| Course Unit Code | 714-0567/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Compulsory |
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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 | |
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| Prerequisities | Course Unit Code | Course Unit Title |
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| 714-0565 | Basics of Mathematics |
| 714-0566 | Bachelor Mathematics I |
| Name of Lecturer(s) | Personal ID | Name |
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| POL12 | RNDr. Jiří Poláček, CSc. |
| DLO44 | Mgr. Dagmar Dlouhá, Ph.D. |
| DRO03 | Mgr. Jaroslav Drobek, Ph.D. |
| SKA141 | Mgr. Pavel Skalný, Ph.D. |
| URB0186 | RNDr. Zbyněk Urban, Ph.D. |
| Summary |
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| The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three advanced parts of mathematics, according to which the learning material is structured. In Integral Calculus, the main motive is the preparation to general use of definite and indefinite integrals of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Differential Equations is an emphasis on interpretation of the basic procedures for the solution of selected types of differential equations. |
| Learning Outcomes of the Course Unit |
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Mathematics is 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
analyze problems, distinguish between important and unimportant, suggest a
method of solution, verify each step of a method, generalize achieved results,
analyze 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 |
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Week. Lecture
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1st Integral calculus: antiderivative and indefinite integral for functions of one variable.
2nd Integration methods - substitution, integration by parts.
3rd Integration of rational functions, irrational functions, trigonometric functions.
4th Definite integrals: basic concepts, properties, Newton-Leibniz rule.
5th Substitution method and integration by parts for the definite integral.
6th Applications of integrals in geometry.
7th Differential calculus for functions of two variables: definition, domain, limits and continuity.
8th Partial derivatives of first order and higher orders. Total differential.
9th The equation of the tangent plane and of the normal.
10th Extrema of functions of two variables.
11th Implicit function and its derivatives.
12th Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear.
13th Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients.
14th Linear differential equations of higher orders. |
| Recommended or Required Reading |
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| Required Reading: |
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[1] Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X
http://mdg.vsb.cz/portal/en/Mathematics2
[2] Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1 |
Literatura:
Krček, J., Kreml, P., Poláček, J.: Matematika II, Učební texty VŠB-TU Ostrava, Ostrava 2006, ISBN 978-80-248-1316-5,
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaII/m2.pdf
|
| Recommended Reading: |
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[1] Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X
http://mdg.vsb.cz/portal/en/Mathematics2
[2] Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1 |
Doporučená literatura:
Škrášek, J. a kol.: Základy aplikované matematiky I. a II. SNTL, Praha 1986, ISBN 04-0544-89
Pavelka, L., Pinka, P.: Integrální počet funkce jedné proměnné. Matematika
IIIa. Učební texty VŠB - TUO,1999, ISBN 80-7078-654-X
Dobrovská, V., Vrbický, J.: Diferenciální počet funkcí více proměnných.
Matematika IIb. Učební texty VŠB - TUO,2004, ISBN 80-248-0656-8
Vlček,J., Vrbický, J.: Diferenciální rovnice. Matematika IV.Učební texty VŠB -
TUO,1997, ISBN 80-7078-438-5
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| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Other activities |
| 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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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 20 | 5 |
| Examination | Examination | 80 (80) | 30 |
| Written examination | Written examination | 60 | 25 |
| Oral | Oral examination | 20 | 5 |