Lecturer(s)


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.

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.
