# 310-2211/01 – Mathematics I (M I)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 7 Subject guarantor Mgr. Zuzana Morávková, Ph.D. Subject version guarantor Mgr. Zuzana Morávková, 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 FMT Intended for study types Bachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
LAM0028 RNDr. Alžběta Lampartová
MOR74 Mgr. Zuzana Morávková, Ph.D.
KAH14 Mgr. Marcela Rabasová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+4
Part-time Credit and Examination 22+0

### Subject aims expressed by acquired skills and competences

The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithmus and methods. Students should learn how to analyze problem,suggest a method of solution, analyze correctness of achieved results with respect to given conditions.

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

Differential calculus of function of one real independent variable: function of one variable, elementary functions, limit and continuity of a function, differentiation, extreme values of function, point of inflection, convex and concave function, L’Hospital’s rule. Linear algebra: determinants, matrices, systems of linear equations. Analytic geometry of the 3-dimensional space.

### Compulsory literature:

[1] DOLEŽALOVÁ, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3, http://mdg.vsb.cz/portal/en/Mathematics1.pdf [2] BIRD, J. O. Higher engineering mathematics. Eighth edition. London: Routledge, Taylor & Francis Group, 2017. ISBN 978-1-138-67357-1 [3] TRENCH, W.F.: Introduction to real analysis, Free Edition 1.06, January 2011,ISBN 0-13-045786-8

### Recommended literature:

[1] 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 -participation on tutorials is obligatory, 20% of absence can be apologized, -elaborate programs, -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://lms.vsb.cz

### Other requirements

No special requirements.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1 Functions of one real variable (definitions and basic properties) 2 Elementary functions 3 Limit of the function, continuity of the functions , basic rules 4 Differential calculus functions of one real variable. the derivative of function (basic rules for differentiation) 5 Derivatives of selected functions 6 Differential of the function, parametric differentiation, highes-order derivative 7 Applications of the derivatives 8 Monotonic functions and extremes of function, convexity and concavity of a function 9 Linear algebra: Matrice (basic properties), determinants (basic properties, calculation, evaluation) 10 Matrix inversion 11 Systems of linear equations, Cramer’s rule 12 Gaussian elimination 13 Product of vectors (basic properties) 14 Analytical geometry in E3

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 30 3
písemka Written test 60  25
teorie Oral examination 20  5
Mandatory attendence participation: 80%

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Conditions for subject completion and attendance at the exercises within ISP: In order to complete credit, students submit homeworks and pass three tests. Participation in the exercises is not required. Based on a successfully completed credit, they can pass the exam.

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### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner