# 714-0366/04 – Mathematics I (MI)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor RNDr. Jan Kotůlek, Ph.D. Subject version guarantor Mgr. Monika Jahodová, Ph.D. Study level undergraduate or graduate Study language Czech Year of introduction 2010/2011 Year of cancellation Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
JAH0037 Mgr. Monika Jahodová, Ph.D.
KOT31 RNDr. Jan Kotůlek, Ph.D.
LUN44 Mgr. Milena Luňáčková, Ph.D.
SVO19 Mgr. Ivona Tomečková, Ph.D.
ZID76 Mgr. Arnošt Žídek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined Credit and Examination 12+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

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

Course-credit For the participation on tutorials a student is classified with 5-20 points. In the case of absence, a homework can be handed in. 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://www.studopory.vsb.cz http://mdg.vsb.cz/M http://mdg.vsb.cz/wiki

### Další požadavky na studenta

No more requirements are put on the student.

### Prerequisities

Subject codeAbbreviationTitleRequirement
714-0365 ZM Basics of Mathematics Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

I. Linear Algebra and Analytic Geometry Linear algebra. Vector spaces, bases, dimension. Matrices, rank of a matrix. Determinant. Matrix inversion. Systems of linear equations, Gaussian elimination. Analytic geometry in Euclidean space. Dot product and cross product. Line and plane in 3D-Euclidean space. II. Functions of one real variable Definitions and basic properties, elementary functions, inverse function. Parametric and implicit functions. Limit and continuity of the function. III. Differential calculus functions of one real variable The derivative of function (basic rules for differentiation), parametric differentiation, higher-order derivative, applications of the derivatives, monotonic functions and extremes of function, convexity and concavity of a function

### Conditions for subject completion

Combined form (validity from: 2010/2011 Winter semester)
Task nameType of taskMax. number of points
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20 (20) 5
Zápočtová písemka Written test 20  5
Examination Examination 80 (80) 31
Test z derivací Written test
Praktická část Written test 60  25
Teoretická část Oral examination 20  5
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2018/2019 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2012/2013 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - FS - K - cs 2018/2019 Combined Czech Optional FS - Faculty of Mechanical Engineering stu. block