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Repetition of Mathematics 1

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

Course Unit Code230-0323/01
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
DLO44Mgr. Dagmar Dlouhá, Ph.D.
JAR71Mgr. Marcela Jarošová, Ph.D.
STR78Mgr. Jakub Stryja, Ph.D.
CER365doc. Ing. Martin Čermák, Ph.D.
POS220Ing. Lukáš Pospíšil, Ph.D.
VOL18RNDr. Jana Volná, Ph.D.
VIT0060Mgr. Aleš Vítek, Ph.D.
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. Repetition will focus on the practical part of the exam.
Learning Outcomes of the Course Unit
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.
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.
http://mdg.vsb.cz/portal/en/Mathematics1.pdf
Burda, Pavel; Havelek, Radim; Hradecká, Radoslava; Kreml, Pavel: Matematika I, VŠB – TUO, Ostrava 2006, 80-248-1199-5 (CD-R).
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaI/MI.html
http://mdg.vsb.cz/portal
Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3

Recommended Reading:
Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and
Company 1990, ISBN 0-669-21145-1.
Vrbenská, H., Němčíková, J.: Základy matematiky pro bakaláře I. Skriptum VŠB-TUO, Ostrava 1999. ISBN 80-7078-351-6
Vrbenská, H., Bělohlávková, J.: Základy matematiky pro bakaláře II. Skriptum VŠB-TUO, Ostrava 1998. ISBN 80-7078-545-4
Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and
Company 1990, ISBN 0-669-21145-1.
Planned learning activities and teaching methods
Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
CreditCredit