# 230-0301/01 – Mathematics I (MI)

 Gurantor department Department of Mathematics Credits 6 Subject guarantor Mgr. Kateřina Kozlová, Ph.D. Subject version guarantor Mgr. Kateřina Kozlová, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties FBI Intended for study types Bachelor
Instruction secured by
TUZ006 RNDr. Michaela Bobková, Ph.D.
DUB02 RNDr. Viktor Dubovský, Ph.D.
KRA44 Mgr. Kateřina Kozlová, Ph.D.
STA50 RNDr. Jana Staňková, Ph.D.
URB0186 RNDr. Zbyněk Urban, Ph.D.
VOL18 RNDr. Jana Volná, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+4

### 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

Mathematics I is connected with secondary school education. It is divided in three parts, differential calculus of functions of one real variable, linear algebra and analytic geometry in the three dimensional Euclidean space E3. The aim of the first chapter is to handle the concept of a function and its properties, a limit of functions, a derivative of functions and its application. The second chapter emphasizes the systems of linear equations and the methods of their solution. The third chapter introduces the basics of vector calculus and basic linear objects in three dimensional space.

### Compulsory literature:

[1] Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3 [2] http://mdg.vsb.cz/portal/en/Mathematics1.pdf

### Recommended 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] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

### 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/Mathematics1.pdf

### Other requirements

No more requirements are put on the student.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Real functions of one real variable. Definition, graph. Bounded function, monotonic functions, even, odd and periodic functions. One-to-one functions, inverse and composite functions. 2. Elementary functions (including inverse trigonometric functions). 3. Limit of a function, infinite limit of a function. Limit at an improper point. Continuous and discontinuous functions. 4. Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical meaning. Derivative rules. 5. Derivative of elementary functions. 6. Differential of a function. Derivative of higher orders. l’Hospital rule. 7. Relation between derivative and monotonicity, convexity and concavity of a function. 8. Extrema of a function. Asymptotes. Plot graph of a function. 9. Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse. 10. Determinants, properties of a determinant. 11. Solution of systems of linear equations. Frobenius theorem. Cramer’s rule. Gaussian elimination algorithm. 12. Analytic geometry. Euclidean space. Scalar, cross and triple product of vectors, properties. 13. Equation of a plane, line in E3. Relative position problems. 14. Metric or distance problems.

### 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
2020/2021 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan
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2020/2021 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management P Czech Ostrava 1 Compulsory study plan
2020/2021 (B3908) Fire Protection and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2020/2021 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3908) Fire Protection and Industrial Safety P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner