| Course Unit Code | 230-0222/01 |
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| Number of ECTS Credits Allocated | 1 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| DUB02 | RNDr. Viktor Dubovský, Ph.D. |
| Summary |
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Repetition of Mathematics 2 is intended for students who, for whatever reasons,
fail the exam of Mathematics II 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.
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| Learning Outcomes of the Course Unit |
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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.
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| Course Contents |
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Syllabus of tutorial
1. Course of a function of one real variable.
2. Integration by a direct method. Integration by substitution.
3. Integration by substitution. Integration by parts.
4. Integration of rational functions.
5. 1st test (basic methods of integration). Definite integrals.
6. Applications of definite integrals.
7. Functions of more variables, domain, partial derivatives.
8. Equation of a tangent plane and a normal to a graph of functions of two variables. Derivation of implicit functions.
9. Extrema of functions. 2nd test (functions of two variables).
10. Differential equations, separable and homogeneous differential equations.
11. Linear differential equations of 1st order. Exact differential equations.
12. 2nd order linear differential equations with constant coefficients.
13. Method of undetermined coefficients. 3rd test (differential equations).
14. Reserve.
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| Recommended or Required Reading |
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| Required Reading: |
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| Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X |
Vrbenská, H.: Základy matematiky pro bakaláře II. Skripta VŠB - TU, Ostrava
1998.
Pavelka, L. – Pinka, P.: Integrální počet funkce jedné proměnné. Skripta VŠB-
TU, Ostrava 1999.
Vlček, J. – Vrbický, J.: Diferenciální rovnice. Skripta VŠB-TU, Ostrava 1997.
Píšová, D. a kol.: Diferenciální počet funkcí více proměnných. Skripta VŠB,
Ostrava 1989.
Škrášek, J. a kol.: Základy aplikované matematiky I. a II. SNTL, Praha 1986.
mdg.vsb.cz/M/
www.studopory.vsb.cz/
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| Recommended Reading: |
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Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications.
D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992.
ISBN 0-201-1805456
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mdg.vsb.cz/M/
www.studopory.vsb.cz/
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| Planned learning activities and teaching methods |
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| Individual consultations, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit | Credit | | |