714-0567/02 – Bachelor Mathematics II (BM II)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor RNDr. Zbyněk Urban, Ph.D. Subject version guarantor RNDr. Zbyněk Urban, Ph.D. Study level undergraduate or graduate Study language Czech Year of introduction 1999/2000 Year of cancellation Intended for the faculties HGF Intended for study types Follow-up Master, Bachelor
Instruction secured by
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DRO03 Mgr. Jaroslav Drobek, Ph.D.
DUB02 RNDr. Viktor Dubovský, Ph.D.
POL12 RNDr. Jiří Poláček, CSc.
SKA141 Mgr. Pavel Skalný, 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
Combined 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 [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 [2] Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1

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

no more requierents.

Prerequisities

Subject codeAbbreviationTitleRequirement
714-0565 ZM Basics of Mathematics Compulsory
714-0566 BM I Bachelor Mathematics I Compulsory

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

Combined form (validity from: 2014/2015 Winter semester)
Min. number of points
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
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
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2018/2019 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
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2018/2019 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2018/2019 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Ostrava 2 Compulsory study plan
2018/2019 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Most 2 Compulsory study plan
2018/2019 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2018/2019 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Most 2 Compulsory study plan
2018/2019 (B2102) Mineral Raw Materials (3902R064) System Engineering in Industry K Czech Ostrava 2 Compulsory study plan
2018/2019 (B2102) Mineral Raw Materials (3902R064) System Engineering in Industry K Czech Most 2 Compulsory study plan
2018/2019 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 2 Compulsory study plan
2018/2019 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 2 Compulsory study plan
2018/2019 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Most 2 Compulsory study plan
2018/2019 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2017/2018 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2017/2018 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Most 1 Compulsory study plan
2017/2018 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2017/2018 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2017/2018 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2017/2018 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Most 1 Compulsory study plan
2017/2018 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2017/2018 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Most 1 Compulsory study plan
2017/2018 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
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2017/2018 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2017/2018 (B2102) Mineral Raw Materials (3902R064) System Engineering in Industry K Czech Ostrava 2 Compulsory study plan
2017/2018 (B2102) Mineral Raw Materials (3902R064) System Engineering in Industry K Czech Most 2 Compulsory study plan
2017/2018 (B2111) Mining (2101R014) Blasting Operations in Mining Engineering K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2111) Mining (2101R014) Blasting Operations in Mining Engineering K Czech Most 1 Compulsory study plan
2017/2018 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2017/2018 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Most 2 Compulsory study plan
2017/2018 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Ostrava 2 Compulsory study plan
2017/2018 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 1 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (3902R064) System Engineering in Industry K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (3902R064) System Engineering in Industry K Czech Most 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2016/2017 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
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2016/2017 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Most 1 Compulsory study plan
2016/2017 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2016/2017 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Most 1 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Most 2 Compulsory study plan
2016/2017 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2016/2017 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Most 1 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Ostrava 2 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (3902R064) System Engineering in Industry K Czech Ostrava 2 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (3902R064) System Engineering in Industry K Czech Most 2 Compulsory study plan
2015/2016 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Most 1 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2015/2016 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Most 1 Compulsory study plan
2015/2016 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2015/2016 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Most 2 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2015/2016 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2015/2016 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Most 1 Compulsory study plan
2014/2015 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Most 1 Compulsory study plan
2014/2015 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2014/2015 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2014/2015 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2014/2015 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2014/2015 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2014/2015 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2014/2015 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2014/2015 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2014/2015 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2014/2015 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2014/2015 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2014/2015 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2013/2014 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2013/2014 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2013/2014 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Most 1 Compulsory study plan
2013/2014 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2111) Mining (2101R008) Mining Engineering K Czech Most 1 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2013/2014 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2013/2014 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2012/2013 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2012/2013 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2012/2013 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2111) Mining (2101R008) Mining Engineering K Czech Most 1 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Most 1 Compulsory study plan
2012/2013 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2012/2013 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2011/2012 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2011/2012 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2011/2012 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2011/2012 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2111) Mining (2101R008) Mining Engineering K Czech Most 1 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Most 1 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2010/2011 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2010/2011 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2010/2011 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2010/2011 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2010/2011 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2010/2011 (B2111) Mining (2101R008) Mining Engineering K Czech Most 1 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 2 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Most 1 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2010/2011 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2009/2010 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2009/2010 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2009/2010 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2111) Mining (2101R008) Mining Engineering K Czech Most 1 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Most 1 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Most 1 Compulsory study plan
2008/2009 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2111) Mining (2101R008) Mining Engineering K Czech Most 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2008/2009 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2008/2009 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2008/2009 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Most 1 Compulsory study plan
2007/2008 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2111) Mining (2101R008) Mining Engineering K Czech Most 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 2 Compulsory study plan
2007/2008 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 2 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2007/2008 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2007/2008 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 2 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 2 Compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Most 1 Compulsory study plan
2006/2007 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2111) Mining (2101R008) Mining Engineering K Czech Most 1 Compulsory study plan
2006/2007 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2006/2007 (N2110) Geological Engineering (2101T003) Geological Engineering (00) Geologické inženýrství K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2006/2007 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Most 1 Compulsory study plan
2005/2006 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2111) Mining (2101R008) Mining Engineering K Czech Most 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 1 Compulsory study plan
2005/2006 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Most 1 Compulsory study plan
2005/2006 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2005/2006 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Most 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 1 Compulsory study plan
2005/2006 (N2110) Geological Engineering (2101T003) Geological Engineering (00) Geologické inženýrství K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (3902R006) Automation and Computers in Raw Material Industry K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2111) Mining (2101R008) Mining Engineering K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Ostrava 1 Compulsory study plan
2004/2005 (B3646) Geodesy and Cartography (3646R006) Geoinformatics K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (6209R013) Information and System Management K Czech Ostrava 1 Compulsory study plan
2004/2005 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2004/2005 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 1 Compulsory study plan
2003/2004 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2003/2004 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 1 Compulsory study plan
2002/2003 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials K Czech Ostrava 1 Compulsory study plan
2002/2003 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 1 Compulsory study plan
2002/2003 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 1 Compulsory study plan
2002/2003 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 1 Compulsory study plan
2002/2003 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 1 Compulsory study plan
2002/2003 (B2110) Geological Engineering (2101R003) Geological Engineering K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner