Course: Mathematics 1

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Course title Mathematics 1
Course code KMA/M1
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
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
Lecturer(s)
  • Vrbková Jana, Mgr. Ph.D.
  • Rachůnková Irena, prof. RNDr. DrSc.
  • Pavlačková Martina, RNDr. Ph.D.
  • Bebčáková Iveta, Mgr. Ph.D.
  • Pavlačka Ondřej, RNDr. Ph.D.
  • Kouřilová Pavla, Mgr. Ph.D.
Course content
1. Introduction to mathematical logic, statements, quantifiers, negation, logical structure of mathematics, proofs of mathematical theorems. 2. Sets, relationship between sets, set operations, Cartesian product of sets, mapping, number sets. 3. Intervals, neighbourhood of a point, properties of a subsets of set of real numbers, relationship between a set and a point. 4. Sequences - definition, properties, algebraic operations with sequences. 5. Limit of a sequence - definition, properties. 6. Limit of a sequence - properties and calculation. 7. Function of a single real variable - definition, properties. 8. Function of a single variable - properties, algebraic operations with functions, function composition, inverse function. 9. Limit of a function - motivation, definition. 10. Limit of a function - properties, one-sided limits. 11. Limit of a function - calculation. Function continuity - definition, properties. 12. Points of discontinuity, functions continuous on a set, function continuous on a closed interval. 13. Differentiation of a function at a point - definition, tangent line and normal line, differentiation of a function on a set. 14. Calculation of derivatives, higher derivatives, the interpretation of the second derivative. 15. Elementary theorems of differential calculus. 16. Approximation of a function - differential, Taylor polynomial. 17. The application of differential calculus - analysing properties of a function - part I. 18. The application of differential calculus - analysing properties of a function - part II 19. Indefinite integral - primitive functions, calculation of primitive function. 20. Indefinite integral - integration of rational functions. 21. Indefinite integral - special substitutions. 22. Riemann integral - motivation, definition. 23. Riemann integral - conditions of integrability, properties. 24. Riemann integral - calculation, application.

Learning activities and teaching methods
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
Learning outcomes
Master basic tools of differential and integral calculus of functions of a single variable.
Comprehension Understand the mathematical tools of differential and integral calculus of functions of a single variable.
Prerequisites
Knowledge of secondary school mathematics.

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.
  • J. Brabec, F. Martan, Z. Rozenský. (1989). Matematická analýza I. Praha: SNTL.
  • K. Rektorys. (1963). Přehled užité matematiky. SNTL Praha.
  • V. Mádrová, J. Marek. (2004). Řešené příklady a cvičení z matematické analýzy I. VUP Olomouc.
  • V. Mádrová. (2004). Matematická analýza I. VUP, Olomouc.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester