MU:MU03035 Partial Differential Eq. II - Course Information
MU03035 Partial Differential Equations II
Mathematical Institute in OpavaWinter 2007
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Guaranteed by
- doc. RNDr. Kristína Smítalová, CSc.
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
- Geometry (programme MU, M1101)
- Mathematical Analysis (programme MU, M1101)
- Mathematics (programme MU, B1101)
- Physics for Secondary School Teachers (programme FPF, M1701 Fyz)
- Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz) (2)
- Secondary School Teacher Training in Mathematics (programme FPF, M7504)
- Secondary school teacher training in general subjects with specialization in Mathematics (programme FPF, M7504)
- 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 úlohy nelineárnu).
- Syllabus (in Czech)
- 1.Elliptic equations. Potentials: volume potential, simple layer potential, double layer potential. Green formulas. Generalized Green formula. Harmonic functions: Dirichlet integral, Gauss integral theorem. Dirichlet problem and Neumann problem. Poisson formula
2.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. The Laplace transform
3.Modern methods of solving PDEs. Sobolev spaces. Generalized solutions. Lax-Milgram theorem
- 1.Elliptic equations. Potentials: volume potential, simple layer potential, double layer potential. Green formulas. Generalized Green formula. Harmonic functions: Dirichlet integral, Gauss integral theorem. Dirichlet problem and Neumann problem. Poisson formula
- Literature
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Enrolment Statistics (Winter 2007, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2007/MU03035