# 714-0567/03 – 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 English Year of introduction 2016/2017 Year of cancellation 2019/2020 Intended for the faculties HGF Intended for study types Bachelor, Follow-up Master
Instruction secured by
DLO44 Mgr. Dagmar Dlouhá, Ph.D.  DRO03 Mgr. Jaroslav Drobek, 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

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:

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

### Recommended literature:

 Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X http://mdg.vsb.cz/portal/en/Mathematics2  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 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.

### Other requirements

No more reqieremwents

### 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:

Week. Lecture ------------- 1st Integral calculus: antiderivative and indefinite integral for functions of one variable. 2nd Integration methods - substitution, integration by parts. 3rd Integration of rational functions, irrational functions, trigonometric functions. 4th Definite integrals: basic concepts, properties, Newton-Leibniz rule. 5th Substitution method and integration by parts for the definite integral. 6th Applications of integrals in geometry. 7th Differential calculus for functions of two variables: definition, domain, limits and continuity. 8th Partial derivatives of first order and higher orders. Total differential. 9th The equation of the tangent plane and of the normal. 10th Extrema of functions of two variables. 11th Implicit function and its derivatives. 12th Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear. 13th Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients. 14th Linear differential equations of higher orders.

### Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty 2018/2019 (B2110) Geological Engineering (2101R003) Geological Engineering P English Ostrava 2 Compulsory study plan
2018/2019 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics P English Ostrava 2 Compulsory study plan
2017/2018 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics P English Ostrava 2 Compulsory study plan
2017/2018 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization P English Ostrava 1 Compulsory study plan
2017/2018 (B2110) Geological Engineering (2101R003) Geological Engineering P English Ostrava 2 Compulsory study plan
2016/2017 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics P English Ostrava 2 Compulsory study plan
2016/2017 (B2110) Geological Engineering (2101R003) Geological Engineering P English Ostrava 2 Compulsory study plan
2016/2017 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization P English 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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