Course: Introduction to Differential Equations

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Course title Introduction to Differential Equations
Course code UMB/587
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Frequency of the course In each academic year, in the summer semester.
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Eisner Jan, Mgr. Dr.
  • Křivan Vlastimil, prof. RNDr. CSc.
Course content
Content of lectures: 1. Differential equations as description of dynamical processes in science. 2. Existence of a solution for the Cauchy problem 3. Piccard-Lindelof method of approximate solutions 4. Elementary methods of solution, separation of variables 5. Linear differential equations of the n-th order, fundamental system of solutions, method of variation of constants 6. Linear differential equations of the n-th order with constant coefficients. 7. Systems of linear differential equations. Fundamental set of solutions as a linear vector space. 8. Systems of linear differential equations with constant parameters 9. Stability of zero solution for linear systems of differential equations 10. Non-linear systems of differential equations. Local stability of equilibria. 11. Analysis of Lotka-Volterra equations 12. Lyapunov stability 13. Limit cycles, Poincaré-Bendixon theory Content of practicals: Solving differential equations.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Work with text (with textbook, with book)
  • Class attendance - 42 hours per semester
  • Preparation for classes - 42 hours per semester
  • Preparation for exam - 42 hours per semester
Learning outcomes
To develop basic concepts of ordinary differential equations.
Students can build, analyse and solve Cauchy problems for ordinary differential equations.
Prerequisites
Single variable differential and integral calculus, linear algebra.
UMB/565 and UMB/CV551
----- or -----
UMB/551

Assessment methods and criteria
unspecified
1. Attendance at least 80% 2. Students must obtain at least 50% points from tests during the course
Recommended literature
  • C. H. Edwards, D. E. Penny: Elementary differential equations. Prentice Hall.
  • J. Kurzweil: Obyčejné diferenciální rovnice. Praha 1978.
  • B. Krajc, P. Beremlijski. Obyčejné diferenciální rovnice.


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