# 714-0365/06 – Basics of Mathematics (ZM)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 2 Subject guarantor Mgr. Milena Luňáčková, Ph.D. Subject version guarantor Mgr. Monika Jahodová, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2013/2014 Year of cancellation Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
JAH0037 Mgr. Monika Jahodová, Ph.D.
KOT31 RNDr. Jan Kotůlek, Ph.D.
LUN44 Mgr. Milena Luňáčková, Ph.D.
SVO19 Mgr. Ivona Tomečková, Ph.D.
VAV14 RNDr. Eva Vavříková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined 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.

Seminars
Other activities

### Summary

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

### 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

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

Combined form (validity from: 2015/2016 Winter semester)
Min. number of points
Credit Credit 100 (100) 51
Písemka Written test 100  51
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2018/2019 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2018/2019 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2017/2018 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner