Course: Mathematics 2

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Course title Mathematics 2
Course code KMA/M2N
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 11
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
  • Kouřilová Pavla, Mgr. Ph.D.
  • Andres Jan, prof. RNDr. dr hab. DSc.
  • Bebčáková Iveta, Mgr. Ph.D.
  • Pavlačka Ondřej, RNDr. Ph.D.
Course content
1. Definite integral - motivation, definition, the conditions for integrability, calculation of the Riemann definite integral and its applications. 2. Integral as a function of upper/lower limit, improper integral - definition, properties, methods of calculation. 3. Limit of a bivariate function - definition, properties, methods of calculation. 4. Continuity of a bivariate function - definition, properties of continuous functions. 5. Partial derivatives of a bivariate functions - definition, interpretation, properties, partial derivative of higher order. 6. The approximation of a bivariate function - total differential, Taylor polynomial. 7. Extrema of a bivariate function - local extrema, conditional extrema, global extrema. 8. Double Riemann integral - motivation, definition, properties, integrability conditions, methods of calculation, application of double integral. 9. Number sequences - definition, properties, algebraic operations with number sequences, limit of a sequence. 10. Number series - definition, properties, convergence and divergence criteria, the absolute and relative convergence. 11. Function sequences and function series - definition, properties, pointwise and uniform convergence. 12. Power series - definition, properties, the expansion of a function at a point in a power serie.

Learning activities and teaching methods
  • Attendace - 78 hours per semester
  • Homework for Teaching - 70 hours per semester
  • Preparation for the Course Credit - 60 hours per semester
  • Preparation for the Exam - 120 hours per semester
Learning outcomes
Understand the mathematical tools of differential and integral calculus of functions of several variables.
Comprehension Understand the mathematical tools of differential and integral calculus of functions of several variables.
Knowledge of differential and integration calculus of a function of one variable.

Assessment methods and criteria
Oral exam, Written exam

Credit: attend the classes and pass the written test. Exam: pass the written part and show knowledge and understanding during the oral exam.
Recommended literature
  • B. P. Děmidovič. (2003). Sbírka úloh a cvičení z matematické analýzy. Fragment, Praha.
  • Bartsch, H.-J. (1983). Matematické vzorce. Praha: SNTL.
  • Brabec J., Hrůza B. (1989). Matematická analýza II. SNTL, Praha.
  • J. Brabec, F. Martan, Z. Rozenský. (1989). Matematická analýza I, II. SNTL, Praha.
  • K. Rektorys. (1963). Přehled užité matematiky. SNTL Praha.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Statistics (2015) Mathematics courses 1 Summer
Faculty of Science Mathematics-Economics of Banking / Insurance Systems (1) Mathematics courses 1 Summer