Lecturer(s)


Petrášková Vladimíra, doc. RNDr. Ph.D.

Samková Libuše, RNDr. Ph.D.

Course content

1. The sequences of real numbers and its properties. 2. Limit of sequences  limits of sequences formed by arithmetic operations. 3. Limit of sequences  inequality theorems. 4. Subsequences and its limits. Limit of monotone sequences. 5. Cauchy sequences, Weierstrass theorem. 6. Heine theorem. 7. Numerical series and conditions of the convergence 8. Series with nonnegative elements  nonlimit and limit criteria. 9. Absolute convergence, Leibniz criterion. 10. First  order differential equations. 11. Differential equations  separation of variables. 12. First order linear differential equations. 13. Second order linear differential equations with constant coefficients  homogeneous. 14. Second order linear differential equations with constant coefficients  heterogeneous equations.

Learning activities and teaching methods

Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming)

Learning outcomes

The sequences of real numbers and limits of them. Numerical series and its sums. Conditions of the convergence. First and second order differential equations.
The student will have a good grasp of the sequences of real numbers, numerical series and first and second order differential equations.

Prerequisites

knowledge of the content of subject Calculus I and Calculus II

Assessment methods and criteria

Combined exam
Active participation at lectures and seminars, 2x written test. The first term of the exam must be completed before June 30 of the corresponding academic year. Otherwise it expires.

Recommended literature


Jarník, V.:. Diferenciální počet I. Praha, Academia. Praha, Academia, 1974.

Jarník, V.:. Matematická analýza pro III. semestr, Praha 1978.

Pelikán, Š., Zdráhal, T.:. Matematická analýza: číselné řady, posloupnosti a řady funkcí, PF UJEP, Ústí nad Labem, 1994.

Zmeškalová, E., Petrášková, V.:. Posloupnosti, PF JU, Č. Budějovice, 1999.
