# 230-0404/03 – Mathematics I (MI)

 Gurantor department Department of Mathematics Credits 5 Subject guarantor Mgr. Dagmar Dlouhá, Ph.D. Subject version guarantor Mgr. Dagmar Dlouhá, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties HGF Intended for study types Bachelor
Instruction secured by
DLO44 Mgr. Dagmar Dlouhá, 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
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 toanalyze 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

The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three basic parts of mathematics, according to which the learning material is structured. In Differential Calculus, the main motive is the preparation to general use of derivatives of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Analytic geometry, there are, based on vector calculus, described basic linear formations of three-dimensional Euclidean space and some tools to evaluate their mutual position from qualitative and also quantitative point of view.

### Compulsory literature:

Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3. http://mdg.vsb.cz/portal/en/Mathematics1.pdf Bartsch, Hans Jochen: Handbook of Mathematical Formulas. Burdette, A.C.:An Introduction to Analytic Geometry and Calculus,Academic Press,1973.

### Recommended literature:

Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1. Leon, S., J.: Linear Algebra with Aplications, Macmillan Publishing Company, New York, 1986, ISBN 0-02-369810-1. Jain, P.K.:A Textbook of Analytical Geometry of Three Dimensions,New Age International Publisher,1996. Moore,C: Math quations and inequalities, Science & Nature, 2014.

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

Conditions for obtaining the course-unit credit: participation in exercises, 30% of absences can be excused, submission of programs assigned by the supervisor in the prescribed course, passing of written tests. The student will get 5 b for fulfilling the conditions. The student can get 0 - 15 b for the tests. (The student who gets the credit will be evaluated 5 - 20 b). The condition for participation in the exam is a written credit from the relevant course. The exam consists of a written and an oral part. Students must pass both parts of the exam and achieve the necessary number of points.

### E-learning

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

### Other requirements

There are no other requests for students.

### Prerequisities

Subject codeAbbreviationTitleRequirement
230-0400 ZM Basics of Mathematics Compulsory

### 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, Taylor polynom, parametric differentiation, highes-order derivative, L'Hospital rule 7.Applications of the derivatives, convexity and concavity of a function 8.Extremes of function, asmptotes, function graph constructing 9.Linear algebra: Vectors, linear independence. Matrices (basic properties) 10.Determinants (basic properties, calculation, evaluation) 11.Rank of matrix, matrix inversion 12.Systems of linear equations, Frobenius theorem, Gaussian elimination 13.Products of vectors (basic properties) 14.Line and plane equation in E3, mutual positions of lines and planes

### Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 30
Písemná zkouška Written examination 60  25
Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation: 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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### Occurrence in special blocks

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