MAT-61006 Introduction to Functional Analysis, 7 cr
Lisätiedot
Kurssin kotisivu on Moodlessa:
https://moodle2.tut.fi
Suitable for postgraduate studies.
Vastuuhenkilö
Lassi Paunonen
Opetus
| Toteutuskerta | Periodi | Vastuuhenkilö | Suoritusvaatimukset |
| MAT-61006 2017-01 | 1 - 2 |
Lassi Paunonen |
Twomidterml exams during the course or final exam. Kaksi välikoetta tai tentti. |
Osaamistavoitteet
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.
Sisältö
| Sisältö | Ydinsisältö | Täydentävä tietämys | Erityistietämys |
| 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. |
Ohjeita opiskelijalle osaamisen tasojen saavuttamiseksi
Two midterm during the course or final exam. Kaksi välikoetta tai tentti.
Arvosteluasteikko:
Numerical evaluation scale (0-5)
Oppimateriaali
| Tyyppi | Nimi | Tekijä | ISBN | URL | Lisätiedot | Tenttimateriaali |
| Book | Fuctional Analysis in Applied Mathematics and Engineering | Pedersen Michael | Chapman& Hall 2000 | No | ||
| Summary of lectures | Introduction to Functional Analysis | Seppo Pohjolainen and Lassi Paunonen | Yes |
Tietoa esitietovaatimuksista
Recommended prerequisite is BSc level mathematics major (or minor).
Esitietoina suositellaan matematiikan pää tai sivuainetta kanditutkinnossa.
Esitietoina suositellaan tekniikan kandidaatin matematiikan aineopintoja.
Vastaavuudet
| Opintojakso | Vastaa opintojaksoa | Selite |
| 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 |