230-0221/01 – Repetition of Mathematics 1 (Repet 1)

Gurantor departmentDepartment of MathematicsCredits1
Subject guarantorRNDr. Petr Volný, Ph.D.Subject version guarantorRNDr. Petr Volný, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year1Semestersummer
Study languageCzech
Year of introduction2018/2019Year of cancellation
Intended for the facultiesFASTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
DUB02 RNDr. Viktor Dubovský, Ph.D.
PAL39 RNDr. Radomír Paláček, Ph.D.
VOL06 RNDr. Petr Volný, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit 0+2
Combined Credit 0+16

Subject aims expressed by acquired skills and competences

Goals and competence Mathematics is an 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 analyse problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyse 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

Tutorials

Summary

Repetition of Mathematics 1 is intended for students who, for whatever reasons, fail the exam of Mathematics I and are interested in passing this exam. Its content essentially coincides with the content of the course Mathematics I. The aim is to enable better understanding of mathematics by the solving of concrete examples and problems. Repetition will focus on the practical part of the exam and they will be solved examples matching the written part of the exam.

Compulsory literature:

Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3. Trench, W.F.: Introduction to real analysis, Free Edition 1.06, January 2011, ISBN 0-13-045786-8.

Recommended literature:

Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1.

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

There are no additional requirements.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Syllabus of tutorial 1. Domain of a real function of one real variable. 2. Bounded function, monotonic functions, even, odd and periodic functions. 3. One-to-one functions, inverse and composite functions. Elementary functions. 4. Inverse trigonometric functions. Limit of functions. 5. Derivative and differential of functions. 6. l’Hospital rule. Monotonic functions, extrema of functions. 7. Concave up function, concave down function, inflection point. 8. Asymptotes. Course of a function. 9. Matrix operations. 10. Elementary row operations, rank of a matrix, inverse. 11. Determinants. 12. Solution of systems of linear equations. Gaussian elimination algorithm. 13. Analytic geometry. 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 yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B0731A010004) Architecture and Construction P Czech Ostrava 1 Optional study plan
2019/2020 (B0732A260001) Civil Engineering P Czech Ostrava 1 Optional study plan
2019/2020 (B0732A260001) Civil Engineering K Czech Ostrava 1 Optional study plan
2018/2019 (B3502) Architecture and Construction (3501R011) Architecture and Construction P Czech Ostrava 1 Optional study plan
2018/2019 (B3607) Civil Engineering K Czech Ostrava 1 Optional study plan
2018/2019 (B3607) Civil Engineering P Czech Ostrava 1 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner