Course: Calculus III

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Course title Calculus III
Course code KMA/MA3
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study 2
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
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 non-negative elements --- non-limit 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.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer