# 310-2111/03 – Mathematics I (MI)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor RNDr. Jan Kotůlek, Ph.D. Subject version guarantor RNDr. Jan Kotůlek, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language English 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.
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 subject is divided into four chapters. In the first chapter we study real functions of one real variable and their properties, in the second chapter we introduce the notion of derivative and study its properties and applications. In the third chapter we study linear algebra. We introduce Gauss elimination method for solution of systems of linear algebraic equations. In the last chapter we apply it to the geometric problems in three-dimensional Euclidean space.

### Compulsory literature:

[1] BIRD, J.: Engineering Mathematics, 4th ed. Newnes 2003. [2] DOLEŽALOVÁ, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3 [3] NEUSTUPA, J.: Mathematics I., ČVUT, Praha 2004

### Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington 1990, ISBN 0-669-21145-1 James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 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

- participation on tutorials is obligatory, 20% of absence can be excused, - submission of problem sheets, - passing 10 written tests, maximally 2 points each. Point classification: 5-20 points.

### E-learning

http://mdg.vsb.cz/portal/

Exam: Practical part of an exam is classified by 0 - 60 points. Student passes the practical part if (s)he obtains at least 25 points. Theoretical part of the exam is classified by 0 - 20 points. Student passes the theoretical part if (s)he 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

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject codeAbbreviationTitle
310-2110 ZM Basics of Mathematics

### Subject syllabus:

Syllabus of lectures 1 Functions of one real variable (definitions and basic properties). Inverse functions. 2 Elementary functions. Parametric and implicit functions. 3 Limit of the function, continuous functions. 4 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives. 5 Applications of the derivatives, l'Hospital rule. Taylor polynomial. 6 Applications of the derivatives on the behaviour of the graph. Monotonic functions. Convex and concave functions. 7 Asymptotes. Constructing graph of a function. 8 Linear algebra. Vector spaces, bases, dimension. 9 Matrices, rank of a matrix. 10 Determinant. Matrix inversion. 11 Systems of linear equations, Gaussian elimination. 12 Analytic geometry in Euclidean space. Dot product and cross product. 13 Line and plane in 3D-Euclidean space. 14 Reserve. Syllabus of tutorials 1 Functions of one real variable (definitions and basic properties). Inverse functions. 2 Elementary functions. Parametric and implicit functions. 3 Limit of the function, continuous functions. 4 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives. 5 Applications of the derivatives, l'Hospital rule. Taylor polynomial. 6 Applications of the derivatives on the behaviour of the graph. Monotonic functions. Convex and concave functions. 7 Asymptotes. Constructing graph of a function. 8 Linear algebra. Vector spaces, bases, dimension. 9 Matrices, rank of a matrix. 10 Determinant. Matrix inversion. 11 Systems of linear equations, Gaussian elimination. 12 Analytic geometry in Euclidean space. Dot product and cross product. 13 Line and plane in 3D-Euclidean space.

### 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.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B2341) Engineering P English Ostrava 1 Compulsory study plan
2019/2020 (B0715A270012) Engineering P English Ostrava 1 Compulsory study plan
2019/2020 (B0713A070003) Energetics and Environments P English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner