FP-MA1_MAcad. year: 2020/2021
The subject is a part of theoretical fundamentals. The aim is to manage calculations with numeric variables (including the use of IT) and the analysis of functions of one real variable, including their applications in economic disciplines.
Learning outcomes of the course unit
Acquired knowledge and practical mathematical skills will be an important starting point for mastering new knowledge in the follow-up courses of mathematical character; they will also be essential for acquiring knowledge in courses on economy and for the correct use of mathematical software.
Knowledge of secondary-school mathematics.
Recommended optional programme components
Recommended or required reading
MEZNÍK, I. Základy matematiky pro ekonomii a management. Základy matematiky pro ekonomii a management. 2017. s. 5-443. ISBN: 978-80-214-5522-1. (CS) (CS)
Marošová,M.,Mezník,I.:Cvičení z matematiky I. FP VUT v Brně, Brno 2008 (CS)
Mezník,I.: Matematika II.FP VUT v Brně, Brno 2009 (CS)
Mezník, I: Diskrétní matematika. FP VUT v Brně v Akademickém nakladatelství CERM, s.r.o. Brno, Brno 2004. ISBN 80-214-2754-X. (CS)
Mezník,I.:Matematika I. FP VUT v Brně, Brno 2008 (CS)
Planned learning activities and teaching methods
Instructing is divided into lectures and exercises. Lectures are focused on the theory referring to applications, exercises on practical calculations and solving of application tasks.
Assesment methods and criteria linked to learning outcomes
Conditions for awarding course-unit credits:
- fulfilment of individual tasks and successful completion of written assignments,
- completion of partial written test´s (more than 55% points)
Awarding of course-unit is a necessary condition to be admitted to the exam.
The exam has a written and an oral part with the written part being more important.
Language of instruction
1. Basic mathematical concepts (sets - operations with them, Venn diagrams; real and complex numbers - calculation with them, representations, significant subsets, absolute value)
2. Mathematical logic (statements, operations and laws, Boolean algebras and functions, representations, applications)
3. Relation (between sets and on a set, properties, tolerances, equivalence, arrangement)
4. Graphs (undirected, oriented and evaluated, Dijkstra's shortest path algorithm, Kruskal's algorithm)
5. Languages, grammars, automata (characteristics, Chomsky hierarchy, finite automaton, Kleene's characterization)
6. Matrices (properties, operations with matrices, rank calculation and inverse matrices)
7. Determinants (properties, rules and calculation of determinants)
8. Systems of linear equations (solvability, GEM and Cramer's rule)
9. Functions and operations with them (basic characteristics, properties, rational operations with functions, compound, simple, inverse functions, elementary constructions and shifts of graphs)
10. Polynomials and rational polynomials (roots and their determination, Horner's scheme, decomposition into partial fractions)
11. Elementary functions (basic properties and graphs)
12. Limits (proper and improper limits in proper and improper point, basic properties, limits of elementary functions, rules for calculating limits)
13. Continuity (continuity at a point and at an interval, continuity of elementary functions, rules for calculating with continuous functions, properties of continuous functions on a closed interval)
The aim is for students to master numerical calculations (including the use of IT) and the analysis of functions of one real variable, including their economic applications.
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures and exercises (seminars) is not controlled.