Course: Calculus II

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Course title Calculus II
Course code KMA/MA2
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study 1
Semester Summer
Number of ECTS credits 6
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.
  • Kobera Marek, Mgr. Bc. Ph.D.
Course content
1. Two- and three - variable function.A limit of two- and three - variable function. 2. Continuity of two- and three - variable function 3. Partial derivative.Total differential, directional derivative 4. Tangent hyperplane. Relative extremes 5. Constrained extremes 6. Primitive functions (definition, properties). Proper integral. 7. Per partes and substitutions for proper integral. 8. Integration of rational function. 9. Riemannian integral, definition. 10. Inequality theorems. 11. Relation between improper and Riemannian integral. 12. Generalized Riemannian integral. 13. Applications, volumes and areas in space. 14. Application, curve length.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming)
Learning outcomes
The theory of Riemannian integral. Generalized Riemannian integral. Applications. Differential calculus of two- and three- variable function.
The student will have a good grasp of the theory Riemann integral and the elements of differential calculus of two- and three- variable function.
Prerequisites
knowledge of the content of subject Calculus I

Assessment methods and criteria
Combined exam

active participation in colleges and tutorials, 2x written test
Recommended literature
  • Grossmann,S.,I.:. Calculus, Saunders College Publishing, 2001. Liberec, 1997.
  • Jarník, V.:. Diferenciální a integrální počet II., Academia, Praha 1976.
  • Jirásek,F. a kolektiv:. Sbírka řešených příkladů z matematiky II, SNTL, Praha 1989.


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 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer