Course: Mathematics 1

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Course title Mathematics 1
Course code KMA/M1N
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
  • Burkotová Jana, Mgr. Ph.D.
  • Vrbková Jana, Mgr. Ph.D.
  • Rachůnková Irena, prof. RNDr. DrSc.
  • Pavlačka Ondřej, RNDr. Ph.D.
  • Bebčáková Iveta, Mgr. Ph.D.
  • Kouřilová Pavla, Mgr. Ph.D.
  • Machů Hana, Mgr.
  • Pavlačková Martina, RNDr. Ph.D.
  • Stoklasa Jan, Mgr. et 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, operations with sets, Cartesian product of sets, mapping, number sets. 3. Metric spaces - definition and properties of metric, neighborhood of a point, relationship between a set and a point, properties of sets in metric spaces 4. Extended real numbers, intervals, properties of subsets of real numbers. 5. Function - definition, properties, function of one and two variables, basic elementary functions. 6. Limit of a function of one variable - definition, properties, calculation, the importance of limit for analyzing properties of a function. 7. Continuity of a function of one variable - definition, properties, points of discontinuity 8. Derivative of a function of one variable at a point - definition, properties, interpretation, tangent line and normal line, derivative of a function on a set, the application of derivative of a function to analyzing the properties of a function. 9. The approximation of a function of one variable - differential , Taylor polynomial, their application to approximate calculations. 10. The application of differential calculus - analyzing the properties of function (local extremes of a function, monotonicity, convexity, concavity, inflex points, graph). 11. Indefinite integral of a function of one variable - definition and properties of primitive function, calculation of primitive function. 12. The calculation of a primitive function - integral of rational functions, special substitutions.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 91 hours per semester
  • Homework for Teaching - 70 hours per semester
  • Preparation for the Course Credit - 50 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.
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
Faculty of Science Mathematics-Economics of Banking / Insurance Systems (1) Mathematics courses 1 Winter
Faculty of Science Applied Statistics (2015) Mathematics courses 1 Winter