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

Course Unit Code | 230-0221/01 | |||||
---|---|---|---|---|---|---|

Number of ECTS Credits Allocated | 1 ECTS credits | |||||

Type of Course Unit * | Optional | |||||

Level of Course Unit * | First Cycle | |||||

Year of Study * | First Year | |||||

Semester when the Course Unit is delivered | Summer Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech | |||||

Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

VOL06 | RNDr. Petr Volný, 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. 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 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.
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. http://www.studopory.vsb.cz/studijnimaterialy/MatematikaI/MI.html http://mdg.vsb.cz/M/ | ||||||

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 | ||||||

Tutorials | ||||||

Assesment methods and criteria | ||||||

Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing | |||

Credit | Credit |