MU:MU03035 Partial Differential Eq. II - Course Information
MU03035 Partial Differential Equations II
Mathematical Institute in OpavaWinter 2015
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Guaranteed by
- doc. RNDr. Jana Kopfová, Ph.D.
Mathematical Institute in Opava - Prerequisites (in Czech)
- MU02037 Partial Differential Equations
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Mathematical Analysis (programme MU, M1101)
- Mathematics (programme MU, B1101)
- Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
- Course objectives (in Czech)
- Prednáška je úvodom do modernej teórie PDR, teórie, ktorá sa zaoberá PDR pre ktoré klasické riešenia neexistujú ( pretože napríklad dáta úlohy nie sú hladké, alebo úlohu riešime na komplikovanej oblasti, alebo ide o úlohu nelineárnu).
- Syllabus
- 1.Elements of distribution theory. Test functions. Decomposition of the unity. Localization. Support. Regular and singular distributions. Operations over distributions. Convolution. Method of integral transforms. The Fourier transform.
2.Elliptic equations. Potentials: volume potential, simple layer potential, double layer potential. Green formulas. Generalized Green formula. Harmonic functions. Dirichlet problem and Neumann problem.
Poisson formula. Maximum principle
3.Modern methods of solving PDEs. Sobolev spaces. Sobolev imbeddings Theorems. Generalized solutions. Lax-Milgram theorem. Weak and variational formulation.
- 1.Elements of distribution theory. Test functions. Decomposition of the unity. Localization. Support. Regular and singular distributions. Operations over distributions. Convolution. Method of integral transforms. The Fourier transform.
- Literature
- recommended literature
- V. I. Averbuch. Partial differential equations. MÚ SU, Opava. info
- J. Franců. Moderní metody řešení diferenciálních rovnic. Brno, 2002. info
- R. Strichartz. A guide to distribution theory and Fourier transforms. 1994. info
- M. Renardy, R. C. Rogers. An introduction to partial differential equations. New York, 1993. info
- C. Zuily. Problems in distributions and partial differential equations. 1988. info
- D. Gilbarg, N. S. Trudinger. Elliptic partial differential equations of second order. Second edition. Springer, Berlin, 1983. info
- L. Schwartz. Matematické metody ve fyzice. Státní nakladatelství technické literatury, Prah, 1972. info
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Enrolment Statistics (Winter 2015, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2015/MU03035