics (MLMOM/11.DT)
Mathematics (MLMM/11.DT)
Mathematics (MLMM/10.DT)
Teacher of Mathematics (MLMOM/10.DT)