MAT-61007 Introduction to Functional Analysis, 5 cr
Additional information
Kurssin kotisivu on Moodlessa:
https://moodle2.tut.fi
Suitable for postgraduate studies.
Person responsible
Petteri Laakkonen
Lessons
| 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
| 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 |
Prerequisites
| 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