310-2110/02 – Basics of Mathematics (ZM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits2
Subject guarantorMgr. Monika Jahodová, Ph.D.Subject version guarantorMgr. Monika Jahodová, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation2021/2022
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.
MUL0086 RNDr. PhDr. Ivo Müller, Ph.D.
OTI73 Mgr. Petr Otipka, Ph.D.
SVO19 Mgr. Ivona Tomečková, 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

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.

Teaching methods

Seminars
Tutorials
Other activities

Summary

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.

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:

http://education-portal.com/academy/course/precalculus-course.html

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.

E-learning

http://education-portal.com/academy/course/precalculus-course.html

Other requirements

There are no other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

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
2020/2021 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2020/2021 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2020/2021 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2020/2021 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2019/2020 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2019/2020 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2020/2021 Winter
2019/2020 Winter