Czech

Not applicable.

Students will acquire knowledge of basic types of differential equations. They will be made familiar with differential equations as mathematical models of given problems, with problems of the existence and uniqueness of the solution and with the choice of a suitable solving method. They will master solving of problems of the convergence of infinite series as well as expansions of functions into Taylor and Fourier series.

Linear algebra, differential and integral calculus of functions in a single and more variables.

Not applicable.

The lessons consist of three-hour lecture and three-hour practical seminar. The lecture combines theory with illustrative examples. The practical exercise is concerned on handling numerical tasks.

Course-unit credit is awarded on the following conditions: Active participation in seminars. Fulfilment of all conditions of the running control of knowledge. At least half of all possible points in both check tests (the first test takes place in 8th week of the semester, the second one in 13th week of the semester). If a student does not fulfil this condition, the teacher can set an alternative one.
Examination: The examination tests the knowledge of definitions and theorems (especially the ability of their application to the given problems) and practical skills in solving of examples. The exam is written (possibly followed by an oral part). The final grade reflects especially the result in the written part of the exam. However, the examiner can also take account of the results in the check tests completed in seminars.
Grading scheme is as follows: excellent (90-100 points), very good
(80-89 points), good (70-79 points), satisfactory (60-69 points), sufficient (50-59 points), failed (0-49 points). The grading in points may be modified provided that the above given ratios remain unchanged.

1. Number series. Convergence criteria. Absolute and non-absolute convergence.
2. Function and power series. Pointwise and uniform convergence.
3. Power series. Convergence radius. Properties of power series.
4. Taylor series and expansions of functions into Taylor series.
5. Fourier series. Problems of the convergence and expansions of functions.
6. ODE. Basic notions. Types of solutions. Initial and boundary value problem.
7. Analytical methods of solving of 1st order ODE. Problem of existence and uniqueness.
8. Higher order ODEs. Properties of solutions of linear equations.
9. Methods of solving of higher order homogeneous linear ODEs.
10. Boundary value problem for 2nd order ODEs.
11. Systems of 1st order ODEs. Properties of solutions of linear systems.
12. Methods of solving of linear systems of 1st order ODEs.
13. Stability of ODEs and their systems.

Not applicable.

The aim of the course is to explain basic notions and methods of solving ordinary differential equations, and foundations of infinite series theory. The task of the course is to show that knowledge of the theory of differential equations can be utilized especially in physics and technical branches. Moreover, it is shown that foundations of infinite series theory are important tools for solving various problems.

Attendance at lectures is recommended, attendance at seminars is checked. Lessons are planned according to the week schedules. Absence from seminars may be compensated for by the agreement with the teacher.

Not applicable.

Not applicable.

Fichtengolc, G.M.: Kurs differencialnogo i integralnogo isčislenija, tom II, Moskva, 1966. (RU)
Fichtengolc, G.M.: Kurs differencialnogo i integralnogo isčislenija, tom III, Moskva, 1966. (RU)
Hartman, P.: Ordinary differential equations, New York, 1964. (EN)

Čermák, J.: Sbírka příkladů z Matematické analýzy III a IV, Brno, 1998. (CS)
Čermák, J., Ženíšek, A.: Matematika III, Brno, 2001. (CS)
Kalas, J., Ráb, M.: Obyčejné diferenciální rovnice, Brno, 1995. (CS)
Ženíšek, A.: Vybrané kapitoly z matematické analýzy, Brno, 1997. (CS)