# 310-2112/02 – Mathematics II (MII)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor Ing. Petra Schreiberová, Ph.D. Subject version guarantor Ing. Petra Schreiberová, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
KOT31 RNDr. Jan Kotůlek, Ph.D.
KRC76 Mgr. Jiří Krček
MUL0086 RNDr. PhDr. Ivo Müller, Ph.D.
OTI73 Mgr. Petr Otipka
KAH14 Mgr. Marcela Rabasová, Ph.D.
SKN002 Ing. Petra Schreiberová, Ph.D.
SKA141 Mgr. Pavel Skalný, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 11+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

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:

Kreml, P.: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X

### Recommended literature:

James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

### Way of continuous check of knowledge in the course of semester

Course-credit -pass the written tests, Point classification: 5-20 points. Exam Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points. Theoretical part of the exam is classified by 0 - 20 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

### E-learning

http://mdg.vsb.cz/portal/m2/index.php

### Other requirements

more requierements are not

### Prerequisities

Subject codeAbbreviationTitleRequirement
310-2110 ZM Basics of Mathematics Recommended
310-2111 MI Mathematics I Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1 Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary functions. 2 Integration by substitutions, integration by parts. 3 Integration of rational functions. 4 Definite integral and methods of integration. 5 Geometric application of definite integrals. 6 Differential calculus of functions of two or more real variables. Functions of two or more variables, graph, 7 Partial derivatives of the 1-st and higher order. 8 Total differential of functions of two variables, tangent plane and normal to a surface, extrema of functions. 9 Ordinary differential equations. General, particular and singular solutions. Separable homogeneous equations. 10 Homogeneous 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. 13 2nd order LDE with constant coefficients - method of undetermined coefficients. 14 Application of differential equations

### Conditions for subject completion

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

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2021/2022 (B0715A270011) Engineering P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A270011) Engineering P Czech Šumperk 1 Compulsory study plan
2021/2022 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2021/2022 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0713A070002) Energetics and Environments P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A040001) Transport Systems and Equipment P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270011) Engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2020/2021 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2020/2021 (B0715A270011) Engineering P Czech Šumperk 1 Compulsory study plan
2020/2021 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0713A070002) Energetics and Environments P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A040001) Transport Systems and Equipment P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2020/2021 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2020/2021 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2019/2020 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0713A070002) Energetics and Environments P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A040001) Transport Systems and Equipment P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering P Czech Šumperk 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2019/2020 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - FS - P - cs 2020/2021 Full-time Czech Optional FS - Faculty of Mechanical Engineering stu. block