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Lecturer(s)
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Fačevicová Kamila, Mgr. Ph.D.
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Andres Jan, prof. RNDr. dr hab. DSc.
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Bebčáková Iveta, Mgr. Ph.D.
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Pavlačka Ondřej, RNDr. Ph.D.
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Tomeček Jan, doc. RNDr. Ph.D.
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Ludvík Pavel, RNDr. Ph.D.
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Course content
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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.
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Learning activities and teaching methods
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Lecture
- 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
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Learning outcomes
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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.
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Prerequisites
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Knowledge of differential and integration calculus of a function of one variable.
KMA/M1N
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Assessment methods and criteria
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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.
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Recommended literature
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B. P. Děmidovič. (2003). Sbírka úloh a cvičení z matematické analýzy. Fragment, Praha.
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Bartsch, H.-J. (1983). Matematické vzorce. Praha: SNTL.
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Brabec J., Hrůza B. (1989). Matematická analýza II. SNTL, Praha.
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J. Brabec, F. Martan, Z. Rozenský. (1989). Matematická analýza I, II. SNTL, Praha.
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K. Rektorys. (1963). Přehled užité matematiky. SNTL Praha.
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