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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 Code310-2112/02
Number of ECTS Credits Allocated4 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
310-2117Mathematics 1
Name of Lecturer(s)Personal IDName
SKN002Ing. Petra Schreiberová, Ph.D.
KOT31RNDr. Jan Kotůlek, Ph.D.
SWA0013RNDr. Martin Swaczyna, Ph.D.
MUL0086RNDr. PhDr. Ivo Müller, 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
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.
Course Contents
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.
Recommended or Required Reading
Required Reading:
Kreml, P.: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X
http://mdg.vsb.cz/portal/m2/PV_PracovniListyM2.pdf
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.
Kreml, P.: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X
Recommended Reading:
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456
http://homel.vsb.cz/~skn002/dl/MII_priklady.pdf
http://mdg.vsb.cz/portal/
Škrášek, J. a kol.: Základy aplikované matematiky I. a II. SNTL, Praha 1986.
Pavelka, L. – Pinka, P.: Integrální počet funkce jedné proměnné – Matematika III. Skriptum VŠB-TU, Ostrava 1999. ISBN 80-7078-654-X.
Vrbenská, H.: Základy matematiky pro bakaláře II. Skriptum VŠB - TU, Ostrava 1998. ISBN 80-7078-545-4.
Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1
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
                Praktická částWritten examination60 25
                Teoretická částWritten examination20 5