# 714-0365/08 – Basics of Mathematics (ZM)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 2 Subject guarantor Mgr. Milena Luňáčková, Ph.D. Subject version guarantor RNDr. Jan Kotůlek, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language English Year of introduction 2016/2017 Year of cancellation Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
BEL10 Mgr. Jana Bělohlávková
DOL10 RNDr. Milan Doležal, CSc.
DOL30 doc. RNDr. Jarmila Doležalová, CSc.
HOM44 PaedDr. Zdenka Homolová
JAR71 Mgr. Marcela Jarošová
KOT31 RNDr. Jan Kotůlek, Ph.D.
LUN44 Mgr. Milena Luňáčková, Ph.D.
NIK01 Ing. Marek Nikodým, Ph.D.
OTI73 Mgr. Petr Otipka
RYH40 RNDr. Irena Rychtarová
SKN002 Ing. Petra Schreiberová, Ph.D.
SKA74 Mgr. Sylvie Skalníková
MIC75 Mgr. Magda Štěpánová
SVO19 Mgr. Ivona Tomečková, Ph.D.
VLC20 doc. RNDr. Jaroslav Vlček, CSc.
VOL18 RNDr. Jana Volná, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit 0+2

### 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

Students receive 5-10 point for activities in the seminars. Students write 3 control tests, every with 3 problems. For solution of each problem they receive up to 10 points. Students who get 51-100 points receive the credit.

### E-learning

compulsory attendance

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Week Syllabus of tutorial -----------------------------------------------------------------------------1. Sets (integers, whole numbers, rational and irrational numbers, real numbers), intervals, operations on intervals (intersection, union, complement,…), neighbourhood of a point, absolute value. 2. 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. 3. 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. 4. Sine and Cosine functions, trigonometric functions. Definition by means of unit circle, values in radian measure, graphs, goniometric identities. 5. Test 1 (examining time: 20-30 minutes). Rational expressions: polynomials, fractions, exponents and roots. 6. Rational expressions: polynomials, fractions, exponents and roots. 7. Algebraic equations: linear equations (possibly with a parameter), quadratic equations (solutions in real numbers and in the complex plane), irrational equations. 8. Systems of two linear (and non-linear) equations in two unknowns. Linear inequalities (solutions by null point method), system of linear inequalities 9. The Exponential and logarithmic equations (inequalities respectively), properties of logarithms. Inverse functions. 10. Test 2 (examining time:20- 30 minutes). Domains of more complicated functions. 11. Analytic geometry in a geometric plane: point, vector, line (equations and a graph), circle (equations, determining its centre and radius). 12. 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. 13. Tangents to conic sections. Finding common points of a line and a conic. Test 3 (examining time: 20-30 minutes). 14. Reserve. ---

### Conditions for subject completion

Full-time form (validity from: 2016/2017 Winter semester)
Min. number of points
Credit Credit 100  51
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2018/2019 (B2341) Engineering P English Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering P English Ostrava 1 Compulsory study plan
2016/2017 (B2341) Engineering P English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner