Course: Partial Differential Equations I

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Course title Partial Differential Equations I
Course code MU/02027
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Summer
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
Lecturer(s)
  • KOPFOVÁ Jana, doc. RNDr. Ph.D.
Course content
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

Learning activities and teaching methods
unspecified
Recommended literature
  • Jan Franců. Parciální diferenciální rovnice. Brno, 1998.
  • L. C. Evans. Partial diferential equations. 1998.
  • M. Renardy, R. C. Rogers. An introduction to partial differential equations. New York, 1993.
  • 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 Mathematics (2014-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Methods in Economics (2) Economy 3 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Applied Mathematics (2014-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Applied Mathematics in Risk Management (3) Mathematics courses 3 Summer
Mathematical Institute in Opava Applied Mathematics (2014-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Methods in Economics (3) Economy 3 Summer