# 230-0306/02 – Mathematics II (MII)

 Gurantor department Department of Mathematics Credits 4 Subject guarantor RNDr. Jana Volná, Ph.D. Subject version guarantor RNDr. Jana Volná, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2020/2021 Year of cancellation Intended for the faculties FBI Intended for study types Bachelor
Instruction secured by
CER365 doc. Ing. Martin Čermák, Ph.D.
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
POS220 Ing. Lukáš Pospíšil, Ph.D.
STR78 Mgr. Jakub Stryja, Ph.D.
VOL18 RNDr. Jana Volná, 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

### Summary

Mathematics II is divided in three parts: 1. Integral calculus of functions of one real variable - indefinite integral, some properties, elementary methods of integration. 2. Differential calculus of functions of two real variables - the partial derivations, extremes of functions of two variables., 3. Ordinary differential equations - ordinary differential equation of the 1st and 2nd order.

### Compulsory literature:

[1] Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990. ISBN 0-669-21145-1 [2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0- 201-1805456 [3] http://mdg.vsb.cz/portal/en/Mathematics2.pdf

### Recommended literature:

[1] Buchanan, James., L.,Turner, Peter., R.: Numerical Methods and Analysis. McGraw-Hill, Inc. New York 1992. ISBN 0-07-008717-2

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

Passing the course, requirements Course-credit (full-time study): 5 points: -participation on tutorials is obligatory, 20% of absence can be accepted, -submition of semestral project in predefined form. 5 – 15 poinst: -accomplish the written tests, -each test can be repeated once, -it is necessary to get at least 5 out of 15 points. Student has to gain at least 10 points in total to obtain credit and procced to final exam. Course-credit (distance study): Based on participation in consultations student can get 5 - 20 points, in case of absence student can get 5 points for elaboration of additional project. 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 National grading scheme 100 – 86 excellent 85 – 66 very good 65 – 51 satisfactory 50 – 0 failed

### E-learning

http://mdg.vsb.cz/portal/en/Mathematics2.pdf

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

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

### Conditions for subject completion

Part-time form (validity from: 2020/2021 Winter semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  10
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).

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

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2023/2024 (B1022A020001) Bezpečnost práce a procesů K Czech Ostrava 1 Compulsory study plan
2023/2024 (B1022A020001) Bezpečnost práce a procesů K Czech Praha 1 Compulsory study plan
2023/2024 (B1022A020001) Bezpečnost práce a procesů K Czech Lázně Bohdaneč 1 Compulsory study plan
2023/2024 (B1032A020009) Fire Protection Engineering and Industrial Safety K Czech Ostrava 1 Compulsory study plan
2023/2024 (B1032A020009) Fire Protection Engineering and Industrial Safety K Czech Praha 1 Compulsory study plan
2023/2024 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Lázně Bohdaneč 1 Compulsory study plan
2023/2024 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Praha 1 Compulsory study plan
2023/2024 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Ostrava 1 Compulsory study plan
2022/2023 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Lázně Bohdaneč 1 Compulsory study plan
2022/2023 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Ostrava 1 Compulsory study plan
2022/2023 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Praha 1 Compulsory study plan
2022/2023 (B1032A020009) Fire Protection Engineering and Industrial Safety K Czech Ostrava 1 Compulsory study plan
2022/2023 (B1032A020009) Fire Protection Engineering and Industrial Safety K Czech Praha 1 Compulsory study plan
2022/2023 (B1032A020007) Technická bezpečnost osob a majetku K Czech Ostrava 1 Compulsory study plan
2022/2023 (B1022A020001) Bezpečnost práce a procesů K Czech Lázně Bohdaneč 1 Compulsory study plan
2022/2023 (B1022A020001) Bezpečnost práce a procesů K Czech Ostrava 1 Compulsory study plan
2022/2023 (B1022A020001) Bezpečnost práce a procesů K Czech Praha 1 Compulsory study plan
2022/2023 (B1032A020007) Technická bezpečnost osob a majetku K Czech Praha 1 Compulsory study plan
2022/2023 (B1032A020007) Technická bezpečnost osob a majetku K Czech Lázně Bohdaneč 1 Compulsory study plan
2021/2022 (B1032A020007) Technická bezpečnost osob a majetku K Czech Ostrava 1 Compulsory study plan
2021/2022 (B1032A020007) Technická bezpečnost osob a majetku K Czech Lázně Bohdaneč 1 Compulsory study plan
2021/2022 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Ostrava 1 Compulsory study plan
2021/2022 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Lázně Bohdaneč 1 Compulsory study plan
2021/2022 (B1022A020001) Bezpečnost práce a procesů K Czech Lázně Bohdaneč 1 Compulsory study plan
2021/2022 (B1022A020001) Bezpečnost práce a procesů K Czech Ostrava 1 Compulsory study plan
2020/2021 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Ostrava 1 Compulsory study plan
2020/2021 (B1032A020008) Ochrana obyvatestva a krizový management K Czech Lázně Bohdaneč 1 Compulsory study plan
2020/2021 (B1032A020007) Technická bezpečnost osob a majetku K Czech Ostrava 1 Compulsory study plan
2020/2021 (B1032A020007) Technická bezpečnost osob a majetku K Czech Lázně Bohdaneč 1 Compulsory study plan
2020/2021 (B1022A020001) Bezpečnost práce a procesů K Czech Ostrava 1 Compulsory study plan
2020/2021 (B1022A020001) Bezpečnost práce a procesů K Czech Lázně Bohdaneč 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner