FP-ma1PAcad. year: 2018/2019
The subject is part of the theoretical basis of the field. Learning outcomes of the course unit The aim of the course is to unify and supplement the students' knowledge in the areas of further teaching of basic mathematical concepts and to teach students the comprehension of using the linear algebra system to solve the linear equations and the differential functions of one variable (including basic applications in economic disciplines).
Learning outcomes of the course unit
The acquired knowledge and practical mathematical skills will in particular serve as a basis for acquiring knowledge and disseminating skills in economically oriented fields and for the correct use of mathematical software, and will be an important starting point for learning new knowledge in math mathematical subjects.
Knowledge of secondary-school mathematics.
Recommended optional programme components
Recommended or required reading
Mezník,I.: Matematika I. 8. vydání, FP VUT v Brně, Brno 2008 (CS)
Marošová,M. - Mezník,I.: Cvičení z matematiky I. 2. vydání, FP VUT v Brně, Brno 2008 (CS)
Mezník,I.: Matematika II.FP VUT v Brně, Brno 2009 (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
Requirements for credit:
- Active participation in exercises, exercises are obligatory,
- fulfillment of individual tasks and written assignments,
- Absence of a control test during the semester with a rating of at least "sufficient" (E).
Assignment of the credit is a necessary condition for the examination
The examination has a written and an oral part, with the written part of the exam.
Language of instruction
1. Basic mathematical concepts, numbers (basics of set theory - sets, operations with them, Vennov diagrams, real and
complex numbers - properties, counting, absolute value, intervals, complex numbers plane)
2. Matrices and determinants (matrices and operations with them, properties and calculation of determinants)
3. Systems of linear equations (solving conditions, Gaussian elimination method, Cramer rule)
4. Function (real function of one real variable and its basic characteristics - odd, even, periodic, limited and
monotone functions and its graph, elementary functions -power, goniometric and cyclometric functions, exponential and
logarithmic functions, general power)
5. Operations with functions (rational functions with functions, compound, simple, inverse functions, elementary structures and
6. Polynomials and rational fracture functions (zero points - polynomial roots, polynomial decomposition, Horner scheme, pure
and neryze-laced rational function, decomposition into partial fractions)
7. Limit (own and improper limit at own and stepped points, basic properties, limit of elementary functions,
rules for calculating the limit)
8. Continuity (continuity at point and interval, continuity of elementary functions, rules for counting with continuous functions,
properties of functions continuous at a closed interval)
9. Sequences (Real Number Sequences, Restricted and Monotone Sequences, Sequence Limit)
10. Derivatives of the 1st order (sense, basic properties and rules, derivation of elementary functions)
11. Derivatives of the first and higher order (differential and its use, higher order derivation, l'Hospitality rule)
12. The course of function I (monotony, local and absolute extremes of function)
13. Functional function II (convexity and concavity, function asymptotes, complete description of function behavior)
Learning outcomes of the course unit The aim of the course is to solve systems of linear equations and detailed analysis of the processes described by the real function of one real variable, including the realization of necessary calculations in general and in economic applications (also with respect to the use of computing).
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures is not controlled. Attendance at exercises (seminars) is compulsory and is regularly checked. A student is obliged to give reasons for his/her absence. If the teacher accepts the reason for the absence (which is completely under his/her competence), he/she will decide about the form of the compensation for the missed lessons.