Czech

8

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 of a single and more variables.

Not applicable.

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

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 each of the both tests.

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 written exam consists in particular of the examples on the following topics:
Number and function series, the expansion of a function into Taylor series, solving of first order ODEs, solving of higher order linear ODEs, solving of system of first order linear ODEs, Fourier series, solving of ODEs via the infinite series and the Laplace tranform method, boundary value problems, basics of PDEs theory. Some theoretical queries concerning basic concepts can be included in the written part as well.
Topics of practical part: The expansion of a function into Taylor series, solving of first order ODEs, solving of higher order linear ODEs, solving of system of first order linear ODEs.
The final grade reflects the result of the written part of the exam (maximum 65 points), the result of the oral part (maximum 15 points), the results achieved in seminars (maximum 14 points), and the results achieved in seminars in computer labs (maximum 6 points).
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).

Not applicable.

Not applicable.

The aim of the course is to explain basic notions and methods of solving ordinary and partial 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 obligatory and 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.

Kalas, J., Ráb, M: Obyčejné diferenciální rovnice, PřF MU, Brno, 2012. (CS)
Hartman, P.: Ordinary Differential Equations, New York, 1964. (EN)
Boyce, W. E., DiPrima, R. C., Elementary Differential Equations, 9th Edition, Wiley, 2008. (EN) (EN)

Kalas, J., Ráb, M: Obyčejné diferenciální rovnice, PřF MU, Brno, 2012. (CS)
Logan, J.D.: A First Course in Differential Equations. New York, Springer, 2006. (EN)
Čermák, J., Nechvátal, L.: Matematika III, Brno, 2016. (CS)
Čermák, J.: Sbírka příkladů z Matematické analýzy III a IV, Brno, 1998. (CS)
Boyce, W. E., DiPrima, R. C., Elementary Differential Equations, 9th Edition, Wiley, 2008. (EN)

13 hours, compulsory

The course is realized in computer labs with utilizing a suitable software (e.g. Matlab). This part of the course is focused mainly on demonstration of the use of the software in numerical methods in differential equations and related topics.