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 |