230-0402/02 – Bachelor Mathematics II (BM II)

Gurantor departmentDepartment of MathematicsCredits5
Subject guarantorRNDr. Zbyněk Urban, Ph.D.Subject version guarantorRNDr. Zbyněk Urban, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation2020/2021
Intended for the facultiesHGFIntended for study typesBachelor, Follow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DUB02 RNDr. Viktor Dubovský, Ph.D.
STA50 RNDr. Jana Staňková, Ph.D.
URB0186 RNDr. Zbyněk Urban, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 18+0

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three advanced parts of mathematics, according to which the learning material is structured. In Integral Calculus, the main motive is the preparation to general use of definite and indefinite integrals of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Differential Equations is an emphasis on interpretation of the basic procedures for the solution of selected types of differential equations.

Compulsory literature:

[1] Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X http://mdg.vsb.cz/portal/en/Mathematics2.pdf [2] Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1

Recommended literature:

[1] Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X http://mdg.vsb.cz/portal/en/Mathematics2.pdf [2] Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1

Additional study materials

Way of continuous check of knowledge in the course of semester

Tests and credits ================= Exercises --------- Conditions for obtaining credit points (CP): - participation in exercises, 20% can be to apologize - completion of three written tests, 0-15 CP - completion of two programs, 5 CP Exam ---- - written exam 0-60 CP, successful completion at least 25 CP - oral exam 0-20 CP, successful completion at least 5 CP The exam questions are analogous to the program of the lectures. Set of questions ------------- The primitive function, indefinite integral, integration of elementary functions. Integration by parts. Integration by substitution. Integration of rational functions. Integration of trigonometric functions. Integrating irrational functions. Definite integral, definition and properties. Calculation of a definite integral using integration by parts. The calculation of definite integral by substitution. Calculation of the area. Calculation of the length of curves. Calculation of the volume of the rotating body. The definition of functions of two variables. Partial derivatives. The equation of the tangent plane and normal to surfaces. Extrema of functions of two variables. Implicit function and its derivatives. Differential equations of the 1st order, general and particular solutions. Separable differential equations. Homogeneous differential equations. Linear differential equation of the first order. Linear differential equations with constant coefficients of the 2nd order - variation of constants. Linear differential equations with constant coefficients of the 2nd order - determinaton of coefficients.

E-learning

Other requirements

no more requierents.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Syllabus of Lectures -------------------- - Integral calculus: antiderivative and indefinite integral for functions of one variable. - Integration methods - substitution, integration by parts. - Integration of rational functions, irrational functions, trigonometric functions. - Definite integrals: basic concepts, properties, Newton-Leibniz rule. - Substitution method and integration by parts for the definite integral. - Applications of integrals in geometry. - Differential calculus for functions of two variables: definition, domain, limits and continuity. - Partial derivatives of first order and higher orders. Total differential. - The equation of the tangent plane and of the normal. - Extrema of functions of two variables. - Implicit function and its derivatives. - Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear. - Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients. - Linear differential equations of higher orders.

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester, validity until: 2020/2021 Summer 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 20  5
        Examination Examination 80 (80) 30 3
                Písemná zkouška Written examination 60  25
                Ústní zkouška Oral examination 20  5
Mandatory attendence participation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

Show history

Conditions for subject completion and attendance at the exercises within ISP:

Show history

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2019/2020 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2019/2020 (B2111) Mining (2101R014) Blasting Operations in Mining Engineering K Czech Ostrava 2 Compulsory study plan
2019/2020 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2019/2020 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Ostrava 2 Compulsory study plan
2019/2020 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Most 2 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Ostrava 2 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (3902R064) System Engineering in Industry K Czech Most 2 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Most 2 Compulsory study plan
2019/2020 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 2 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2019/2020 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 2 Compulsory study plan
2019/2020 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Most 2 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 2 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2019/2020 Winter