Course: Partial Differential Equations II

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Course title Partial Differential Equations II
Course code MU/03135
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • KOPFOVÁ Jana, doc. RNDr. Ph.D.
Course content
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

Learning activities and teaching methods
Recommended literature
  • C. Zuily. Problems in distributions and partial differential equations. 1988.
  • D. Gilbarg, N. S. Trudinger. Elliptic partial differential equations of second order. Second edition. Springer, Berlin, 1983.
  • J. Franců. Moderní metody řešení diferenciálních rovnic. Brno, 2002.
  • L. Schwartz. Matematické metody ve fyzice. Státní nakladatelství technické literatury, Praha, 1972.
  • M. Renardy, R. C. Rogers. An introduction to partial differential equations. New York, 1993.
  • R. Strichartz. A guide to distribution theory and Fourier transforms. 1994.
  • V. I. Averbuch. Partial differential equations. MÚ SU, Opava.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Applied Mathematics (2) Mathematics courses 2 Winter
Mathematical Institute in Opava Geometry and Global Analysis (1) Mathematics courses 1 Winter
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 1 Winter