Mathematics 4B
Code  Completion  Credits  Range  Language 

101MT4B  Z,ZK  4  2P+2C 
 Lecturer:
 Ondřej Zindulka (guarantor), Jan Chleboun
 Tutor:
 Ondřej Zindulka (guarantor), Jan Chleboun
 Supervisor:
 Department of Mathematics
 Synopsis:

1. Eigenvalues and eigenvectors of matrices.
2. Ordinary linear differential equations  basic properties.
3. Boundary value problems for second order differential equations; eigenvalues and eigenfunctions.
4. Solvability of boundary value problems for second order linear differential equations.
5. Solving of second order ordinary differential equations by the finite difference method.
6. Introduction to the theory of linear partial differential equations of the second order.
7. Boundary conditions for partial differential equations and their physical interpretation.
8. Finite difference method for the Poisson equation.
9. Finite difference method for the heat equation  explicit scheme.
10. Mathematical modeling of heat transfer between two bodies with different material properties.
11. Variational formulation of boundary value problems for ordinary differential equations.
12. Finite element methods for solving the second order ordinary differential equations.
13. Fourier method for the solution of the heat equation.
 Requirements:
 Syllabus of lectures:
 Syllabus of tutorials:
 Study Objective:
 Study materials:

[1] Rektorys, K.: Variational methods in mathematics, science and engineering. Translated from the Czech by Michael Basch. Second edition. D. Reidel Publishing Co., DordrechtBoston, Mass., 1980.
[2] Rektorys, K.: Survey of applicable mathematics. Vol. II. Mathematics and its Applications, 281. Kluwer Academic Publishers Group, Dordrecht, 1994.
[3] Bubeník, F.: Mathematics for Engineers, textbook of Czech Technical University, Prague 2007
 Note:
 Timetable for winter semester 2019/2020:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Fri Thu Fri  Timetable for summer semester 2019/2020:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Fri Thu Fri  The course is a part of the following study plans: