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Mathematics II

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code310-2212/01
Number of ECTS Credits Allocated6 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites
PrerequisitiesCourse Unit CodeCourse Unit Title
310-2211Mathematics I
Name of Lecturer(s)Personal IDName
OTI73Mgr. Petr Otipka, Ph.D.
KRC76Mgr. Jiří Krček
SWA0013RNDr. Martin Swaczyna, Ph.D.
Summary
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
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.
Course Contents
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
Recommended or Required Reading
Required Reading:
[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.

[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.


Recommended Reading:
[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.

[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
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit20 5
        ExaminationExamination80 (80)30
                písemkaWritten test60 25
                teorieOral examination20 5