University of West Bohemia in Pilsen
Study programmes & Course catalogue
for academic year 2025/2026
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Course: Seminar on Integral Calculus

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Course title Seminar on Integral Calculus
Course code KMA/SIP
Organizational form of instruction Tutorial
Level of course Bachelor
Year of study 1
Semester Summer
Number of ECTS credits 2
Language of instruction Czech
Status of course Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Caletka Tomáš, RNDr. CSc.
  • Ježek Vladimír, doc. Ing. Ph.D.
  • Hofman Martin, RNDr. Mgr. Ph.D.
  • Breitfelder Ondřej, Mgr.
  • Brada Pavel, Ing. Ph.D.
Course content
1. Differential models of dynamic systems; first-order differential equations and first-order systems; 2. Ordinary linear differential equations n-th order. 3. First and secod-order systems. 4. Scalar functions of several variables, limits, contunuity. 5. Differential calculus of functions of several variables. 6. Optimalization, local and constrained extrems. 7. Integral calculus of functions of several variables. 8. Curve and surface integrals. 9. Scalar and vector fields. 10. Vector functions, differential calculus of vector functions. 11. Differential and integral characteristics of vector fields. 12. Integral's theorems in the vector fields. 13. Integral with parameter.

Learning activities and teaching methods
Seminar
  • Contact hours - 26 hours per semester
  • Preparation for comprehensive test (10-40) - 26 hours per semester
prerequisite
Knowledge
Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/MS1. The course is recommended for students of the course KMA/M2S.
learning outcomes
By the end of the course, a successful student should be able to: 1. Solve differential equation of first order and system of differential equations; 2. Solve initial problems; 3. Describe curves in Rn and work with them; 4. Determine properties of functions of more variables; 5. Compute directional and partial derivatives of functions of more variables; 6. Formulate basic min/max problems and solve them using differential calculus; 7. Evaluate double and triple integrals; 8. Compute curves integral; 9. Deal with differential and integral characteristic of vector fields.
teaching methods
Seminar
assessment methods
Test
Recommended literature
  • Brabec, Jiří; Hrůza, Bohuslav. Matematická analýza II. Praha : SNTL, 1986.
  • Čížek, Jiří; Kubr, Milan; Míková, Marta. Sbírka příkladů z matematické analýzy I. 1. vyd. Plzeň : ZČU, 1995. ISBN 80-7082-216-3.
  • Drábek, Pavel; Míka, Stanislav. Matematická analýza II. 3. nezm. vyd. Plzeň : ZČU, 1999. ISBN 80-7082-528-6.
  • Ivan, Ján. Matematika 2. 1. vyd. Bratislava : Alfa, 1989. ISBN 80-05-00114-2.
  • Jarník, Vojtěch. Integrální počet. II. Praha : Nakladatelství Československé akademie věd, 1955.
  • Jirásek, František; Kriegelstein, Eduard; Tichý, Zdeněk. Sbírka řešených příkladů z matematiky : logika a množiny, lineární a vektorová algebra, analytická geometrie, posloupnosti a řady, diferenciální a integrální počet funkcí jedné proměnné. 2. nezměn. vyd. Praha : SNTL, 1981.
  • Jirásek, František; Vacek, Ivan; Čipera, Stanislav. Sbírka řešených příkladů z matematiky II. 1. vyd. Praha : SNTL, 1989.
  • Mašek, Josef. Řešené úlohy z matematiky : dvojné, trojné, křivkové a plošné integrály. 1. vyd. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-836-6.
  • Tomiczek, Petr. Matematická analýza II. Plzeň : Západočeská univerzita, 2006.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
University of West Bohemia in Pilsen, date of update: 24.04.2025 23:52. Data created for academic year 2025/2026