MAT-61006 Introduction to Functional Analysis, 7 cr

Additional information

Kurssin kotisivu on Moodlessa:

https://moodle2.tut.fi
Suitable for postgraduate studies.

Person responsible

Lassi Paunonen

Lessons

Implementation Period Person responsible Requirements
MAT-61006 2016-01 1 - 2 Lassi Paunonen
Seppo Pohjolainen
Twomidterml exams during the course or final exam. Kaksi välikoetta tai tentti.

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

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 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   Fuctional Analysis in Applied Mathematics and Engineering   Pedersen Michael       Chapman& Hall 2000   No   
Summary of lectures   Introduction to Functional Analysis   Seppo Pohjolainen         Yes   
Summary of lectures   Johdatus funktionaalianalyysiin   Seppo Pohjolainen         No   

Additional information about prerequisites
Recommended prerequisite is BSc level mathematics major (or minor). Esitietoina suositellaan matematiikan pää tai sivuainetta kanditutkinnossa. Esitietoina suositellaan tekniikan kandidaatin matematiikan aineopintoja.



Correspondence of content

Course Corresponds course  Description 
MAT-61006 Introduction to Functional Analysis, 7 cr MAT-41146 Introduction to Functional Analysis, 7 cr  
MAT-61006 Introduction to Functional Analysis, 7 cr MAT-41140 Introduction to Functional Analysis, 7 cr  

Updated by: Suomela Kari, 27.05.2016