714-0365/05 – Basics of Mathematics (ZM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits2
Subject guarantorMgr. Milena Luňáčková, Ph.D.Subject version guarantorMgr. Milena Luňáčková, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2013/2014Year of cancellation2019/2020
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BEL10 Mgr. Jana Bělohlávková
CER0007 Mgr. František Červenka
H1O40 Mgr. Iveta Cholevová, Ph.D.
DOL75 Mgr. Jiří Doležal
JAH0037 Mgr. Monika Jahodová, Ph.D.
JAR71 Mgr. Marcela Jarošová, Ph.D.
KOT31 RNDr. Jan Kotůlek, Ph.D.
LUN44 Mgr. Milena Luňáčková, Ph.D.
OTI73 Mgr. Petr Otipka, Ph.D.
KAH14 Mgr. Marcela Rabasová, Ph.D.
SKN002 Ing. Petra Schreiberová, Ph.D.
SVO19 Mgr. Ivona Tomečková, Ph.D.
VAV14 RNDr. Eva Vavříková, Ph.D.
ZID76 Mgr. Arnošt Žídek, 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.

Teaching methods

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

Recommended literature:

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

Way of continuous check of knowledge in the course of semester

3 tests

E-learning

http://mdg.vsb.cz/M/ http://www.studopory.vsb.cz/materialy.html

Other requirements

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

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
2018/2019 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2018/2019 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2017/2018 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2016/2017 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2015/2016 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2013/2014 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2013/2014 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2013/2014 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2013/2014 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2018/2019 Winter
2017/2018 Winter
2016/2017 Winter
2015/2016 Winter
2014/2015 Winter
2013/2014 Winter