MAT-61256 Geometric Analysis, 7 cr
Lisätiedot
Moodle is used during the course
Suitable for postgraduate studies.
Ei toteuteta lukuvuonna 2016-2017.
Vastuuhenkilö
Sirkka-Liisa Eriksson
Opetus
| Toteutuskerta | Periodi | Vastuuhenkilö | Suoritusvaatimukset |
| MAT-61256 2016-01 | - |
Sirkka-Liisa Eriksson |
The final exam or two partial exams |
Osaamistavoitteet
After completion of the course the students knows the foundations of topological tools and differential calculus in Rn. The Student learn geometric algebras and their importance. The student is capable of applying them in geometric problems. The student knows the foundations of the analysis in higher dimensions using geometric algebras and the special case quaternions.
Sisältö
| Sisältö | Ydinsisältö | Täydentävä tietämys | Erityistietämys |
| 1. | Topological concepts and main results in R and in Rn. Continuous and differentiable functions. | ||
| 2. | Inverse function theorom and implicit function theerem. | Primitive functions | |
| 3. | Introduction to geometric algebras, quaternions and their basic elements scalars, vectors, bivectors and multivectors | ||
| 4. | Exterior product, contraction and geometric product and their geometric meaning. Calculation of vector derivatives and integrals using geometric algebras |
Ohjeita opiskelijalle osaamisen tasojen saavuttamiseksi
The grade of the course is based on the final exam or two partial exams. When the points for the final exam or the partial exams are 30% of the maximum, the grade of the course may be improved by bonus points collected from the instructed exercises and homework. The passing limit is 50% of the maximum. If the student is mastering the concepts, results, short proofs and examples type of problems the evaluation is 3. For the grade 4 the student should in addition to the previous level be able to independently apply theory more. For the grade 5 the student should independently deduce results, invent solutions and compare results more than in the previous levels.
Arvosteluasteikko:
Numerical evaluation scale (0-5)
Osasuoritukset:
Oppimateriaali
| Tyyppi | Nimi | Tekijä | ISBN | URL | Lisätiedot | Tenttimateriaali |
| Summary of lectures | Geometric Analysis | Eriksson | Yes | |||
| Summary of lectures | No |
Esitietovaatimukset
| Opintojakso | P/S | Selite |
| MAT-60206 Mathematical Analysis | Advisable |
Vastaavuudet
Opintojakso ei vastaan mitään toista opintojaksoa