MU03035 Partial Differential Equations II

Mathematical Institute in Opava
Winter 2023
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jana Kopfová, Ph.D. (lecturer)
RNDr. Petra Nábělková, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jana Kopfová, Ph.D.
Mathematical Institute in Opava
Timetable
Thu 11:25–13:00 108
  • Timetable of Seminar Groups:
MU03035/01: Mon 11:25–13:00 R1, P. Nábělková
Prerequisites (in Czech)
MU02037 Partial Differential Eq. I && TYP_STUDIA ( N )
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
Course objectives
The lectures will be an introduction into the modern theory of Partial differential equations. The aim is to be able to deal with equations, whose classical solutions does not exists (because the data are not smooth enough, the region on which the problem is posted is too complicated, or the equation is nonlinear).
Syllabus
  • 1. Elements of distribution theory.
    2. Modern methods of solving PDEs - motivation and introduction.
    3. Sobolev spaces. Sobolev imbeddings Theorems.
    4. Generalized solutions. Lax-Milgram Theorem. Weak and variational formulation.
    5. Numerical solutions of partial differential equations, Galerkin's method.
    6. Fourier's and Laplace transformation
Literature
    required literature
  • J. Franců. Moderní metody řešení diferenciálních rovnic. Brno, 2002. info
  • M. Renardy, R. C. Rogers. An introduction to partial differential equations. New York, 1993. info
    recommended literature
  • V. I. Averbuch. Partial differential equations. MÚ SU, Opava. info
  • R. Strichartz. A guide to distribution theory and Fourier transforms. 1994. 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
Assessment methods
Grade
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 1997, Summer 1998, Winter 1998, Summer 1999, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (recent)
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