310-2212/02 – Mathematics II (M II)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorMgr. Zuzana Morávková, Ph.D.Subject version guarantorMgr. Zuzana Morávková, Ph.D.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction2017/2018Year of cancellation
Intended for the facultiesFMTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
MOR74 Mgr. Zuzana Morávková, Ph.D.
KAH14 Mgr. Marcela Rabasová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Individual consultations
Other activities


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.

Compulsory literature:

[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.

Recommended literature:

[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.

Way of continuous check of knowledge in the course of semester

Course-credit -participation on tutorials is obligatory, 20% of absence can be apologized, -pass the written three tests Point classification: 15-35 points. Exam Practical part of an exam is classified by 0 - 55 points. Practical part is successful if student obtains at least 20 points. Theoretical part of the exam is classified by 0 - 10 points. Theoretical part is successful if student obtains at least 5 points. Point quantification in the interval 100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0 ECTS grade A B C D E F Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0 National grading scheme excellent very good satisfactory failed



Other requirements

No special requirements.


Subject codeAbbreviationTitleRequirement
310-2211 M I Mathematics I Compulsory


Subject has no co-requisities.

Subject syllabus:

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

Conditions for subject completion

Full-time form (validity from: 2023/2024 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 35 (35) 15 2
                Písemka 1 Written test 15  5 2
                Písemka 2 Written test 10  3 2
                Písemka 3 Written test 10  3 2
        Examination Examination 65 (65) 30 3
                Praktická část Written examination 55  20 3
                Teoretická část Written test 10  5 3
Mandatory attendence participation: 80%

Show history

Conditions for subject completion and attendance at the exercises within ISP: In order to complete credit, students submit homeworks and pass three tests. Participation in the exercises is not required. Based on a successfully completed credit, they can pass the exam.

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2023/2024 (B0712P130001) Environmental technology P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0712P130001) Environmental technology P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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