| Course Unit Code | 714-0367/03 |
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| Number of ECTS Credits Allocated | 4 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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| 714-0365 | Basics of Mathematics |
| 714-0366 | Mathematics I |
| Name of Lecturer(s) | Personal ID | Name |
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| DOL30 | doc. RNDr. Jarmila Doležalová, CSc. |
| H1O40 | Mgr. Iveta Cholevová, Ph.D. |
| KRC76 | Mgr. Jiří Krček |
| SKN002 | Ing. Petra Schreiberová, 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. |
| 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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Syllabus of lecture
1 Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary functions.
2 Integration by substitutions, integration by parts.
3 Integration of rational functions.
4 Definite integral and methods of integration.
5 Geometric application of definite integrals.
6 Differential calculus of functions of two or more real variables. Functions of two or more variables, graph,
7 Partial derivatives of the 1-st and higher order.
8 Total differential of functions of two variables, tangent plane and normal to a surface, extrema of functions.
9 Ordinary differential equations. General, particular and singular solutions. Separable homogeneous equations.
10 Homogeneous 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.
13 2nd order LDE with constant coefficients - method of undetermined coefficients.
14 Application of differential equations
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. 3rd test (differential equations).
13 Method of undetermined coefficients.
14 Application of differential equations.
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| Recommended or Required Reading |
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| Required Reading: |
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| Kreml, P.: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X |
http://mdg.vsb.cz/wiki/index.php/MatematikaII
http://www.studopory.vsb.cz
Pavelka, L. – Pinka, P.: Integrální počet funkce jedné proměnné – Matematika
III. Skriptum VŠB-TU, Ostrava 1999. ISBN 80-7078-654-X.
Dobrovská, V.- J.-Vrbický, J.: Diferenciální počet funkcí více proměnných -
Matematika IIb. Skriptum VŠB - TU, Ostrava 2004, ISBN 80-248-0656-8.
Vlček, J. – Vrbický, J.: Diferenciální rovnice – Matematika IV. Skriptum
VŠB-TU, Ostrava 1997. ISBN 80-7078-438-5.
Vrbenská, H.: Základy matematiky pro bakaláře II. Skriptum VŠB - TU, Ostrava
1998. ISBN 80-7078-545-4.
|
| 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
|
Škrášek, J. a kol.: Základy aplikované matematiky I. a II. SNTL, Praha 1986.
http://www.vsb.cz/714/cs/Studijni-materialy/ |
| 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 |