## MA0012 Mathematical Analysis 3

Faculty of Education
Spring 2021
Extent and Intensity
0/2/0. 3 credit(s). Type of Completion: k (colloquium).
Taught online.
Teacher(s)
doc. Dr. András Rontó (lecturer)
RNDr. Břetislav Fajmon, Ph.D. (seminar tutor)
RNDr. Karel Lepka, Dr. (seminar tutor)
Guaranteed by
RNDr. Břetislav Fajmon, Ph.D.
Department of Mathematics - Faculty of Education
Supplier department: Department of Mathematics - Faculty of Education
Timetable of Seminar Groups
MA0012/01: Tue 17:00–18:50 učebna 37, K. Lepka
MA0012/02: Thu 10:00–11:50 učebna 33, K. Lepka
Prerequisites
The subject is aimed at acquiring knowledge and skills in the theory of differential and difference equations. THE PREREQUISITE IS: THE KNOWLEDGE OF THE SUBJECTS "MATHEMATICAL ANALYSIS 1" AND "MATHEMATICAL ANALYSIS 2".
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of the course the SS will know basic concepts of the theory of differential and difference equations, especially: initial value problem, separable ordinary differential equations (ODEs), homogeneous ODEs, first-order ODEs, second-order linear ODEs especially with constant coefficients, methods of their solution and applications. difference calculus, linear difference equations, methods of their solution and applications. The SS will actively use the concepts in problem solving, in their follow-up study at the faculty and in their own lessons as school teachers.
Learning outcomes
After the completion of the course the students will a) acquire knowledge in the theory of ordinary differential equations; b) acquire skills in solving ordinary differetial equations (= ODE), such as separable ODEs, ODEs solved using substitution, linear ODEs of first order, linear ODEs of higher order with constant coefficients; c) have an important insight into the role of ODEs in mathematical modelling.
Syllabus
• 1. Basic notions from the theory of ordinary differential equations (ODEs), motivation, geometrical meaning, initial value problem.
• 2. Separable ODEs, homogeneous ODEs, linear ODEs of first order, methods of solution.
• 3. Linear differential equations of second order, especially with constant coefficients, methods of their solution.
• 4. Application of differential equations.
• 5. Basic information on differential equations, motivational problems.
• 6. Methods of solution for simple difference equations, application.
Literature
recommended literature
• KUBEN, Jaromír. Asymptotické vlastnosti obyčejných diferenciálních rovnic druhého řádu. 1978. 34 l. info
Teaching methods
Teaching methods chosen will reflect the contents of the subject and the level of students.
Assessment methods
Check-up test and colloquium. The students will be allowed to sit for the colloquium after a successful completion of the check-up test.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2019, Spring 2020, Spring 2022.
• Enrolment Statistics (recent)
• Permalink: https://is.muni.cz/course/ped/spring2021/MA0012