| Course Unit Code | 230-0302/01 |
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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 * | 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 | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| STR78 | Mgr. Jakub Stryja, Ph.D. |
| CER365 | doc. Ing. Martin Čermák, Ph.D. |
| VOL18 | RNDr. Jana Volná, Ph.D. |
| Summary |
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Indefinite integral, some properties, elementary methods of integration. The
differential calculus of functions of two variables,the partial derivations,
extremes of functions of two variables. Ordinary differential equations,first
order differential equations, types of solution, separable, homogenous and
linear equations. Linear equations of the 2nd order with constant coefficients. |
| 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 matematics. |
| Course Contents |
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1. Integrational calculus of function of one veriable. Primitive function and undefinite integral. Integration of elementary functions.
2. Basic integrational methods - per partes and substitution.
3. Integration of rational functions.
4. Integration of goniometric functions and irational functions.
5. Definite integral: basic terms, their properties, Newton-Leibniz theorem. Geometrical meaning of definite integral. Substitution and per partes in definite integral.
6. Geometrical applications of definite integral - length of a curve, volume and surface of a rotating body.
7. Differential calculus of functions of two variables: its definition, graph, limits and continuity, partial derivatives of the first and higher order.
8. Equation of a tangential plane and normal to a surface. Local extrema of functions of two variables.
9. Constrained extrema of functions of two variables. Function given implicitly and its derivative.
10. Ordinary differential equations of first order: General, particular and singular solutions. Separable equations.
11. Homogeneous differential equations.
12. 1st order linear differential equation - method of variation of arbitrary constants
13. 2nd order linear differential equation with constant coefficients - method of undetermined coefficients.
14. Reserve
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| Recommended or Required Reading |
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| Required Reading: |
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[1] Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath
and Company, Lexington1990. ISBN 0-669-21145-1
[2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-
201-1805456
|
[1] Vrbenská, H., Bělohlávková, J.: Základy matematiky pro bakaláře II.
Skriptum VŠB-TUO, Ostrava 1998. ISBN 80-7078-545-4
[2] Pavelka, L., Pinka, P.: Integrální počet funkcí jedné proměnné,
Matematika III a. Skriptum VŠB-TUO, Ostrava 1999. ISBN 80-7078-654-X
[3] Vlček, J., Vrbický, J.: Diferenciální rovnice (Matematika IV). VŠB-TU, 1998
[4] http://www.studopory.vsb.cz/studijnimaterialy/MatematikaII/m2.pdf
[5] http://mdg.vsb.cz/portal/ |
| Recommended Reading: |
|---|
[1] Buchanan, James., L.,Turner, Peter., R.: Numerical Methods and Analysis.
McGraw-Hill, Inc. New York 1992. ISBN 0-07-008717-2
|
[1] Škrášek, J., Tichý, Z.: Základy aplikované matematiky I,II. SNTL,Praha 1990.
[2] Rektorys, K.: Co je a k čemu je vyšší matematika. ACADEMIA, Praha 2001.
ISBN 80-200-0883-7
[3] Píšová, D. a kol.: Diferenciální počet funkcí více proměnných. Skripta VŠB,
Ostrava 1989.
|
| 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 | 10 |
| Examination | Examination | 80 (80) | 30 |
| Písemná zkouška | Written examination | 60 | 25 |
| Ústní zkouška | Oral examination | 20 | 5 |