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, Compulsoryoptional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Course availability  The course is available to visiting students 
Lecturer(s) 


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. CauchyKowalewska 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. Threedimensional 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 

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 (2014IVT)  Mathematics courses  3  Summer 
Mathematical Institute in Opava  Mathematics (2014F)  Mathematics courses  3  Summer 
Mathematical Institute in Opava  Mathematical Methods in Economics (2)  Economy  3  Summer 
Mathematical Institute in Opava  Mathematical Analysis (1IVT)  Mathematics courses  3  Summer 
Mathematical Institute in Opava  Mathematics (2F)  Mathematics courses  3  Summer 
Mathematical Institute in Opava  Mathematics (1IVT)  Mathematics courses  3  Summer 
Mathematical Institute in Opava  Applied Mathematics (2014IVT)  Mathematics courses  3  Summer 
Mathematical Institute in Opava  Applied Mathematics in Risk Management (3)  Mathematics courses  3  Summer 
Mathematical Institute in Opava  Applied Mathematics (2014F)  Mathematics courses  3  Summer 
Mathematical Institute in Opava  Mathematical Methods in Economics (3)  Economy  3  Summer 