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

 Gurantor department Department of Mathematics Credits 5 Subject guarantor RNDr. Zbyněk Urban, Ph.D. Subject version guarantor RNDr. Zbyněk Urban, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 2 Semester winter Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties HGF Intended for study types Bachelor, Follow-up Master
Instruction secured by
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

### 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 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)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 30
Písemná zkouška Written examination 60  25
Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation: 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).

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### Occurrence in special blocks

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