Course Unit Code | 310-2212/01 |
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Number of ECTS Credits Allocated | 6 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 * | First Year |
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Semester when the Course Unit is delivered | Summer 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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| 310-2211 | Mathematics I |
Name of Lecturer(s) | Personal ID | Name |
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| OTI73 | Mgr. Petr Otipka, Ph.D. |
| KRC76 | Mgr. Jiří Krček |
| SWA0013 | RNDr. Martin Swaczyna, Ph.D. |
Summary |
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Integral calculus of function of one real variable: the indefinite and definite integrals, properties of the indefinite and definite integrals, application in the geometry and physics.
Differential calculus of functions of several independent variables.
Ordinary differential equations of the first and the second order.
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Learning Outcomes of the Course Unit |
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The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods.
Students should learn how to: analyze problems, suggest a method of solution, analyze correctness of achieved results with respect to given conditions,
aply these methods while solving technical problems.
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Course Contents |
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1 Differential calculus of functions of two or more real variables. Functions of two or more variables, graph,
2 Partial derivatives of the 1-st and higher order.
3 Total differential of functions of two variables, tangent plane and normal to a surface, extrema of functions.
4 Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary functions.
5 Integration by substitutions, integration by parts.
6 Integration of rational functions.
7 Definite integral and methods of integration.
8 Geometric and physical application of definite integrals.
9 Ordinary differential equations. General, particular and singular solutions. Separable equations.
10 Homogeneous equations. Exact equations. Linear differential equations of the first order, method of variation of arbitrary constant.
11 2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian,fundamental
system of solutions.
12 2nd order LDE with constant coefficients - method of variation of arbitrary constants, method of undetermined coefficients.
13 Application of differential equations
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Recommended or Required Reading |
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Required Reading: |
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[1] KREML, P: Mathematics II, Ostrava 2005, 80-248-0798-X. http://mdg.vsb.cz/portal/en/Mathematics2.pdf
[2] JAMES, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456.
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[1] PAVELKA, L., PINKA, P.: Integrální počet funkcí jedné proměnné, Matematika IIIa,Ostrava, VŠB-TUO, 1999, ISBN 80-7078-654-X.
[2] DOBROVSKÁ, V., VRBICKÝ, J.: Diferenciální počet funkcí více proměnných.
[2] VLČEK, J., VRBICKÝ, J.: Diferenciální rovnice, Matematika IV, Ostrava, VŠB-TUO,1997, ISBN 80-7078-438-5.
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Recommended Reading: |
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[1] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6.
[2] Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1.
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[1] Škrášek, J.,Tichý, Z.: Základy aplikované matematiky I,II, Praha, SNTL 1986, ISBN 014-0544-89.
[2] Rektorys a spolupracovníci: Přehled užité matematiky I,II, Praha, Prometheus, 1995,ISBN 80-85849-72-0.
[3] BIRD, J. O. Higher engineering mathematics. Eighth edition. London: Routledge, Taylor & Francis Group, 2017. ISBN 978-1-138-67357-1
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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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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 20 | 5 |
Examination | Examination | 80 (80) | 30 |
písemka | Written test | 60 | 25 |
teorie | Oral examination | 20 | 5 |