Repetition of Mathematics 1

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code230-0221/01
Number of ECTS Credits Allocated1 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
VOL06RNDr. Petr Volný, Ph.D.
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.
Learning Outcomes of the Course Unit
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
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.
Course Contents
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.
Recommended or Required Reading
Required Reading:
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.
Burda, Pavel; Havelek, Radim; Hradecká, Radoslava; Kreml, Pavel: Matematika I, VŠB – TUO, Ostrava 2006, 80-248-1199-5 (CD-R).
Burda, Pavel; Kreml, Pavel: Diferenciální počet funkcí jedné proměnné. Matematika IIa, VŠB – TUO, Ostrava 2004, ISBN 80-248-0634-7.
Burda, Pavel; Havelek, Radim; Hradecká, Radoslava: Algebra a analytická geometrie, 2. vyd., VŠB – TUO, Ostrava 2005, 80-248-0966-4.
Recommended Reading:
Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and
Company 1990, ISBN 0-669-21145-1.
Vrbenská, Helena; Bělohlávková, Jana;: Základy matematiky pro bakaláře I, 2. vyd., VŠB – TUO, Ostrava 2003, 80-248-0519-7, 978-80-248-0519-1.
Láníček, Josef; Mičulka, Břetislav; Píšová, Dagmar; Restl, Čestmír; Řehák, Miroslav: Cvičení z matematiky I. VŠB – TUO, Ostrava 1999, 80-7078-973-5.
Dobrovská, Věra; Mičulka, Břetislav; Šarmanová, Jana; Žižka, Jan: Cvičení z matematiky II, 9. vyd., VŠB – TUO, Ostrava 1997, 80-7078-987-5.
Planned learning activities and teaching methods
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing