714-0365/07 – Basics of Mathematics (ZM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits2
Subject guarantorMgr. Milena Luňáčková, Ph.D.Subject version guarantorMgr. Monika Jahodová, Ph.D.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction2015/2016Year of cancellation2019/2020
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
JAH0037 Mgr. Monika Jahodová, Ph.D.
KOT31 RNDr. Jan Kotůlek, Ph.D.
LUN44 Mgr. Milena Luňáčková, Ph.D.
VAV14 RNDr. Eva Vavříková, Ph.D.
VOL18 RNDr. Jana Volná, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit 8+0

Subject aims expressed by acquired skills and competences

Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.

Teaching methods

Other activities


The set of real numbers, operations with algebraic expressions, equations and inequalities, functions, exponential and logarithmic equations, trigonometric functions and equations, analytic geometry, arithmetic and geometric sequences.

Compulsory literature:

[1] BIRD, J.: Engineering Mathematics, 4th ed. Newnes 2003. [2] https://www.khanacademy.org/math/ Harshbarger, R.J. - Teynolds, J.J.: Calculus with Applications. D.C. Heath and Company, Lexington 1990, ISBN 0-669-21145-1

Recommended literature:


Way of continuous check of knowledge in the course of semester

Course credit is granted for 1. Participation on tutorials. In the case of absence, homework can be handed in. 10 points. 2. Written exam classified by 0 - 90 points. The course is successfully passed if student obtains at least 45 points for written exam and participate in tutorials.



Other requirements

There are no other requirements


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

Sets (integers, whole numbers, rational and irrational numbers, real numbers), intervals, operations on intervals (intersection, union, complement,…), neighbourhood of a point, absolute value. Rational expressions: polynomials, fractions, exponents and roots. Functions of one real variable (definition, domain, range, graph,…) Operations on functions (sum, difference, product, quotient), composite functions, properties of functions (even and odd functions, monotonic functions, bounded functions), one-to-one and inverse functions. Elementary functions (linear, quadratic, rational and algebraic functions, exponential and logarithmic functions) and their properties. Drawing a sketch of the graph, graphs containing an absolute value. Sine and Cosine functions, trigonometric functions. Definition by means of unit circle, values in radian measure, graphs, goniometric identities. Algebraic equations: linear equations (possibly with a parameter), quadratic equations (solutions in real numbers and in the complex plane), irrational equations. Systems of two linear (and non-linear) equations in two unknowns. Linear inequalities (solutions by null point method), system of linear inequalities The Exponential and logarithmic equations (inequalities respectively), properties of logarithms. Analytic geometry in a geometric plane: point, vector, line (equations and a graph), circle (equations, determining its centre and radius). The conic sections: the ellipse, the hyperbola (as a graph of a linear rational function), the parabola (as a graph of a quadratic function). Properties of conics. Tangents to conic sections. Finding common points of a line and a conic.

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2016/2017 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

2016/2017 Winter
2015/2016 Winter