Course: Mathematical Analysis 4

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Course title Mathematical Analysis 4
Course code KMA/MA4M
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
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
  • Burkotová Jana, Mgr. Ph.D.
  • Pavlačková Martina, RNDr. Ph.D.
  • Pastor Karel, doc. Mgr. Ph.D.
  • Kouřilová Pavla, Mgr. Ph.D.
Course content
Line integrals of first and second kind. Multiple integrals. Surface integrals of first order and second order. Green's theorem, Stokes' formula, the Gauss-Ostrogradskii formula. Applications of integral calculus in mechanics. Riemann's and Lebesgue's approach to integration - comparison. Integrals depending on a parametr: continuity, differentiability, integration. The Beta function, the Gamma function. Elements of vector analysis. Exact differential equations.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 78 hours per semester
  • Preparation for the Course Credit - 25 hours per semester
  • Preparation for the Exam - 75 hours per semester
Learning outcomes
Understand integral calculus of functions of several variables.
Comprehension Understand integral calculus of several variables.
Knowledge of the notions of derivative of function of several variables and integral of one variable.

Assessment methods and criteria
Oral exam, Written exam

Credit: active participation, homework solving, to obtain at least 60 percent of the possible points in a written test. Exam: the student has to understand the subject and be able to prove the principal results.
Recommended literature
  • Brabec J., Hrůza B. (1989). Matematická analýza II. SNTL, Praha.
  • Jarník V. (1976). Integrální počet II. Academia, Praha.
  • Kopáček J. (2002). Matematická analýza pro fyziky III. Matfyzpress, Praha.
  • V.A. Zorich. (2004). Mathematical Analysis II. Springer, Berlin.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Mathematics and Applications (1) Mathematics courses 2 Summer