MU:MU24027 Partial Differential Equations - Course Information
MU24027 Partial Differential Equations I
Mathematical Institute in OpavaSummer 2016
- Extent and Intensity
- 2/2/0. 2 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Jana Kopfová, Ph.D. (lecturer)
doc. RNDr. Jana Kopfová, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Jana Kopfová, Ph.D.
Mathematical Institute in Opava - 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
- Applied Mathematics (programme MU, N1101)
- Course objectives (in Czech)
- PDR sú v istom zmysle vyvrcholením matematickej analýzy, uplatňujú sa tu výsledky z integrálneho a diferenciálneho počtu, algebry, geometrie, komplexnej analýzy. Prednáška je prehĺadom klasických výsledkov a metód z PDR, budeme sa zaoberať rovnicami prvého a druhého rádu.
- Syllabus
- 1.Basic notations and definitions. Some known equations. Well posed problems. Generalized solutions. Short history of PDEs
2.PDE's of first order. Cauchy problem. Characteristic ordinary differential equations. Homogenized linear equations of first order . Quasilinear equations. Nonlinear equations of first order. Plane elements. Monge cone
3.Cauchy initial problem. Cauchy-Kowalewska theorem. Generalized Cauchy problem. Characteristics
4.Classification of equations of second order. Linear PDE's with constant coefficients. Linear PDE's of second order: reduction to the canonical form
5.Parabolic equations. Derivation of the physical model. Correctly stated boundary value problems. Cauchy problem: fundamental solution; existence and uniqueness theorem. Maximum principle
Fourier method. Boundary value problems for parabolic equations. Hyperbolic equations. The Laplace equation on a circle
6.Hyperbolic equations. Method of characteristics. D'Alembert formula. Hyperbolic equations on a halfline and on a finite interval. Three-dimensional wave equation. Riemann method for the Cauchy problem. Riemann formula
7.Elliptic equations. Laplace equation. Poisson equation. Physical motivation. Harmonic functions. Symmetric solutions. Maximum principle. Uniqueness of solutions
- 1.Basic notations and definitions. Some known equations. Well posed problems. Generalized solutions. Short history of PDEs
- Literature
- recommended literature
- V. I. Averbuch. Partial differential equations. MÚ SU, Opava. info
- Jan Franců. Parciální diferenciální rovnice. Brno, 1998. info
- L. C. Evans. Partial diferential equations. 1998. info
- M. Renardy, R. C. Rogers. An introduction to partial differential equations. New York, 1993. info
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Enrolment Statistics (Summer 2016, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2016/MU24027