MAT-61007 Introduction to Functional Analysis, 5 cr

Additional information

Kurssin kotisivu on Moodlessa:
Suitable for postgraduate studies.

Person responsible

Petteri Laakkonen


Implementation Period Person responsible Requirements
MAT-61007 2019-01 3 Petteri Laakkonen
Final examination and exercise activity.

Learning Outcomes

After passing the course the student - understands how mathematical analysis has developed recently. - knows the basic concepts of modern analysis and is able to operate with them. - is able to prove the most important theorems. - can apply the knowledge e.g. in solving integral equations.


Content Core content Complementary knowledge Specialist knowledge
1. Metric spaces and its properties. Continuous functions. Cauchy- sequences and completion of spaces. Fixed point theorem.     
2. General vector spaces and normed spaces. Basics of Banach spaces and operator theory in Banach spaces.      
3. Basics of Hilbert spaces. Operator theory in Hilbert spaces. Minimum norm theorem and Riesz reperesentation theorem.     
4. Spectral theory, especially for compact self-adjoint operators.     
5. Applications to integral equations.     

Instructions for students on how to achieve the learning outcomes

Two midterm exams during the course or final exam. Kaksi välikoetta tai tentti.

Assessment scale:

Numerical evaluation scale (0-5)

Study material

Type Name Author ISBN URL Additional information Examination material
Book   Functional Analysis in Applied Mathematics and Engineering   Michael Pedersen       Chapman & Hall 2000   No   
Summary of lectures   Introduction to Functional Analysis   Seppo Pohjolainen & Lassi Paunonen         Yes   


Course Mandatory/Advisable Description
MAT-60000 Matriisilaskenta Mandatory   1
MAT-60006 Matrix Algebra Mandatory   1
MAT-60100 Kompleksimuuttujan funktiot Mandatory   2
MAT-60106 Complex Analysis Mandatory   2
MAT-60206 Mathematical Analysis Advisable    

1 . Matriisilaskenta

2 . Kompleksimuuttujan funktiot

Additional information about prerequisites
Recommended prerequisite is BSc level mathematics major (or minor) (the course is inteded for students in Master's programs). Esitietoina suositellaan matematiikan pää tai sivuainetta kanditutkinnossa (kurssi on pääosin tarkoitettu maisterivaiheen opiskelijoille). Esitietoina suositellaan tekniikan kandidaatin matematiikan aineopintoja.

Correspondence of content

There is no equivalence with any other courses

Updated by: Kunnari Jaana, 05.03.2019